^ > XiOm^JX 2 • > .2: ^ v' > XL'UiIsnx 5:
CO * Z - ^ k Z C/0 Z 00 z ^ £
TION MOlinillSNI NVIN0SH1IWS S3IBVBan LIBRARIES SMITHSONIAN INSTITUTION NOIlfUllSNI NVIN0SH1IWS S3IBV
to — co -7 _ 00 _ 00 _ — (/)
co
-1
c
H
o _ x^uii^x O X2!iV ~ W" o o
I a 11 U B RAR I ES^SMITHSONIAN^INSTITUTION NOIlfUllSNI “nVINOSHIIWS SSIBVHail^LIBRAR I E S^SMITHSONIAN^INSTITl
r* z r- z i~ , z r- z r-
oX xToq^oX 0 m XfO£*o?x 9 m xfo^A^x O _ XoTi
TION NOlinilJLSNI NVIN0SH1MS S3IBVB8H LIBRARIES SMITHSONIAN INSTITUTION NOIlfllllSNI NVIN0SH1IWS S3 I B V
to z to z , <0 _ z » oo z co
\ 5 €», 5 9 H 2 /&W2&
CO
- uw^y § /
z _ _ > g -w- § 5 ^ 1 I Vl^/ >
JOIl LIBRARIES SMITHSONIAN INSTITUTION NOIlfllllSNI _ NVIN0SH1IWS S3 I BVB 8 IT LIBRARIES SMITHSONIAN INSTITL
Z 00 77 _ CO - - Z \ 00 _ _ 5 CO —
SCS^v “ to fS.A* S /^n&\ co S5 /£*•
.# I
r I’
O X^O^JVX _ o w y>jr — <_} X^OSVAVX _ o
JTION NOIlfUllSNI NVIN0SH1WS S3 I B VB a ll^L I B R A R I E S SMITHSONIAN INSTITUTION NOlinillSNI^NVINOSHlMS I 8 V
z r_ _ ? r . — . x
rn '"V '±L x^ijus^x m ’x^i^x 7 m _ x^uustix m
CO \ 5 CO ± CO £ - 00
Ban LIBRARIES SMITHSONIAN INSTITUTION NOIlfllllSNI NVIN0SH1IINS S3IBVB8n LIBRARIES SMITHSONIAN INSTITI
CO z co Z ^ CO z . CO z
z
.<
x o x . 'Wjfap o /^' x /ytf- o X; x
co Infe 3rC) co ^ co to ISC 3= co co co
2 V*6L w3|/ X o X 51 o x %|k O
x uViii>S/ t- ▼ z t \3'4l£py z t ^ z r-
CO ‘ Z CO V Z CO Z CO z ^
JTION NOIlfllllSNI NVIN0SH1IWS S3iaVB8ll LIBRARIES SMITHSONIAN INSTITUTION NOIlfllllSNI NVIN0SH1IWS S3IBV
,n 5 co _ 5 _ _ _ co = _ _ <0 _ — . co
.v^j f “ .. , .« - /jSSSDx m .J&.K “ ^2
— CC /Pi4
H
CC
“ ^
c
O ~ X^/)ju‘^X O o ^ *^0^’ O _ _ - _ q
Bail LIB RAR I ES^" SMITHSONIAN- "INSTITUTION NOlinillSNI^NVINOSHlIINS S3 I B VB 3 IT I B R AR I E s"2 SMITHSONIAN-" INSTITI
d X d z rj , z r- Z r~
_ ZToOVoV O jr/lfos . ™ 0 X^vyioX m ° “ xfSov>v. O ~ XofT
t\
LU\
X)
AC
|c)
>
1 - i
.0/
^3
lirl
\-Z-
co £ co £ co £ co — £ co
JTION NOIlfllllSNI NVIN0SH1IINS S3IBVBan LIBRARIES SMITHSONIAN INSTITUTION NOIlfllllSNI NVIN0SH1IWS S3 1 B V
z w z •, ^ ^ z * co z to
^ 3 m § 3 s ^s. 3 z ^
> ' 2 V^os.oy > 2 ^ > ' 2 >"
B a n_LI BRAR I ES°° SMITHSON I AN INSTITUTION W NOIlfllllSNI _ NVINOSHIIWS^ S3 I BVB 9 d\l B RAR I ES^SMITHSONIAN ^INSTITI
Z _ 4/5 -7 _ CO _ Z \ ^ ^ -r CO
CO xfSL?oX ^ co ciJ X^nr^v co V. ^ tn ttl >o_
— C
c
_ O X^osv^x — o .V?- _ o N^VosvAiX — o
X _j z _ j X _j Z Z
UT10N NOIlfllllSNI NVIN0SH1IWS S3 I BVB 8 11 LIBRARIES SMITHSONIAN INSTITUTION NOIlfllllSNI NVINOSHilWS S3IBV
m ^ W O y^I^X ra 2 , C3 ySSfS&X Z ro JjK X 2
CD X 2 CD y^rtra^X 2 CO /^rtT^t\ 2 m «
70
>
70
Rjojus^y m ^ co rn — xioju^x rn
co \ X — co £ co £ — co _
B8 1 LIBRARIES SMITHSONIAN 'INSTITUTION NOIlfllllSNI NVINOSHimS S3IBVB9I1 LIBRARIES SMITHSONIAN INS TIT
co z vv- to z _ _ co Z -7. co z
co
z
z
<
3 R A R I ES SMITHSONIAN INSTITUTION NOlinillSNI NVINOSH1IWS S3 I d VB 8 1*1 LI B RAR 1 ES SMITHS0NIAN_ INSTITUTION N
(/) Z _ CO _ “ ... CO —
z
co
co ''//MP z ^ m
Q 's^N_DC>Z __ X^UllS^X q — XgUlxS^X O O
inillSNI^NVINOSHHWS^Sa laVaan^LIBRARI ES^SMITHSONIAN^INSTITUTION^N01irulISNI^NVINOSHXIIAIS2S3 I ava a n^L
m ^ m ' m E? pi ' Z ' ^
tp ^ co ? co _ co — co
3RARIES SMITHSONIAN INSTITUTION NOlinillSNI NVIN0SH1IWS S3 I dVd 9 IT L I B RAR I ES SMITHSONIAN INSTITUTION N
CO Z* CO Z CO Z \ _ _ _ Z »
- = .% P ^#A S I /jfe. i A . q /^fy^s
i m 1 jr
>• 5 X^oyvX >• 5 ' # > S >SV >
AT ^ 7X ■ /*’ ^ ff\ 2 CO ^ CO 2
uniiisNi NviNOSHiiiNS S3idvaan libraries Smithsonian institution NoiiniusNi_NviNOSHims S3 1 dva a m_l
— •_ m — rn — CO _ -7 T,
OC.
o W - 5 2r'V' /V' 5 i | W - '‘ysss^ o
BRARIES SMITHSONIAN INSTITUTION NOlinillSNI NVIN0SH1IWS SBIdVdaiT L I B RAR I ES SMITHSONIAN INSTITUTION N
Z r- _ Z “ — ^ ^
m 2 ^uix^X rn -x
DiinmsNrNViNosHims^sa i dvda n~u b rar i esl°smithsonian“institution,/1 NoiinuiSNi nvinoshiiws S3 i dVda n l
Z _ co Z .A,v co Z -
> ^ i i
to Z CO * Z CO
BRARIES SMITHSONIAN INSTITUTION NOlinillSNI NVIN0SH1MS S3ldVd8l1_
co 5 _ _ _ ^ _ _ _ Z co
z
<
‘ z
\'ZW co
E
z ' co z co
LIBRARIES SMITHSONIAN INSTITUTION N
-7 _ CO 2 CO
o
z
o
z
JlinillSNI^NVINOSHlIWS^Sa IBVdan^LIBRARI ES^SMITHSONiAN-1 INSTITUTION NOlinillSNI NVINOSHHWS S3 I d Vd 9 ll^ L
z r* z r“ ' —
B RAR I E S ^SMITHSONIAN INSTITUTlON^NOlinillSNI NVIN0SH1IIMS S3 I dVd 3 IT LI B RAR I E S^SMITHSONIAN INSTITUTION b
z . co “ -
X
CO
I i ^ ' ' i r § 5 ^ s - ,z
JlinillSNI^NVINOSHlIWS^SB I dVd a n^LI B RAR I ES^SMITHSONIAN ^INSTITUTION ^NOlinillSNI NVIN0SH1IWS^S3 I BVd 8 I 1_L
I < JZfi JZr 5 It
7 cc wY /<>■> 5 vS
V to r r S - \K
O o
BRAR I ES*2 SMITHSONIAN^ INST I TUT I ON*2 NOIinillSNI^NVINOSHlIlMS^SB I dVd a 1*1 LI B RAR I ES SMITHSONIAN INSTITUTION I
m ^ n^xix^z rn
0IXnXIXSNI_NVIN0SHXUMS1/'s3 I HVUan~LIBRAR I ES^SMITHSONIAN “INSTITUTION NOlinXIXSNI NVINOSHXIWS^Sa I BV« 8 11^1
§ S .1 ^C' 2 ^BBv 1 * _< i
\V
.
TWENTY-THIRD ANNUAL REPORT
OF THE
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
1937
INCLUDING TECHNICAL REPORTS
Nos. 577 to 611
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON : 1938
For sale by the Superintendent of Documents, Washington, D. C.
Price, §2.50 (Buckram)
.
TECHNICAL REPORTS
Page
No. .577. Prechamber Compression-Ignition Engine Per¬
formance. By Charles S. Moore and John H.
Collins, Jr _ 49
No. 578. Flight Measurements of the Dynamic Longi¬
tudinal Stability of Several Airplanes and a
Correlation of the Measurements With Pilots’
Observations of Handling Characteristics. By
Hartley A. Soule _ 69
No. 579. A Study of the Two-Control Operation of an
Airplane. By Robert T. Jones _ 75
No. 580. Heat Transfer to Fuel Sprays Injected Into
Heated Gases. By Robert F. Selden and
Robert C. Spencer _ 91
No. 581. Measurements of Intensity and Scale of Wind-
Tunnel Turbulence and Their Relation to the
Critical Reynolds Number of Spheres. By
Hugh L. Dryden, G. B. Schubauer, W. C.
Mock, Jr., and H. Iv. Skramstad _ 109
No. 582. A Theory for Primary Failure of Straight Cen¬
trally Loaded Columns. By Eugene E.
Lundquist and Claude M. Fligg _ 141
No. 583. The Rolling Friction of Several Airplane Wheels
and Tires and the Effect of Rolling Friction on
Take-Off. By J. W. Wetmore _ 169
No. 584. Strength of Welded Aircraft Joints. By W. C.
Brueggeman _ 177
No. 585. Span Load Distribution for Tapered Wings
With Partial-Span Flaps. By H. A. Pearson. 209
No. 586. Airfoil Section Characteristics as Affected by
Variations of the Reynolds Number. By
Eastman N. Jacobs and Albert Sherman _ 227
No. 587. Blower Cooling of Finned Cylinders. By
Oscar W. Schey and Herman H. Eller-
brock, Jr _ 269
No. 588. Fuel Spray and Flame Formation in A Com¬
pression-Ignition Engine Employing Air Flow.
By A. M. Rothrock and C. D. Waldron _ 281
No. 589. An Analysis of Lateral Stability In Power-Off
Flight With Charts For Use In Design. By
Charles H. Zimmerman _ 297
No. 590. Pressure- Distribution Measurements of An
0-2H Airplane In Flight. By H. A. Pearson. 319
No. 591. An Analytical and Experimental Study of the
Effect of Periodic Blade Twist on the Thrust,
Torque, and Flapping Motion of an Autogiro
Rotor. By John B. Wheatley _ 353
No. 592. Full-scale Tests of N. A. C. A. Cowlings. By
Theodore Theodorsen, M. J. Brevoort, and
George W. Stickle _ 361
No. 593. Cooling of Airplane Engines At Low Air Speeds.
By Theodore Theodorsen, M. J. Brevoort, and
George W. Stickle _ 391
No. 594. Characteristics of Six Propellers Including the
H igh-Speed Range. By Theodore Theodorsen,
George W. Stickle, and M. J. Brevoort _ 401
I’m se
No. 595. Full-Scale Tests of A New Type N. A. C. A.
Nose-Slot Cowling. By Theodore Theodor¬
sen, M. J. Brevoort, George W. Stickle, and
M. N. Gough _ 439
No. 596. Cooling Test of A Single-Row Radial Engine
With Several N. A. C. A. Cowlings. By M.
J. Brevoort, George W. Stickle, and Herman
H. Ellerbrock, Jr _ 449
No. 597. Air Propellers In Yaw. By E. P. Lesley, George
F. Worley, and Stanley Moy _ 459
No. 598. Alternating-Current Equipment For the Meas¬
urement of Fluctuations of Air Speed In Tur¬
bulent Flow. By W. C. Mock, Jr _ 475
No. 599. Flight Tests of the Drag and Torque of the Pro¬
peller in Terminal-Velocity Dives. By Rich¬
ard V. Rhode and Henry A. Pearson _ __ 493
No. 600. An Analysis of the Factors That Determine the
Periodic Twist of an Autogiro Rotor Blade,
With A Comparison of Predicted and Meas¬
ured Results. By John B. Wheatley _ 503
No. 601. Torsion Tests of Tubes. By Ambrose H. Stang,
Walter Ramberg, and Goldie Back _ 515
No. 602. Wind-Tunnel and Flight Tests of Slot-Lip
Ailerons. By Joseph A. Shortal _ 537
No. 603. Wind-Tunnel Investigation of Wings With Ordi¬
nary Ailerons and Full-Span External-Airfoil
Flaps. By Robert C. Platt and Joseph A.
Shortal _ _ _ 563
No. 604. Pressure-Distribution Measurements At Large
Angles of Pitch On Fins of Different Span-
Chord Ratio on A 1 /40-Scale Model of the
U. S. Airship “Akron”. By James G.
McHugh _ 585
No. 605. Resume and Analysis of N. A. C. A. Lateral
Control Research. By Fred E. Weick and
Robert T. Jones _ 605
No. 606. Electrical Thermometers For Aircraft. By John
B. Peterson and S. H. J. Womack _ 633
No. 607. Spinning Characteristics of the XN2Y-1 Air¬
plane Obtained From the Spinning Balance
and Compared With Results From the Spin¬
ning Tunnel and From Flight Tests. By M.
J. Bamber and R. O. House _ 649
No. 608. Stress Analysis of Beams With Shear Deforma¬
tion of the Flanges. By Paul Kuhn _ 669
No. 609. Experimental Investigation of Wind-Tunnel In¬
terference On the Downwash Behind an Air¬
foil. By Abe Silverstein and S. Katzoff _ 689
No. 610. Tests of Related Forward- Camber Airfoils in the
Variable-Density Wind Tunnel. By Eastman
N. Jacobs, Robert M. Pinkerton, and Harry
Greenberg _ 697
No. 611. Wind-Tunnel Investigation of Tapered Wings
With Ordinary Ailerons and Partial-Span
Split Flaps. By Carl J. Wenzinger _ 733
hi
LETTER OF TRANSMITTAL
To the Congress of the United States:
In compliance with the provisions of the act of March 3, 1915, establishing the National Advisory Committee
for Aeronautics, I transmit herewith the Twenty-third Annual Report of the Committee covering the fiscal year
ended June 30, 1937.
Franklin D. Roosevelt.
The White House,
January 7, 1938.
LETTER OF SUBMITTAL
National Advisory Committee for Aeronautics,
Washington, D. C., November 29, 1937.
Mr. President:
In compliance with the provisions of the act of Congress approved March 3, 1915 (U. S. C., title 50, sec. 153),
I have the honor to submit herewith the Twenty-third Annual Report of the National Advisory Committee for
Aeronautics covering the fiscal year 1937.
During the past year the United States has maintained its position in the forefront of progressive nations in
the technical development of aircraft for both military and commercial purposes. This has been due chiefly to
sound organization and liberal support of scientific laboratory research in aeronautics in this country.
The War, Navy, and Commerce Departments, having equal representation on the Committee, cooperate in
every way in its work, and each receives the results of the scientific investigations conducted. Thus the research
needs of all branches of aviation are met without overlapping or duplication of effort. The Committee’s activi¬
ties, however, are limited to research. They do not include experimental engineering in the application of research
results to the development of military, naval, or commercial aircraft.
The greatly increased interest of the major powers in fostering aeronautical research and their determined
efforts to excel in this rapidly advancing engineering science constitute a scientific challenge to America’s present
leadership. It is the responsibility of the National Advisory Committee for Aeronautics to see to it that the
United States will not become dependent upon any foreign nation for fundamental scientific data on which to base
the design of American aircraft. To do this effectively it will be necessary that this Committee continue to have
the liberal and far-sighted support of the President and of the Congress.
Respectfully submitted.
Joseph S. Ames, Chairman.
The President,
The White House, Washington, D. C
VI 1
t
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
HEADQUARTERS, NAVY BUILDING, WASHINGTON, D. C.
LABORATORIES, LANGLEY FIELD, VA.
Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific
study of the problems of flight (U. S. Code, Title 50, Sec. 151). Its membership was increased to 15 by
act approved March 2, 1929. The members are appointed by the President, and serve as such without
compensation.
Joseph S. Ames, Ph. D., Chairman,
Baltimore, Md.
David W. Taylor, D. Eng., Vice Chairman,
Washington, D. C.
Willis Ray Gregg, Sc. D Chairman, Executive Committee,
Chief, United States Weather Bureau.
William P. MacCracken, J. D., Vice Chairman, Executive
Committee,
Washington, D. C.
Charles G. Abbot, Sc. D.,
Secretary, Smithsonian Institution.
Lyman J. Briggs, Ph. D.,
Director, National Bureau of Standards.
Arthur B. Cook, Rear Admiral, United States Navy,
Chief, Bureau of Aeronautics, Navy Department.
Fred D. Fagg, Jr., J. D.,
Director of Air Commerce, Department of Commerce.
Harry F. Guggenheim, M. A.,
Port Washington, Long Island, N. Y.
Sydney M. Kraus, Captain, United States Navy,
Bureau of Aeronautics, Navy Department.
Charles A. Lindbergh, LL. D.,
New York City.
Augustine W. Robins, Brigadier General, United States
Army,
Chief Materiel Division, Air Corps, Wright Field,
Dayton, Ohio.
Edward P. Warner, M. S.,
Greenwich, Conn.
Oscar Westover, Major General, United States Army,
Chief of Air Corps, War Department.
Orville Wright, Sc. D.,
Dayton, Ohio.
George W. Lewis, Director of Aeronautical Research
John F. Victory, Secretary
Henry J. E. Reid, Engineer-in-Char g e , Langley Memorial Aeronautical Laboratory, Langley b ield, V a.
John J. Ide, Technical Assistant in Europe, Paris, France
TECHNICAL COMMITTEES
aerodynamics
power plants for aircraft
AIRCRAFT MATERIALS
AIRCRAFT STRUCTURES
AIRCRAFT ACCIDENTS
INVENTIONS AND DESIGNS
Coordination of Research Needs of Military and Civil Aviation
Preparation of Research Programs
Allocation of Problems
Prevention of Duplication
Consideration of Inventions
LANGLEY MEMORIAL AERONAUTICAL LABORATORY
LANGLEY FIELD, VA.
Unified conduct, for all agencies, of
scientific research on the fundamental
problems of flight.
OFFICE OF AERONAUTICAL INTELLIGENCE
WASHINGTON, D. C.
Collection, classification, compilation,
and dissemination of scientific and tech¬
nical information on aeronautics.
IX
38548—38 - 2
The New N. a. C. a. Free Flight Wind Tunnel in Which Investigations of Airplane Stability and Control Characteristics can Be Made on an
airplane Model in Free Flight.
TWENTY-THIRD ANNUAL REPORT
OF THE
NATIONAL ADVISORY COMMITTEE FOR
AERONAUTICS
Washington. D. C., November 10 , 1937.
To the Congress of the United States:
In accordance with the act of Congress approved
March 3, 1915 (U. S. C., title 50, section 151), which
established the National Advisory Committee for
Aeronautics, this Committee submits herewith its
twenty-third annual report, covering the fiscal year
1937.
Responsibilities of this organization. — The prescribed
functions of this organization are to “supervise and
direct the scientific study of the problems of flight,
with a view to their practical solution,” and to “direct
and conduct research and experiment in aeronautics.”
In the discharge of its functions under the law the
primary responsibilities of the National Advisory
Committee for Aeronautics are: (1) To recognize in
advance the trend of aeronautical development, civil
and military; (2) to anticipate the research problems
that will arise; and (3) to design and provide research
equipment to meet the needs of this rapidly advancing
engineering science, and then to conduct the necessary
scientific investigations.
Created by law in 1915 as an independent Govern¬
ment establishment, the Committee, with the consistent
and liberal support of the President and of the Con¬
gress, has gradually developed a large and wejl-
equippecl aeronautical research laboratory at Langley
Field, Virginia. In this laboratory it has conducted
fundamental scientific research in aeronautics with the
sincere and indispensable cooperation and assistance of
the War, Navy, and Commerce Departments. As a
result, the scientific basis for aircraft design in the
United States for both military and civil uses is not
excelled in any other country. Long adherence to
sound policy has won for the United States general
recognition as a leader among the progressive nations
in improving the performance, efficiency, and safety
of aircraft.
The continued improvement in the performance of
both military and commercial aircraft has confronted
this Committee with a variety of problems that are
pressing for immediate solution. Among examples of
such problems may be mentioned the need for devising
a method for studying the stalling characteristics of
highly tapered wings; the determination of the neces¬
sary load factors and their variation with size and
speed; the problem of reducing or eliminating if pos¬
sible the formation of ice on wings, propellers, and
control surfaces, and of providing effectively for the
automatic removal of ice when it does form; problems
involved in the design of wings, control surfaces, and
flaps, as well as other devices to secure better control
at low speeds incident to taking off and landing; prob¬
lems of suppressing vibration and flutter, improving
engine and propeller efficiency, capacity, and dependa¬
bility, extending the range, enlarging the capacity,
and at the same time constantly increasing the speed
and safety of aircraft.
In addition to meeting urgent needs of the present,
the Committee tries to look into the future and to
anticipate some of the problems that may arise. For
example, what are the maximum requirements for mili¬
tary and commercial aircraft going to be? Will speeds
in excess of 400 miles per hour be required ? How much
will the size of commercial aircraft exceed 50 tons
within the next few years? What are the problems
that will require scientific analysis before such craft
can be successfully designed and constructed? Will
airships be further developed for naval use or for
transoceanic transportation and, if so, what are funda¬
mental problems this Committee should investigate?
The organization of research. — To analyze the present
and probable research needs of aviation, civil and mili¬
tary, the N. A. C. A. has set up standing technical
subcommittees on aerodynamics, power plants for air¬
craft, aircraft materials, and aircraft structures. The
subcommittees are organized along lines similar to the
main Committee and include specially qualified repre¬
sentatives of all the governmental agencies concerned
with aeronautical development, as well as experts from
private life. The members of the subcommittees, like
the members of the main Committee, serve as such
2
REPORT NATIONAL ADVISORY
without compensation. The subcommittees prepare
and recommend research programs. The more funda¬
mental problems are usually assigned for investigation
at the Committee’s laboratory at Langley Field, Vir¬
ginia, primarily because of its special equipment for
aeronautical research. Problems are also assigned to
the National Bureau of Standards, so as to make the
best use of available Government facilities and at the
same time to avoid duplication in the field of aero¬
nautical research. In the same manner problems are
assigned and funds transferred to universities and
technical schools. In this way aeronautical research
is stimulated and coordinated.
Advances in the science of aeronautics have given
rise to various trends, as the possibilities of aircraft
increase. At the present time the trend of design of
aircraft in all nations is definitely toward higher speeds
and larger structures, with greater range and carry¬
ing capacity. This is true in both the military and
commercial fields. Scientific and technical problems do
not diminish but on the contrary increase in number
and in difficulty with each advance in speed or size.
It is the duty of this Committee to supply the funda¬
mental data on which the design of new aircraft is
based. If the Committee does not meet this responsi¬
bility adequately, the United States will quickly fall
behind, because of the great emphasis now being placed
on aeronautical research and development by other
progressive nations.
Research facilities. — Up to 1932 the Committee had
constructed at its laboratories at Langley Field, Vir¬
ginia, known as the Langley Memorial Aeronautical
Laboratory, special equipment such as the variable-
density tunnel, the propeller-research tunnel, the full-
scale tunnel, and the hydrodynamic laboratory — a sea¬
plane towing basin. They were at the time of con¬
struction the only such pieces of equipment in the
world. The possession of such equipment was one of
the chief factors in enabling the United States to be¬
come the recognized leader in the technical develop¬
ment of aircraft. Since 1932 this research equipment
lias been reproduced by foreign countries and in some
cases special research equipment for the study of
problems in aeronautics has been developed and con¬
structed abroad which is more modern than and su¬
perior to the equipment existing at Langley Field.
Since 1932 the importance of scientific research in
aeronautics has been more generally appreciated by
European nations and several of the larger powers have
greatly augmented their research facilities and activi¬
ties. The competition in the development of research
equipment and facilities between the progressive na¬
tions is just as intense as the competition in the produc¬
tion of aircraft of superior performance. This condi¬
tion has impressed the Committee with the advisability
COMMITTEE FOR AERONAUTICS
of providing additional facilities promptly as needed
for the study of problems that are necessary to be
solved, in order that American aircraft development,
both military and commercial, will not fall behind.
In answering this scientific challenge the Committee
has under construction at its laboratories at Langley
Field a new wind tunnel having a diameter of 19 feet
that can be operated under a pressure of three or more
atmospheres at an air speed of more than 200 miles per
hour. This tunnel will permit the investigation of the
characteristics of large models of aircraft at much
higher values of Reynolds Number than can be obtained
in any of the Committee’s existing wind tunnels. The
Committee also has under construction a refrigerated
wind tunnel for the investigation of the problems of
ice formation on aircraft. This tunnel has throat di¬
mensions of 7Y2 by 3 feet and will embody features
and principles which, it is believed, will make it an
effective instrument for the purpose intended.
The Committee during the past year developed an
entirely new type of wind tunnel. The experience of
the Committee in the operation of the free-spinning
wind tunnel indicated the advantage of being able to
reproduce and observe aircraft motion under controlled
conditions in a wind tunnel. Methods of studying sta¬
bility, control, and motion of an aircraft in previous
types of wind tunnels, where the model is fixed on a
balance, are long and laborious, and leave much to be
desired in accuracy. Realizing the need for studying
stability, control, and motion of a model of an aircraft
when flying unrestrained, the Committee developed in
the past year a new form of wind tunnel known as a
“free-flight wind tunnel.”
The first tunnel of this type constructed was 5 feet
in diameter, and was so arranged that by tilting the
tunnel its longitudinal axis could be set parallel to
the glide path of the model under test. To do this the
tunnel was suspended from above at a single point so
that the axis of the wind tunnel could be varied through
a wide range of angles, making this tunnel what might
be called a “tilting wind tunnel.”
The results obtained with this small tunnel were so
encouraging that the Committee proceeded with the
construction of a free-flight wind tunnel having a
diameter of 20 feet.
With the establishment of commercial service across
the Pacific Ocean by seaplane transports and the early
prospect of such service across the Atlantic, operators
and designers are focusing their attention on aircraft
of larger sizes having improved efficiency and carrying
more passengers and a heavier mail and express load.
The design of the seaplane hull is a most important
factor affecting the efficiency of transoceanic transports.
Anticipating the need for extensive investigation of
seaplane hull models in connection with the develop-
3
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ment of larger seaplanes, the Committee during the
past year modernized its hydrodynamic laboratory.
The towing basin was lengthened from 2,000 feet to
2,900 feet. The towing carriage was enlarged and the
operating speed increased so that investigations can
now be made at speeds corresponding to the higher
take-off and landing speeds of seaplanes.
The Committee’s laboratories are on a portion of
Langley Field assigned to this organization by the
Secretary of War and are under the direct control of
the Committee. The Committee believes that its lab¬
oratories, despite the recent great expenditures on re¬
search organizations abroad, are as yet unexcelled by
those of any other single nation. In addition to the
new research equipment under construction as noted
above, the Committee’s laboratories include: An 8-foot
500-mile-per-hour wind tunnel; a CO- by 30-foot full-
scale wind tunnel ; a 20-foot propeller-research tunnel ;
a 5-foot variable-density wind tunnel; a T- by 10-foot
wind tunnel; a 5-foot vertical wind tunnel; a 15-foot
free-spinning wind tunnel ; two high-velocity jet -type
wind tunnels of 11- and 24-inch throat diameters, re¬
spectively; a hydrodynamic laboratory; an engine re¬
search laboratory; a flight research laboratory; and an
instrument research laboratory.
Relation of Committee’s work to national defense. — The
relationship of the work of this organization to national
defense has long been recognized and appreciated by the
War and Navy Departments. The Army and Navy air
organizations rely upon the N. A. C. A. to anticipate
and to meet their research needs and thus to enable
them to achieve and maintain leadership in the highly
competitive field of military aircraft development.
The safety and security of our country in time of war
may depend upon a decision in the air. The course of
a war will certainly be influenced in favor of that side
which can gain supremacy in the air. Sound tactical
organization, large numbers of aircraft, sufficient
trained personnel, and ample productive capacity in
the industry are not in themselves sufficient. The air¬
craft that engage the enemy in action must, if possible,
be superior in performance. The hope of retaining our
present superiority in technical development, in the
face of the increasing emphasis being placed upon aero¬
nautical research and development abroad, will depend
largely upon the ability of this organization to solve
promptly and effectively the fundamental problems at¬
tendant upon rapid progress in this branch of engi¬
neering science.
In this connection, the economic value of the work
of this organization is worthy of reference. The pro¬
curement programs of the Army and Navy call for the
expenditure of large sums to carry into effect the
national defense policy approved by the Congress. Un¬
less the aircraft procured are at least equal in perform¬
ance to those possessed by other nations, their net value
to the Army and Navy in time of war would be almost
at the vanishing point. A national investment in in¬
ferior military aircraft would not only invite the risk of
loss of the aircraft in time of war, but also the trained
flying personnel. It would be as disappointing and
disastrous as it usually is to try to win on the second-
best hand in a poker game. Without up-to-date, re¬
liable results of scientific laboratory research, our
Army and Navy would not be able, even with the most
sincere cooperation of the industry, to design and pro¬
cure aircraft with any assurance that they would not
be “second best” in time of war.
Commercial aviation. — The continued search for trends
of development, and the effort to meet these trends
by the provision of adequate research facilities and
investigation of the right problems, also have a very
important bearing upon the development of commer¬
cial aviation. Researches initiated primarily to meet
military needs are in many cases broadened in scope
to meet the needs of commercial aviation. Research
problems peculiar to commercial aviation alone are
also investigated. The Committee is materially as¬
sisted in this respect by suggestions from the Bureau
of Air Commerce and from the air transport lines.
Aircraft manufacturers also offer research suggestions
and are alert to incorporate changes which the Com¬
mittee’s researches indicate will improve the safety or
efficiency of aircraft. That the United States leads
the world in the development and operation of com¬
mercial aircraft is due not alone to this healthy condi¬
tion, but also in large measure to the national policy of
air mail payment and to the indispensable assistance
of the Bureau of Air Commerce in providing unexcelled
air navigation facilities and otherwise helping in every
practicable way to promote the safety and efficiency of
air navigation. We cannot in this connection under¬
estimate the importance of the meteorological service of
the Weather Bureau in aid of safety, nor the numerous
and valuable contributions to commercial aviation that
have resulted from the experiments and developments
on aircraft, engines, instruments, and accessories by
the Army and Navy.
Our growing air transport business finds a healthy
reflection in an aircraft production industry better
equipped to respond to the needs of national defense in
time of emergency. A healthy nucleus of an aircraft
industry capable of rapid expansion in time of need is
essential to our national defense. If it were not for
the stimulation and support given the manufacturers
by the growth of commercial air transportation in the
United States, the aircraft industry would be so much
weaker that, in view of disturbed world conditions at
this time, there would be need for some form of arti¬
ficial stimulation and development of productive ca-
4
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
pacity. That we are not confronted with sncli a
problem at this time is due partly to the fact that the
results of the Committee’s researches have made pos¬
sible the development of commercial air transports in
the United States superior to those of any other coun¬
try. This has not only facilitated a rapid growth of
commercial air transportation in this country, but has
given to the American aircraft industry an advantage
in world markets, evidenced by orders received from
foreign countries for commercial airplanes of Amer¬
ican manufacture.
The improved efficiency and safety of American
air transports have permitted economies in operation,
which in turn have resulted in material lessening of the
cost of carrying air mail and of passenger fares.
Economic value of research. — No money estimate can
be placed upon the economic value of greater national
security through development of the means of produc¬
ing superior military aircraft. Nor can a money esti¬
mate be placed upon the economic value of lives and
property saved through improvements in the safety of
aircraft. Nor can the educational advantages offered
by air travel, the time saved, and the pleasure afforded
to passengers be evaluated, nor the value to the nation
of extending its national influence through world trade
routes of the air. The researches of this Committee,
however, do have a tremendous economic value that
can be measured in dollars and cents. Improvements in
aircraft that have resulted from the Committee’s inves¬
tigations and that have a definite economic value are
numerous. Careful computations have been made of
the economic value of a few of the more important con¬
tributions of this organization. These indicate that
the annual savings in money made possible by the Com¬
mittee's researches exceed the total appropriations for
this organization since its establishment in 1915.
Summary. — With the rapid expansion of aviation in
national defense, it is more than ever necessary that
facilities be available for the prompt and adequate study
of those fundamental problems in aeronautics that in¬
fluence the speed, range, capacity, and control of
aircraft.
The Committee believes that the future development
of American aeronautics is largely dependent upon the
support and effort given to the orderly and sustained
prosecution of fundamental scientific research. It is
the confident hope of the Committee that the United
States will never be in a position where fundamental
information necessary for the design of aircraft of
maximum performance, efficiency, and safety will have
to be imported from any foreign nation.
In commercial aviation the major problem is one of
improving safety without penalizing those factors that
are necessary to increase the speed, efficiency, operating
range, and comfort of aircraft. When this Committee
was established over twenty-two years ago there was but
little appreciation of the value of aeronautics to national
defense and practically no appreciation of the possibili¬
ties of aircraft in commerce.
Aviation has now become such an important factor
in national defense, in the promotion of transportation
in the United States, and in the extension of inter¬
national commerce and good will that the organization
and conduct of aeronautical research have attained the
greatest significance and importance.
Foreign nations are making determined efforts to
design and produce superior research facilities and to
develop superior aircraft, both civil and military. The
Committee in order fully to meet its responsibilities is
endeavoring to modernize, improve, and augment its re¬
search facilities so as to maintain the present advantage
of fhe United States.
To assure effective functioning on the urgent prob¬
lems of the Army and Navy in time of war means for
stabilizing the personnel of this organization must be
found. From a study of the problem thus far it ap¬
pears that enactment of legislation for this purpose
may be necessary.
The Committee believes that the results achieved in
the past and the problems to be faced justify a con¬
tinuation of the liberal support of its work, and it fur¬
ther believes that in order to secure the best results
there should be no change in its functions or in its
status as an independent Government establishment.
PART 1
REPORTS OF TECHNICAL COMMITTEES
In order to carry out effectively its principal func¬
tion of the supervision, conduct, and coordination of
the scientific study of the problems of aeronautics, the
National Advisory Committee for Aeronautics has es¬
tablished a group of technical committees and subcom¬
mittees. These technical committees prepare and rec¬
ommend to the main Committee programs of research
to be conducted in their respective fields, and as a result
of the nature of their organization, which includes
representation of the various agencies concerned with
aeronautics, they act as coordinating agencies, provid¬
ing effectively for the interchange of information and
ideas and the prevention of duplication.
In addition to its standing committees and subcom¬
mittees, it is the policy of the National Advisory Com¬
mittees for Aeronautics to establish from time to time
special technical subcommittees for the study of par¬
ticular problems as they arise.
During the past year there has been a major change
in the organization of the Committee’s standing tech¬
nical committees. The Committee on Aircraft Struc¬
tures and Materials, which was one of the three
principal technical committees, its Subcommittee on
Structural Loads and Methods of Structural Analysis
and the latter’s Subcommittee on Research Program
on Monocoque Design have been replaced by two co¬
ordinate committees, both reporting direct to the main
Committee, namely, the Committee on Aircraft Mate-
rials and the Committee on Aircraft Structures. This
change was made in recognition of the greatly in¬
creased importance of the problems of structural design
in the field of aeronautics, and of the need for greater
concentration of effort on these problems.
With this change in organization, the Committee
has four principal technical committees — the Commit¬
tee on Aerodynamics, the Committee on Power Plants
for Aircraft, the Committee on Aircraft Materials, and
the Committee on Aircraft Structures. Under these
committees there are six standing subcommittees.
The membership of these technical committees and
subcommittees is listed in Part II.
The Committees on Aerodynamics and Power Plants
for Aircraft have direct control of the aerodynamic
and aircraft-engine research, respectively, conducted
at the Committee’s laboratory at Langley Field, and
of special investigations conducted at the National Bu¬
reau of Standards. Most of the research under the
supervision of the Committee on Aircraft Materials is
conducted by the National Bureau of Standards. The
greater part of the research under the cognizance of
the Committee on Aircraft Structures is carried on by
the National Bureau of Standards, but a number of
structural investigations, especially those of a theoreti¬
cal nature, are conducted at educational institutions
and at the Committee’s laboratory at Langley Field.
The four technical committees recommend to the main
Committee the investigations in their respective fields
to be undertaken by educational institutions under con¬
tract with the National Advisory Committee for Aero¬
nautics, and keep in touch with the progress of the
work and the results obtained. The experimental in¬
vestigations in aerodynamics, aircraft power plants,
aircraft materials, and aircraft structures undertaken
by the Army Air Corps, the Bureau of Aeronautics
of the Navy, the National Bureau of Standards, and
other Government agencies are reported to these four
committees.
REPORT OF COMMITTEE ON AERODYNAMICS
LANGLEY MEMORIAL AERONAUTICAL LABORATORY
LANDING SPEED AND SPEED RANGE
Flaps. — The use of wing flaps on high-performance
airplanes is now almost universal. The research that
has been conducted by the Committee during the past
several years on the most promising forms of flaps has
resulted in establishing their relative merits and has
made possible the selection of the most satisfactory
type for a given design. During the past year, atten¬
tion has been directed mainly toward obtaining more
specific design data for flap application.
In the variable-density wind tunnel, tests of ordi¬
nary and split flaps of 20-percent wing chord on the
N. A. C. A. 23012 airfoil have been made with a large
range of flap settings at a value of the effective Reyn¬
olds Number of about 8,000,000, for the purpose of
providing designers with more reliable data as to the
airfoil section characteristics for these combinations
at large values of the Reynolds Number. While the
results have not been completely analyzed, they cor¬
roborate, in general, the conclusions drawn from pre¬
vious tests at lower values of the Reynolds Number.
5
6
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The split flap is somewhat more favorable to speed
range and landing speed than is the ordinary flap.
In the 7- by 10-foot wind tunnel a study of slotted
flaps is under way in which tests of flaps of various
shapes with slots of various forms are being con¬
ducted on an N. A. C. A. 23012 wing of 3-foot chord.
With this installation, airfoil characteristics corre¬
sponding to a Reynolds Number of about 2,500,000
are being determined. The results to date indicate
that with a properly designed slotted flap, unusually
high maximum lift coefficients may be obtained. In
addition, very low profile drag coefficients at high lift
coefficients may be obtained with the flap deflected,
which should result in improved take-off and climb
characteristics. For controlling the glide-path angle,
the slotted flap may be deflected beyond the angle for
maximum lift without appreciably changing the lift
coefficients. With this type of operation, the flap is
similar to the glide-control flap previously described
in Technical Note No. 552.
The results of the investigation in flight and in the
full-scale wind tunnel, of a Zap flap mounted on a
Fairchild 22 airplane, previously mentioned, have been
published in Technical Note No. 596. Results of a
similar investigation on the external-airfoil flap are
presented in Technical Note No. 604.
Tests have also been made in the 7- by 10-foot wind
tunnel for private companies and for the Bureau of
Aeronautics of the Navy Department of the aerody¬
namic characteristics of several models equipped with
flaps.
Maxwell slot. — The results of tests of another device
for the improvement of speed range, the Maxwell lead¬
ing-edge slot, mentioned in last year’s report, have been
published in Technical Note No. 598.
Measurement of minimum speed. — Opportunity was af¬
forded during the year, in connection with the investi¬
gation of the maximum lift coefficient of a 2R:12 wing
on a Fairchild 22 airplane, to obtain a comparison be¬
tween the flow conditions in flight and in the full-scale
wind tunnel and thus study the effect of various test
procedures and conditions on the measured minimum
speed of an airplane. The main flight program covered
the effect of wing loading and altitude on minimum
speed. By extension of the program the effects of pro¬
peller position, throttle setting, wing-surface roughness,
and the rate at which the angle of attack was increased
were investigated. It Avas found that for a constant
weight the minimum speed might vary by 5 percent,
depending on the factors. The maximum lift coefficient
obtained Avith one loading cannot be directly applied
to the computation of the minimum speed Avith another
loading, because of the variation of the lift coefficient
with speed.
CONTROL AND CONTROLLABILITY
For a number of years the Committee has been en-
gaged in a systematic Avind-tunnel investigation of lat¬
eral control with special reference to the improvement
of control at Ioav air speeds and at high angles of at¬
tack. Many different ailerons and other lateral-control
devices lraAre been subjected to the same systematic
investigation in the 7- by 10-foot Avind tunnel and the
devices that seemed most promising haAre been tested
in flight. As has been stated in previous reports, the
Avind-tunnel and flight results Avere not always in agree¬
ment and indicated that, in determining actual control
effectiveness from Avind-tunnel results, it Avas necessary
to include Avhat had been previously considered sec¬
ondary factors. A mathematical method of analysis
Avas consequently deATeloped to include those secondary
factors and this method of analysis has been in use for
about tAvo years.
The experience gained has resulted in a revised basis
of comparison of lateral-control devices and on this re¬
vised basis a critical resume and analysis of the Com¬
mittee’s research to date on lateral control has been
made and has been published in Technical Report No.
605. The analysis indicates that for normal-flight con-
ditions, ordinary ailerons with the gap betAveen the
aileron and the wing sealed are the most generally sat¬
isfactory. An added advantage of these ailerons is that
they appear to be practically free from icing hazards.
Slot-lip ailerons. — The complete results of the wind-
tunnel and flight i investigation of slot-slip ailerons ha\7e
been published in Technical Report No. 602. It was
stated in the last annual report that slot-lip ailerons
installed on a Fairchild 22 airplane produced unsatis¬
factorily sluggish control, although such sluggishness
Avas not detected by the pilots Avhen these ailerons Avere
installed on the Wl-A airplane. An analysis made
during the year has shown that the difference betAveen
the response of the two airplanes is explainable by the
difference in their lateral-stability characteristics. Al¬
though some reduction in the drag of the slot-lip ailer¬
ons over that previously reported Avas obtained Avith a
modified slot shape, the drag of this type of aileron is
still considered excessive for modern high-perform¬
ance airplanes.
The wind-tunnel investigation mentioned last year
of the special form of slot-lip aileron, consisting of a
plain aileron forming the trailing edge of an airfoil
equipped Avith an external-airfoil flap, has been com¬
pleted. The characteristics of these ailerons on an N. A.
C. A. 23012 Aving equipped Avith 20 and 30 percent chord
full-span external-airfoil flaps of the same section Avere
measured and are reported in Technical Report No. 603.
These ailerons Avere found to be capable of developing
large rolling moments but the hinge moments had cer-
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
tain undesirable characteristics and should receive
further study.
Ailerons on tapered wing’s. — At the request of the
Army Air Corps an investigation of the effectiveness
of conventional ailerons on a tapered wing was made
for direct comparison with a straight wing having
ailerons of the same size. A 2:1 tapered wing with
conventional flap-type aileron was mounted on a Fair-
child 22 airplane and investigated in flight and in the
full-scale wind tunnel. Conventional ailerons on this
wing were found to be slightly more effective than
ailerons of the same dimensions on a straight wing.
The improvement was of the order of only 5 percent
at low speed, and was so slight that it was not ap¬
parent to the pilots in the handling of the airplane.
The results are being prepared for publication.
An investigation of ordinary sealed ailerons on two
wings having medium and high taper ratios and par¬
tial-span split flaps has been described in Technical
Report No. 611. The report presents aerodynamic in¬
formation necessary for aileron design, including roll¬
ing, yawing, and hinge moments, as well as the aero¬
dynamic characteristics of the wings.
Floating wing-tip ailerons. — Comparative tests were
made in the full-scale wind tunnel and in flight to de¬
termine the relative effectiveness of floating-tip aile¬
rons and conventional trailing-edge ailerons. The
tests were made on a Fairchild 22 airplane equipped
with a 2 : 1 tapered wing the wing tips of which could
be removed and replaced by floating-tip ailerons. The
floating-tip ailerons were made as large as seemed
reasonable from considerations of structural weight.
These ailerons were found to be approximately one-
half as effective in producing rolling moment as con¬
ventional ailerons on the same wing. The floating-tip
ailerons produced small favorable yawing moments
while the trailing-edge ailerons produced appreciable
unfavorable yawing moments.
Combinations of spoilers. — At the request of the Bu¬
reau of Aeronautics of the Navy Department, the lat¬
eral-control possibilities of combinations of spoilers
arranged in tandem were investigated in the 7- by 10-
foot wind tunnel. Since the time of response with
such an arrangement was questionable, the investiga¬
tion consisted primarily of measuring the response
characteristics by means of a motion-picture study of
the motion of a wing model restrained by springs but
free to move when the control device was operated.
The rolling moments produced by the control devices
were measured with the same installation. It was
found that while a combination of front and rear
spoilers without lag was possible, no improvement in
control was obtained over that with the rear spoiler
or retractable aileron alone when the wing was
equipped with a full -span flap.
7
Reduction of aileron control forces. — With the increase
in size and speed of airplanes, increased interest has
been shown in means of reducing the forces required
to operate ailerons. On a large percentage of airplanes
aerodynamic balances of the Frise or slotted types are
used, with an accompanying loss in control effective¬
ness. In addition, such balances, with their projecting
surfaces, are subject to icing difficulties.
The use of trailing-edge tabs in the conventional
manner to balance the control forces of ailerons is ac¬
companied by a sacrifice of some control effectiveness.
A less conventional but apparently more successful
method of applying tabs to ailerons is to use a very
narrow-chord full-span tab to increase the up-floating
angle of the ailerons by deflecting the tabs downward
on both ailerons in conjunction with a proper differ¬
ential movement of the ailerons. A study of aileron
hinge moments as affected by differential linkages has
been made and the results published in Technical Note
No. 586. The value of a tab and differential linkage
system has been investigated with a large wing in the
7- by 10-foot wind tunnel and on a Fairchild 22 air-
*/
plane in flight. The ability of the arrangement to re¬
duce the control forces to any desirable value was veri¬
fied in both installations.
The flight investigation, in addition to verifying, in
general, the principles involved in the theoretcal anal¬
ysis, has indicated certain practical details requiring
further study. The effect of the tabs on the aileron
floating angle appears to be critically dependent on the
tab shape. Tabs consisting of flat plates extending
back of the aileron trailing edge were found to have
very little effect on the aileron floating angle and con¬
sequently little effect on the control forces, whereas
tabs inset within the aileron contour are satisfactory.
Wind-tunnel tests have shown that the effectiveness
of a given aileron may be increased considerably by
sealing the gap between the aileron leading edge and
the wing to prevent leakage of air at this point. The
effectiveness of the seal is greatest for narrow-chord
ailerons, the increase being of the order of 50 percent
when the aileron chord is about 10 percent of the chord.
The increase in effectiveness may be utilized to improve
the controllability or, if the controllability is satisfac¬
tory', to reduce the control forces bv the substitution
of a smaller sealed aileron for one having a gap at the
hinge.
The actual application of this system of improving
lateral control or reducing aileron stick forces de¬
pends on how much leakage occurs at the hinge in a
normal aileron installation. In order to study this
problem, measurements were made of the lateral con¬
trol of the Fairchild 22 airplane, which has ailerons
having a chord of 18 percent of the wing chord, with
the original aileron installation and with a fabric seal
8
REPORT NATIONAL ADVISORY
over the gap at the hinge. A 30-percent improvement
in the control effectiveness was obtained. On the basis
of these findings, sealed ailerons of half the chord of
the original ailerons, or 9 percent of the wing chord,
were installed on the airplane. These ailerons are
about as effective as the original unsealed ailerons but
require less than half the operating effort.
Two-control operation of an airplane. — Control of an
airplane by means of two controls instead of the three
normally used has appeared to offer promise of simpli¬
fying the operation of an airplane. Flights have been
made with airplanes in which both aileron-elevator and
elevator-rudder combinations were utilized for two-con¬
trol operation, but considerable uncertainty remains as
to which of these modes of operation is likely to prove
the better and also whether either of them is capable
of affording the controllability required for safety in
flight.
In order to obtain additional information on the
subject, an analytical study was made of two-control
operation of a conventional airplane by the method of
the theory of disturbed motion and is presented in
Technical Report No. 579. Control maneuvers were
computed for various combinations of rolling and yaw¬
ing moments with an airplane for which the lateral-
stability derivatives were varied. It was concluded
that, while the most desirable control characteristics
would depend somewhat on the lateral-stability char¬
acteristics and on the rate of application of the control
device, the two-control operation of an airplane would
b'e most generally satisfactory with controls which gave
primarily a rolling moment with a slight amount of
favorable yawing moment.
Flying qualities of large airplanes. — As was mentioned
in the last annual report, a research is in progress to
determine how much is known quantitatively regard¬
ing the actual stability, controllability, and maneuver¬
ability of large airplanes, and also what the procedure
should be in any investigation to determine these char¬
acteristics in quantitatve form. During the past year
a program of investigation in flight covering the meas¬
urement of all the quantities believed to be of impor¬
tance with respect to flying qualities, has been formu¬
lated, the instrumentation developed, and the program
successfully tried with a single-engine five-place high-
wing cabin monoplane. Some modifications in the
original program regarding the measurement of the
general stability and the effectiveness of the rudder
control were indicated to be desirable. The modified
program and certain items referring to asymmetric
power conditions that could not be investigated with
a single-engine airplane are being studied with a twin-
engine bombardment monoplane, and the measurements
have been initiated on modern transport airplanes.
Flight with unsymmetrical power. — The problem of
flight with only the propellers on one side operating
COMMITTEE FOR AERONAUTICS
was investigated as part of the investigation of the
power-on characteristics of large multi-engine models
in the full-scale tunnel.
Flight with zero yaw, accomplished by banking the
airplane slightly to balance the side forces due to the
propellers and rudder, was found preferable to balanc¬
ing the side forces by yawing without banking, both as
regards the maximum ceiling and the rudder deflection
required. For unsymmetrical power conditions, the
losses in performance, aside from the reduction of the
thrust, are due to the drag of the inoperative propellers
and the deflected rudder. The propeller drag is the
major item unless the propeller is feathered or allowed
to free-wheel.
MANEUVERABILITY
At the request of the Bureau of Aeronautics, Navy
Department, the Committee is undertaking an investi¬
gation of the maneuverability of several Navy airplanes
primarily for the purpose of determining the maximum
angular accelerations in pitch and roll to which the
machines may be subjected. The tests have been com¬
pleted on two airplanes. The investigation includes
measurements of the angular accelerations in rolling
produced by abrupt use of the ailerons alone and also
by combined use of the ailerons and other controls.
Pitching accelerations are investigated in abrupt pull-
ups from level flight and in recoveries from vertical
dives. In all cases the angular accelerations are cor¬
related with the linear accelerations of the center of
gravity. In addition to the measurements of angular
acceleration, information is being obtained on the pres¬
sure inside the wings during vertical dives and data are
obtained to compare the loss of altitude in recoveries
from dives with that predicted by means of charts de¬
veloped as a result of previous investigations.
In connection with the study of the vertical-dive
maneuver, the velocity -altitude relations for airplanes
have been studied. Charts have been prepared (Tech¬
nical Note No. 599) that present in a readily usable
form the solution of the relation between time, velocity,
and altitude for airplanes having various terminal
velocities. The variation of density with altitude is
taken into account on these charts.
STABILITY
A review of all available previous and contemporary
work on stability, which was mentioned in the last
annual report, has been completed and an extensive pro¬
gram outlined for systematic research in the various
facilities available to the Committee. Work is now in
progress upon several of the projects deemed to be the
most urgent.
The investigation of new equipment for the study of
stability is being continued. An experimental 5-foot
free-flight wind tunnel has been developed to a point
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
9
of satisfactory operation. This tunnel can be used to
study the free-flight behavior of models up to 22 inches
in span. With a tunnel of this type it is possible to
investigate inherent and controlled stability, motion in
gusty air, stalling characteristics, the power of controls,
and many other factors directly related to the actual
free-fliglit behavior of the airplane. Even at the very
low scale of tests possible in the present 5-foot tunnel,
observation of model behavior has led to very inter¬
esting conclusions regarding the effects of such factors
as the adverse yawing moments of ailerons, the effect
of the position of the wing wake on the damping of
longitudinal oscillations, the behavior of an aircraft
when the tail is in the violent wake behind deflected
split flaps, etc. The free-flight tunnel, of which the
present 5-foot experimental version is the first and only
one of the type, gives promise of greatly facilitating
the entire study of aircraft motion.
Lateral stability. — Most existing work on stability
deals with the inherent stability of the craft itself with
the controls either fixed or free. Actually, the most
usual condition of flight is that in which the aircraft
is held to a definite course by either a human pilot or
a compass-controlled automatic pilot. The pilot en¬
deavors to bring the craft back to the course after a
disturbance and in so doing alters the stability char¬
acteristics. A study of the stability of controlled mo¬
tion along a definite course is now in progress and
should show the effects of various ways of using the
controls. It may also lead to a modification of present
ideas regarding the importance and proper values of
certain factors which affect the motion, since the pres¬
ent ideas are based on requirements for inherent
stability.
In any study of stability with reference to a certain
course, it is of great practical importance to know how
the factors that govern the stability influence the mag¬
nitude and violence of the motion when an atmospheric
disturbance is encountered. A mathematical study of
motion in gusty air is being carried out and is ap¬
proaching completion for the case of lateral motion.
A report on lateral stability in power-off flight has
been published as Technical Report No. 589. This
report parallels Technical Report No. 521, which deals
with longitudinal stability. It includes discussions of
the problem and of the individual factors involved. A
number of charts are presented from which tire lateral
stability of a new design can be quickly and easily esti¬
mated.
One of the factors that most critically affects the
lateral-stability characteristics is the rate of change of
yawing moment with change in sideslip. There has
been considerable uncertainty as to what allowance to
make for the effect of the fuselage when this factor is
estimated. During the past year, the Committee has
undertaken a study of all readily available data on this
factor with a view to developing suitable empirical re¬
lationships for its estimation. A technical note is being
prepared giving the results of this investigation.
The investigation of the effect of tip shape and di¬
hedral of rectangular monoplane wings on the lateral-
stability characteristics, reported last year, lias yielded
basic information on the subject. For practical appli¬
cation to complete airplanes, however, the wing-fuselage
interference would seem to be an important factor in
determining the stability characteristics. Quantitative
information on this effect will be obtained from an
investigation that has been started in the 7- by 10-foot
wind tunnel with fuselages of various cross sections and
with tapered, swept -back, swept-forward, and rectangu¬
lar wings.
Longitudinal stability. — Work is now in progress on
a general study of longitudinal stability with power
on. An attempt is being made to prepare charts simi¬
lar to those in Technical Reports 521 and 589 to enable
the designer to estimate quickly the effect of power on
the stability.
The investigation of wing-fuselage interference in
progress in the variable-density wind tunnel has been
extended to include the study of the effects of adding
tail surfaces to typical combinations. Conventional tail
surfaces and horizontal tail surfaces with end plates are
both being investigated with a view toward exploring
the parameters of combination as affecting the aerody¬
namic interference, particularly as regards longitudi¬
nal stability. The effect on the moment of the tail sur¬
faces entering the wing wake is noticeable but small,
particularly when compared with the effect of the wing
stall.
The analysis, reported last year, of the horizontal tail
surface required for airplanes equipped with wing flaps,
has been completed. A rational system for computing
the horizontal tail area was evolved and has been pre¬
sented in Technical Note No. 597.
A comprehensive investigation has been undertaken
in the Committee’s full-scale wind tunnel to determine,
the effect of propeller operation on the important char¬
acteristics of airplanes, such as the lift, stability, con¬
trol, balance, etc. Full-scale data have been obtained
for five airplanes having different geometrical arrange¬
ments, and a report presenting an analysis of these re¬
sults is in preparation. These tests include measure¬
ments of the air-stream velocities and downwash angles
in the region of the tail plane, and a study is being
made to determine the variation of these quantities
with the propeller thrust.
Stalling. — The problem of avoiding excessive danger
from the stall has been a recurrent one. Most airplane
manufacturers dealt with the problem rather satisfac¬
torily several years ago, either empirically or through a
10
REPORT NATIONAL ADVISORY
reasonably sound understanding of the phenomenon,
gained as the result of research work both here and
abroad.
In general, the solutions embodied the use of increased
static longitudinal stability, thus providing a definite
warning of the approaching stall through the backward
movement, position, and forces on the control column,
together with a gradually developing stall secured either
by allowing the upper or lower wing of a biplane to
stall first or by the use of monoplanes with little or no
taper and with “poor” wing-fuselage junctures, which
further tended to bring about a gradually developing
stall, beginning at mid-span. These measures assured
that the stalled condition would develop progressively
after a reasonably definite warning; furthermore, lat¬
eral control was often maintained up to or beyond the
stall (wing maximum lift), owing to the fact that the
essentially effective parts of the wing system remained
unstalled even after the angle of attack had exceeded
that of maximum lift. Inasmuch as the pilot has little
incentive to go beyond this point, such a solution was
and still is considered satisfactory.
With such satisfactory solutions in common use, at¬
tention has for the past few years been diverted from
the problem of minimizing stalling dangers. Recently
however, modern design trends are bringing the
problem back again in an acute form. These trends
are toward higher wing loadings and landing speeds;
the substitution of efficient high-speed sections having
more sudden and hence less desirable stalling charac¬
teristics; the almost exclusive use of tapered-wing mono¬
planes; the use of increased taper; the low-wing posi¬
tion which contributes to reduced longitudinal stability
with increasing lift ; the use of “good” wing-fuselage
junctures; and, finally, high-lift devices. The high-
lift, devices may further add to the dangers of tip stall¬
ing, add to balance and stability difficulties, and usually
cause a vicious section stall corresponding to a sudden,
large, and usually unsymmetrical loss of lift.
These trends have already gone so far that it now
appears that many airplanes in common use cannot
be considered reasonably safe, even for experienced
pilots. The worst offenders may give no indication of
an approaching stall which, when it occurs, is mani¬
fested by a vicious uncontrolled rolling dive, that re¬
sults from a sudden loss of lift on the right or left
wing and a simultaneous loss of lateral control.
During the year practical methods of avoiding these
conditions in modern types of airplanes have been
sought. The investigations have proceeded mainly on
the theory that the vicious stall may best be avoided
in monoplanes by causing the wing to stall progressively
from the center toward the tips. Not only are the sud¬
den loss of lift and violent roll thus avoided, but lat¬
eral control is maintained through the first stages of
COMMITTEE FOR AERONAUTICS
the stall and the tendency toward an upwash on the
tail surfaces associated with the loss of lift near the
center of the wing may be used to bring about a
marked increase in longitudinal stability as the stall
is approached.
In the first investigation conducted in flight, sharp
leading-edge strips extending out along the wing from
either side of the fuselage were employed to bring about
the desired symmetrical center-stalling characteristic.
Wind-tunnel experiments with airfoils having sharp
leading-edge sections over a small portion near their
midspan had indicated how the flight investigation
should proceed. The flight investigations for the power-
off condition showed that an airplane having vicious
stalling characteristics could be improved as expected
by thus bringing about a gradually and symmetrically
developing center stall. The extreme maximum lift
coefficient was, of course, slightly reduced, but the prac¬
tical gliding or approach speed was not increased; in
fact, it was actually reduced. This phase of the flight
investigation is, however, only preliminary in that the
airplane tested had no flaps or other high -lift devices,
whereas the problem is of most practical interest and
is probably more difficult when high-lift devices are
employed. The investigations are being extended.
The method employed to start center stalling may be
objectionable on the grounds that the sharp leading
edges will always tend to reduce the maximum lift.
An investigation in the variable-density tunnel of meth¬
ods of accomplishing the same result without loss of
maximum lift led to the development of a new de¬
vice known as the “stall-control flap.” The flap tends
to produce a well-rounded lift curve similar to that
produced by the sharp leading edge but, together with
a split flap or other conventional high-lift device, high
maximum lift coefficients may be obtained. A special
wing incorporating a stall-control flap has been con¬
structed and installed on an F-22 airplane converted to
a low-wing type. Flight tests are now being started on
this airplane and from preliminary results it appears
that, besides bringing about the desired center stall,
several attendant advantages, such as favorable induced
yawing moments from the ailerons, may be realized
through its use.
SPINNING
The 15-foot, free-spinning wind tunnel has been kept
busy with routine testing of scale models of specific
airplanes. The Materiel Division of the Army Air
Corps, and the Bureau of Aeronautics of the Navy
Department, are requiring spinning tests of models
of new designs that are expected to be spun extensively
in service. Four such models have been tested cl urine:
the past year and three more are being prepared for
testing in the immediate future. The work carried on
11
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
in tliis connection includes not only tests of tlie par¬
ticular design, but also investigation of changes neces¬
sary to improve the spinning characteristics where such
changes appear to be necessary.
The free-spinning tunnel is available for the testing
of models for commercial concerns, and two such models
have been tested during the year.
A certain amount of general information is being
gleaned from the test results with specific designs.
Conclusions stated in the last annual report regarding
the importance of the tail unit in spinning have been
confirmed and amplified during the past year. As a
result of tests of a number of models of modern low-
wing monoplanes, it now appears possible to draw cer¬
tain conclusions about the effect of changes in mass dis¬
tribution on such designs. In most cases the spinning
characteristics of low-wing types have been improved,
and in no case have they been impaired, by moving
weight from the fuselage to the wings. This fact is
of special significance in view of the present trend to¬
ward multi-engine airplanes with the engines in the
wings.
During the past year a method has been developed
for measuring, on free-spinning models, the hinge mo¬
ment required to reverse completely the rudder during
the spin. Such measurements have been made on three
models. Indications are that the requirements of rapid
recovery from the spin and reasonably low rudder mo¬
ments are in certain cases very difficult to meet with
a rudder that is also satisfactory in normal flight.
In addition to the spinning of models of specific air¬
planes, a systematic investigation is being carried out
in the free-spinning tunnel to determine the effects of
changes in wing arrangement, in tail arrangement and
mass distribution. This investigation is about 20 per¬
cent completed. It is designed to reveal the relative
importance of the various factors which affect spinning
and to show which of these factors is most deserving
of more detailed study. The results to date tend to con¬
firm the conclusion that the tail arrangement is the most
important single item. The effects of wing plan form
and tip shape are, however, of considerably greater im¬
portance than has hitherto been thought to be the case.
The effect of wing section appears to be relatively slight.
Tests of a model of the Fleet airplane on the spinning
balance, reported last year, have been published as
Technical Report Xo. 607. An investigation on the
spinning balance of effect of wing plan form on the
spinning characteristics has also been completed and
the results published in Technical Note Xo. 6T2. The
tests included a rectangular wing with square tips and
with rounded tips and a tapered wing with rounded
tips. An investigation in progress will show the effect
of airfoil section on the spinning characteristics of
monoplanes with rounded tips.
An investigation on the spinning balance of the effect
of stagger of rectangular biplane cellules has been
completed and will be the subject of a report. The
range of stagger investigated was from negative 25 per¬
cent stagger to positive 25 percent stagger. While no
general conclusions can be drawn regarding the effect
of stagger, the results can be used in studying the steady
spinning characteristics of particular airplanes.
Tests for the purpose of making a direct comparison
between the actual spinning behavior of a low-wing
monoplane and the behavior of a model of the same air¬
plane in the spinning tunnel have been started. Some
difficulty and delay have been encountered in obtaining
a suitable airplane for tlie tests. Two have been tried
in flight. With one, the oscillating nature of the spin
made measurements impossible. With the second air¬
plane, the rudder forces built up to such a magnitude
on the entry into the spin as to make it extremely un¬
certain that the pilot could supply the force necessary
to assure that the airplane would recover from the pro¬
longed spins required for the measurements. The me¬
chanical advantage available to tlie pilot in operating
the rudder of this airplane was increased and the forces
that the pilot had to apply were reduced to the extent
that it was possible to continue the tests.
TAKE-OFF
The results of the investigation of the rolling friction
of airplane wheels, mentioned in last year’s report, have
been published in Technical Report Xo. 583.
In the calculated prediction of the take-off perform¬
ance of airplanes, common practice has been either to
neglect the transition period between the end of the
ground run and the beginning of the steady climb or
to take it into account by assuming a simple motion,
since the actual motion is too complex for simple mathe¬
matical treatment. This lack of knowledge regarding
the motion of the airplane in the transition introduces,
of course, a degree of uncertainty into the results. As
mentioned last year, an investigation of this phase of
the take-off was undertaken in an effort to eliminate this
uncertainty. The study is now completed and the re¬
sults are being prepared for publication. It was found
that the calculated value of the air-borne distance re¬
quired in taking off over a 50-foot obstacle might be
subject to an error of about 10 percent if the transition
is neglected.
The investigation served also to emphasize the diffi¬
culties which are encountered in attempting to obtain
representative comparisons directly from take-off tests
and which arise from the fact that it is practically
impossible for a pilot to conform exactly to a pre¬
scribed procedure throughout a series of complete take¬
offs, particularly if the air conditions are not abso¬
lutely steady. At present an attempt is being made to
12
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
develop a method whereby the true take-off capabilities
of an airplane may be evaluated without consideration
of the personal element or the air conditions. One
solution that appears promising is to determine from
individual tests the relation between ground run, dis¬
tance, and speed, and the relation between angle of
climb and speed, the latter to be measured at some alti¬
tude where smooth-air conditions prevail. These quan¬
tities should not be appreciably affected by piloting
and when properly combined, together with a suitable
allowance for the transition, should provide an accu¬
rate measure of the take-off performance of an airplane.
An investigation has been made to determine the feasi¬
bility of this system and the results are being analyzed.
The characteristics of the propeller producing the
thrust are an important influence on the take-off.
Available propeller data have to a great extent been
rendered inadequate because of the changes in design
necessitated by higher engine power and airplane
speeds, requiring larger propellers of higher pitch and
with three or more blades. For the purpose of estab¬
lishing the design factor for propellers in this category,
an extensive investigation on full-scale propellers has
recently been made in the propeller-research wind tun¬
nel. The investigation is more completely covered in
a later section of this report.
The above-mentioned investigation that was made
in the variable-density wind tunnel of ordinary and
split flaps of 20 percent of the wing chord on N. A.
C. A. 23012 airfoils indicates that neither of these flaps
can be considered a satisfactory high-lift device for
use in take-off because of the high profile drag caused
by these flaps at high values of the lift coefficient. In
this respect the ordinary flap is inferior to the split
flap. At any value of the lift coefficient where the
flaps are useful, a lower value of the profile drag coeffi¬
cient can be obtained with the split flap than with the
ordinary flap.
The stall-control flap previously mentioned, espe¬
cially when combined with a low-drag trailing-edge
high-lift device, appears to offer improvements in the
take-off characteristics of flying boats and airplanes
equipped with three-wheel landing gears, because this
flap permits high lift coefficients to be obtained with
the airplane in a level attitude.
LANDING
Landing' loads. — At the request of the Bureau of Air
Commerce and the Army Air Corps, the Committee is
undertaking the accumulation of statistical informa¬
tion on the loads sustained by the landing gear in land¬
ings. Investigations have been made with four
airplanes and one autogiro. Measurements of the atti¬
tude and vertical velocities immediately prior to con¬
tact and simultaneous measurements of the linear
accelerations of the center of gravity and the angular
accelerations in pitch are made in order to correlate
the magnitude and direction of the resultant ground
reaction and the approximate distribution of force
between the main and tail wheels with the motion and
attitude of the airplane at contact. The investigation
will be continued as more aircraft become available.
A preliminary analysis is being made of the data ob¬
tained thus far.
Stable landing gears. — The tricycle landing gear has
recently been receiving considerable attention because
of its possibilities for greatly improving the stability
and handling characteristics of the airplane on the
ground and for increasing the ease with which land¬
ings may be made. A study of the various factors
affecting the geometrical arrangement of the landing-
gear has been made.
With the use of tricycle landing gears, the shimmy
of the castering nose wheel has presented a problem.
The Committee has made an analytical investigation of
the stability of castering wheels as a result of which
information was obtained as to the cause of wheel
shimmy and several means of overcoming it were sug¬
gested. The allowance of a certain amount of lateral
freedom of the wheel on its axle was indicated as a
remedy. Model tests, and full-scale tests with the
Wl-A airplane, verified the indications of the analyti¬
cal investigation and have shown that the shimmy of
the castering wheel may be overcome by allowing a
relatively small amount of lateral freedom of the
wheel. To center the wheel, damping of the sidewise
motion should be provided, which in the investigation
described was done by curving the axle slightly.
The accelerations in landing of an airplane with a
tricycle landing gear have been studied to ascertain
whether the passengers might experience relatively
severe accelerations in an emergency landing. The
study revealed that the predominant acceleration was
due to braking forces applied to the main wheels and
that the vertical acceleration due to nosing over on
the nose wheel should not be serious from the stand¬
point of passenger comfort.
AIRFOILS
The work on airfoils carried on by the Committee
during the past year has been confined mainly to the
consolidation of the large amount of data obtained in
recent years and to the extension of its usefulness by
providing more diversified and accurate methods of its
application to practical problems.
Section characteristics. — Airfoil data obtained in the
variable-density wind tunnel since 1930 have been cor¬
rected by the empirical method mentioned last year,
to give more accurate section characteristics than it
has been possible to obtain previously from tests of
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
13
rectangular airfoils in tlie variable-density wind tun¬
nel. These corrected data are to be presented in two
reports. The first of these (Technical Report 610)
presents the complete results obtained from the investi¬
gation of related forward-camber airfoils, of which the
N. A. C. A. 23012 airfoil is representative. The second
report, now in preparation, will contain the complete
results for a large number of miscellaneous airfoils
investigated since 1930 and will also include a table
giving the improved section characteristics for the air¬
foils on which data are presented in Technical Report
No. 460. These results are reasonably complete at one
value of the Reynolds Number. Since airfoil data
must be employed in practice at widely different values
of the Reynolds Number, scale effect must also be taken
into account.
The results of an investigation of airfoil scale effect
which have been available only in condensed form as a
confidential report have been published in full in Tech¬
nical Report No. 586. These data give the most reliable
basis available for the prediction of airfoil-section data
at values of the Reynolds Number other than that at
which the section data published in the reports men¬
tioned in the preceding paragraph were obtained.
However, uncertainties in the present knowledge must
be admitted, and it appears that entirely satisfactory re¬
sults must await future research at full scale in a non-
turbulent air stream. The difficulty is the lack of
knowledge about the transition from laminar to turbu¬
lent flow in the boundary layer of the airfoil.
Many of the effects of scale, turbulence, and surface
condition are intimately connected with the transition
from laminar to turbulent flow in the boundary layer.
The importance of these effects may be realized from
an analysis of the effects of transition on the drag of
airfoil sections. If it is assumed that the boundary
layer over the surface of an airfoil is entirely laminar,
remarkably low drag coefficients are found for the
higher values of Reynolds Number. The drag coeffi¬
cient for a flat plate with laminar boundary layer is
O. 0008 at a Reynolds Number of 10,000,000. If the
boundary layer is assumed to be turbulent from the
leading edge onward, the drag coefficient is more than
seven times as large as the laminar value at the same
value of Reynolds Number, actually amounting to
0.0057.
It is known, however, that it is not possible to have a
laminar boundary layer over the entire airfoil sur¬
face. Calculations made by the method given in Tech¬
nical Report No. 504 show that at zero lift on the
N. A. C. A. 0012 airfoil section separation would be
expected if the boundary layer were laminar at about
55 percent of the chord back of the leading edge, be¬
cause of the adverse pressure gradient existing over the
rearward portion of the airfoil. If transition occurs at
this point, the drag will be intermediate between the
values given for the completely laminar and the com¬
pletely turbulent flows, but will still be markedly less
than that for the completely turbulent layer.
Some experimental results, including data from re¬
cent tests in the 8-foot high-speed wind tunnel and
some theoretical considerations as well, indicate that
with very smooth wings in an air stream having zero
turbulence the transition may tend to remain near the
laminar separation point. If such is the case, savings
of approximately 40 percent of the wing profile drag
at a Reynolds Number of 10,000,000 are indicated, as
compared with that predicted from a normal extrapola¬
tion of data from the variable-density wind tunnel.
In this connection some direct evidence on the nature
of transition has been obtained from an investigation
carried out in the nonturbulent N. A. C. A. smoke tun¬
nel. Boundary-layer surveys were made throughout the
transition region on a smooth flat plate having an ad¬
verse pressure gradient . The investigation showed that
while the extent of the transition region decreased con¬
siderably with an increase in Reynolds Number, the
point at which marked changes in the laminar bound¬
ary-layer flow first occurred was independent of the
Reynolds Number throughout the range included in
the investigation. The transition region was close to
the position at which separation of the laminar bound¬
ary layer was to be expected unless premature transi¬
tion was brought about by slight roughness near the
leading edge of the plate. The tests were carried to a
Reynolds Number of 150.000 based on the distance
from the leading edge to the calculated point of separa¬
tion. Visual observation of the flow over the plate in¬
dicates that similar conditions may exist over the range
of Reynolds Number up to 500,000. A technical note
is being prepared presenting the results of this investi¬
gation.
Wing characteristics. — The calculation of the char¬
acteristics of tapered wings from airfoil section data
has been continued with several wings of varying as¬
pect ratio and taper ratio. The basic section data and
the data on scale effect, if applied by the method de¬
scribed in Technical Report No. 572, will enable the,
user to reduce the wind-tunnel data and to estimate
the best wing for a given airplane. The calculated
characteristics of 20 tapered wings will be compared
with the experimental results for the same wings.
Measurement of profile drag in flight. — It has been
feasible to investigate the profile drag of an airfoil sec¬
tion in flight by means of the pitot traverse method.
This method has been used in an investigation of the
comparison of air-flow conditions in flight and in the
full-scale wind tunnel, the data obtained being evaluat¬
ed to determine the profile drag from the momentum
loss in the wake of an airfoil. The airfoil was an N-22
14
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
section and was first investigated with a smooth sur¬
face that was later modified by the addition of a thread
having a diameter of 0.01 inch and located on the upper
surface about 5 percent of the chord back of the lead¬
ing edge. The results indicated that the addition of
the small thread increased the profile drag of the
smooth airfoil by about 18 percent. The addition of
another small thread to the under surface of the air¬
foil at the same chordwise location further increased
the profile drag, the total increase due to the two
threads being about 32 percent.
EFFECT OF RIVETS AND OTHER SURFACE IRREGULARITIES ON
WING DRAG
Past investigations in the full-scale and variable-
density wind tunnels have shown that rivet heads and
other surface irregularities increase the drag of wings
appreciably. As aircraft have been made otherwise
more efficient, the importance of the increases in drag
due to small surface irregularities has become more
apparent and a need has arisen for more complete
information on the magnitude of such drag increases.
An investigation has been made in the 8-foot high¬
speed wind tunnel to provide data on the effect on wing-
drag, over a comprehensive range, of rivet size, type,
and arrangement, lap type and arrangement, and sur¬
face roughness. This investigation was made with a
model of an N. A. C. A. 23012 airfoil of 5-foot chord
at air speeds from 80 to 500 miles per hour at values of
the Reynolds Number up to 18,500,000.
Rivets. — During the investigation tests were made of
3V and W'incli brazier-head rivets, 3\-incli thin
brazier-head rivets, and 5\-inch countersunk rivets in
various chordwise and spanwise arrangements. The
jjVinch brazier-head rivets in a typical arrangement
increased the drag of the smooth airfoil 27 percent at
225 miles per hour. The drag increases due to the other
protruding rivet heads were approximately propor¬
tional to the height of the heads, indicating that rivets
with the thinnest practical heads should be used. The
countersunk rivets increased the drag C percent under
the same conditions. Increasing the spanwise pitch of
the rivets had little effect unless it was made more than
2.5 percent of the wing chord. The investigation
showed that more than 70 percent of the rivet drag
was due to the rivets on the forward 30 percent of the
wing. About GG percent of the rivet drag was due to
the rivets on the upper surface of the airfoil.
Lapped joints. — A typical arrangement of conven¬
tional plain laps facing aft increased the drag over that
for the smooth airfoil by 8 percent. Joggled laps in¬
creased the drag only half as much. Plain laps facing-
forward were found to be slightly inferior to plain laps
facing aft, but if they were faired by rounding the edges
of the sheets, the increase in drag was less than that
with conventional laps facing aft. Rivets and laps
employed together increased the drag only slightly more
than rivets alone.
Surface roughness. — The effect of five different de¬
grees of surface roughness on airfoil drag was investi¬
gated. At 225 miles per hour the drag of the smooth
airfoil was increased 44 percent by covering the surface
with 0.0013-inch carborundum grains. Even the rough¬
ness due to spray painting increased the drag 14 percent
at this speed. Sandpapering the painted surface with
No. 400 sandpaper made the drag as low as that of the
highly polished airfoil. The investigation showed that
there is considerable scale effect on the drag due to
roughness.
Effect on drag of wing due to manufacturing discrep¬
ancies. — In order to determine the effect on the drag of
a wing due to manufacturing discrepancies, such as
waves in the metal covering sheets and inaccuracies in
the profile, tests were made on a model wing constructed
to represent average present-day tolerances and work¬
manship. The drag of this “service wing” was 11 per¬
cent greater than that of the truer wind-tunnel model
when both had the same arrangement of rivets and laps,
and was 42 percent greater than the drag of the smooth-
surface wind-tunnel model without rivets or laps. This
excess in drag of 42 percent is equivalent to 273 extra
horsepower on airplanes of the size and speed of those
used on present air lines.
AERODYNAMIC INTERFERENCE
Wing-fuselage interference. — A report is now being
prepared on the interference investigation recently com¬
pleted in the full-scale wind tunnel with an Air Corps
YO-31A observation monoplane. The airplane was
first tested with the original gull wing and then with
parasol wing arrangements in which the wing was
placed at various heights above the fuselage. When
the parasol tests were made the gull-wing roots were
replaced by a straight center section. For the purpose
of determining the interference effects the principal
component parts of the airplane were tested separately
in addition to the tests of the complete machine for each
wing arrangement.
An investigation of the effects of triangular and ellip¬
tical cross-sectional fuselage shapes on the aerodynamic
interference between wing and fuselage has been com¬
pleted in the variable-density wind tunnel, together
with tests of a special shape of juncture. During the
course of the tests it was shown that ordinary critical
combinations could be sometimes benefited, as regards
the occurrence of the interference burble, by very
smoothly finished surfaces at the wing junctures. In
this respect one special shape of juncture showed a very
powerful effect, its use resulting in the suppression of
the premature interference burble entirely, with no
increase in the minimum drag.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
15
An investigation has also been made to obtain a com¬
parison between a combination including the airfoil-
type fuselage, and an efficient conventional wing-fuse¬
lage combination. Tail surfaces have been added to
typical combinations in an investigation comprising an
extension of the program of wing-fuselage interference.
An interesting development of this phase thus far is the
surprisingly low drag found possible for such a
complete model combination.
FORCED VIBRATIONS AND AIR DAMPING OF A WING SYSTEM
A theoretical study has been made of the vibration
response and air damping of a wing-aileron system in a
uniform air stream to impressed alternating forces and
moments. The mathematical treatment is a direct con¬
tinuation of that presented in Technical Report No. 496
to analyze the flutter problem. The response character¬
istics of the vibrating wing-aileron system in a complete
range of velocities and frequencies up to the critical
flutter conditions can be determined in any specific case
without extensive calculations. Thus not only are the
critical flutter velocity and frequency readily deter¬
mined. but also the vibration response and the air damp¬
ing at intermediate conditions. The study thus presents
a more complete picture of the phenomenon of flutter
than has previously been available in aerodynamic lit¬
erature. In particular, it is shown that in the case of
forced vibrations large responses may often be expected
when flutter conditions are approached, even when
actual flutter cannot occur. The results of this work are
being prepared for publication.
PROPELLERS
Investigation of full-scale propellers. — The results of
the investigation of six full-scale propellers in conjunc¬
tion with a standard nacelle unit equipped with six
different N. A. C. A. cowlings have been published in
Technical Report No. 594. The investigation covered
the complete range of flight conditions, including
ground operation, take-off, climbing, and high-speed
flight. The range of the advance-diameter ratio was
extended far beyond that of earlier full-scale experi¬
ments, blade angles of 45° at 75 percent radius being
included, which are equivalent to air speeds of more
than 300 miles per hour for propellers of normal size
and diameter.
An extensive investigation of full-scale propellers,
which was planned last year and which will provide
considerable data in addition to those just mentioned,
has been proceeding for several months in the 20-foot
propeller-research tunnel. A large number of tests of
propellers of 10-foot diameter driven by a 600-horse¬
power engine have been made in conjunction with a
cowled nacelle such as would house a radial air-cooled
engine. A number of tests have been made also in
conjunction with a nacelle for liquid-cooled engines.
The propellers on which this investigation is being-
made are of modern type, with the blade gradually
fairing into the hub section, in contrast to the older
type with airfoil sections carried in very close to the
hub. Comparative tests indicate a small aerodynamic
advantage for the latter type, but their use is precluded
by the characteristics of existing engines.
In this investigation blade-angle settings up to 45°
at 75-percent radius were also used and in several cases
blade-angle settings up to 60°. A maximum efficiency
was obtained under the conditions of this investigation
at a setting of about 30° and there was little falling off
even at 60°. This investigation gives further evidence
that the old practice of designing propellers with a low
basic pitch and then setting the blades at much higher
angles should be modified for high-pitch propellers. It
appears that high-pitch propellers should be designed
to have a constant pitch when the blades are set at 20°
to 30° at the 75-percent radius. This method will re¬
sult in a smaller washout of pitch toward the hub at the
higher blade-angle settings, which is of some advan¬
tage in obtaining the best thrust distribution for
minimum energy loss.
During this investigation particular attention has
been paid to the effect of tip speed on the efficiency in
the take-off and climbing range of propeller operation.
A small progressive loss in efficiency begins to appear
when the tip speed reaches approximately 700 feet per
second. There seems to be some variation with the air¬
foil section of the propeller, the Clark Y section hold¬
ing its efficiency under these conditions to higher tip
speeds than does the R. A. F. 6 section. Calculations
from the data obtained show, however, that when ap¬
plied to the controllable propeller the change in power
coefficient is such that the propeller must be set at a
lower blade angle than would be required if no tip-
speed effect were present, with the result that the tip-
speed effect is practically eliminated.
Analysis of the data obtained with propellers differ¬
ing in airfoil sections, but otherwise similar, shows that
the dilferences in characteristics are very small, as was
expected. The analysis is not yet complete and other
deductions may be possible after further examination.
A definite improvement is noted with a spinner on
the propeller of a liquid-cooled engine, in contrast to
radial-engine installations, where it was found that the
use of a spinner over the hub had a negligible effect.
An improvement of about 4 percent in the net efficiency
of the liquid-cooled installation was caused by the spin¬
ner. In this connection a spinner just covering the
hub and having the nacelle lines faired into it was
found to be as good as a larger spinner.
A number of tests have been made in the negative
torque (windmilling) region covering the conditions
from zero thrust to propeller locked at blade-angle
settings from 0° to 90°. The data from these tests will
16
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
provide information on the drag of idling and stopped
propellers and on the braking effect of the propeller
in the diving of military types of aircraft. It appears
that the stopped propeller feathered to a blade-angle
setting of 90° causes the least drag, but an idling pro¬
peller set at 50° and operating against normal engine
friction has nearly as low a drag.
A series of five reports, each covering a section of
this propeller investigation, is now being prepared.
The many factors involved in a study of this scope re¬
quire a division of the subject for the sake of clarity
of presentation, as well as facility in use. Other re¬
ports may be required to present analyses of minor
phases and data yet to be obtained.
Investigation of oppositely rotating tandem propellers. —
The continual increase in the power ratings of air¬
plane engines and the large propellers required, as well
as the effect of torque reaction when large geared
engines are used in small high-performance airplanes,
have turned attention to the possibilities of oppositely
rotating tandem propellers. The Army Air Corps re¬
quested an investigation of the problem, and Stanford
University, which is a pioneer in propeller testing in
the United States, agreed to make the investigation
under contract with the Committee as a part of the
Committee’s program of cooperation with universities.
The investigation was made with model propellers
of 3-foot diameter, and the results indicate that a
4-blade propeller is slightly inferior in performance to
two 2-blade propellers of the same diameter and blade
dimensions rotating in opposite directions. Both are,
of course, inferior to normal 2-blade propellers. The
spacing of the tandem propellers was varied from 8
to 30 percent of the propeller diameter, and practically
no effect of spacing was noted except that the closer
spacings produced more noise. At the lower blade-
angle settings the rear propeller had to be set at a
smaller angle than the front one in order to absorb the
same power, but, as the blade-angle settings of the
propeller were increased to give higher pitches, the
rear propeller gradually required a setting higher than
the front propeller. Increasing the propeller spacing
of the tandem propellers when the blade-angle settings
were in the low range also required an increase in the
setting of the rear propeller. It is proposed to extend
this investigation to compare a 6-blade propeller with
two oppositely rotating 3-blade propellers.
Investigation of model propellers in yaw. — The charac¬
teristics of propellers whose axes are at an angle to
the air stream are of considerable importance in the
study of airplane stability with power on, and to some
extent in the calculation of airplane performance. A
series of tests of model propellers of 3-foot diameter
in yaw has been made at Stanford University under
contract with the Committee to provide data of this
nature, and the results have been published in Techni¬
cal lieport No. 597.
Prediction of propeller performance from airfoil section
data. — The analysis of airfoil section data as applied to
the selection of sections for propeller blades has been
continued during the past year. In addition methods
for predicting the performance of propellers from
the section data are being devised and further analysis
made of the distribution of energy losses for conven¬
tional propellers. The characteristics of three pro¬
pellers having different blade sections have been ana¬
lytically determined from the section data obtained
in the variable-density wind tunnel and the smaller
high-speed wind tunnels, and three full-scale propellers
of the same design will be tested in the 20-foot wind
tunnel. The experimental data obtained should pro¬
vide an excellent check on the method of predicting
the performance analytically.
Propeller vibration. — The model method of determina¬
tion of the dangerous vibration frequencies of pro¬
pellers mentioned in the twenty-first anual report of
the Committee has been verified and superseded by a
method applicable directly to any propeller in ques¬
tion. The method consists in the use of a carbon-
resistance strain gage attached to the propeller and a
means for producing artificially forced vibrations of
any mode, the propeller being electrically driven at
full speed in a partial vacuum.
Propeller noise. — Experimental work on the sound
emission from propellers has been continued, particu¬
larly with a view to obtaining greater absolute ac¬
curacy in the measurements. The intensity of the
sound emitted from the propeller in various directions
has been measured for the five lowest harmonics for
the purpose of obtaining data for use as a basis for
theoretical work. The measurements have been com¬
pleted for the range of propeller tip speeds below the
speed of sound in air and will be continued into the
supersonic speed range.
A paper has been published (Technical Note No.
605) indicating the effect of blade thickness on pro¬
peller noise. The theoretical relations given in the
paper permit calculation of sound intensity of long
wave lengths from a propeller with symmetrical sec¬
tions at zero blade angle. With the aid of experimental
data, an empirical factor was introduced into the
theoretical relations to make possible the calculations
of higher harmonics of the rotation noise.
THEORETICAL AERODYNAMICS
Compressible flow. — The study of compressible flow
about symmetrical Joukowsky profiles has been con¬
tinued, and expressions have been developed for deter¬
mination of the velocity and therefore the pressure dis¬
tribution over the airfoils. In particular, lift and
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
17
pitching-moment formulas have been obtained for thin
profiles at large angles of attack. It has been found
that the expression for lift is analogous to that for in¬
compressible flow, but that the expression for pitching
moment, in addition to being analogous to that for in¬
compressible flow, contains a term which amounts to a
shift in the center of pressure toward the leading edge.
In addition to developing the expressions for lift and
pitching moment, the limiting value of the ratio of the
air-stream velocity to the velocity of sound in an undis¬
turbed stream has been calculated for several Joukow-
sky profiles, and the effect of angle of attack and thick¬
ness upon this ratio has been determined.
Pressure distribution on flapped airfoils. — A method has
been devised for calculating the chordwise pressure dis¬
tribution over airfoils with ordinary flaps. The distri¬
bution has been determined by altering the theoretical
distribution and may be applied to airfoil sections hav¬
ing more than one flap. Technical Reports Nos. 360
and 563 show a disagreement between experimental and
theoretical forces and pressure distribution. In the
more recent analysis the empirical correction to the
theory was determined through knowledge of the lift,
pitching moment, and flap deflection. Work is con¬
tinuing on this method of analysis to develop an expres¬
sion for airfoils with split flaps.
WIND-TUNNEL CORRECTIONS
The interference of the wind-tunnel boundaries on
the downwash behind an airfoil has been experimen¬
tally investigated, and the results have been compared
with the available theoretical results for open-throat
wind tunnels. This investigation has yielded results
that are particularly valuable in correcting the down-
wash angle in the region of the tail plane. The experi¬
mental results show that the theoretical assumption of
an infinite free jet at the test section of the wind tunnel
may lead to erroneous conclusions if applied to the
downwash in the region behind an airfoil where the tail
surfaces would normally be located. The results of a
theory based on the more accurate concept of an open-
jet wind tunnel as a finite length of free jet provided
with a closed exit passage gave good qualitative agree¬
ment with the experimental results. The results of this
investigation have been presented in Technical Report
No. 609.
The investigation to determine the scale effect on the
maximum lift of an airfoil has been extended by addi¬
tional tests in flight and in the full-scale wind tunnel.
The investigation was made with a 2R,12 airfoil
mounted on a Fairchild 22 airplane, and the variations
of Reynolds Number in flight were obtained chiefly by
varying the wing loading of the airplane and by vary¬
ing the altitude at which the tests were made. The
maximum lift as obtained in flight and in the full-scale
wind tunnel agreed within 2 percent, the results thus
further substantiating the agreement obtained with
sphere tests, which indicated a low percentage of tur¬
bulence in the full-scale wind tunnel.
The investigation of the factors leading to discrepan¬
cies between the power-on performance of an airplane
as predicted from wind-tunnel data and as measured in
flight is being continued. In order to avoid the diffi¬
culties usually experienced in obtaining precise meas¬
urements of climbing performance, the excess horse¬
power available for climb is being determined in level
flight.
This determination is accomplished by the towing of
parachutes of various sizes to absorb the excess horse¬
power at various speeds. The horsepower is computed
from the tension in the towing line and the velocitv of
the airplane. This method avoids, in particular, the
errors usually experienced in climb owing to variations
in the wind velocity with altitude. A second airplane
is being equipped to study quantitatively the effect on
climbing performance of variations in the wind velocity
with height by correlating the excess horsepower meas¬
ured in level flight with the rates of climb actually
experienced in several climb tests. The results will be
checked by tests of the same airplanes in the full-scale
wind tunnel under power-on conditions.
COMPRESSIBILITY EFFECTS DUE TO HIGH SPEED
Aerodynamic phenomena encountered at high speeds
have heretofore been considered of importance mainly
in relation to the adverse effects on propellers operat¬
ing at high tip speeds. It has now been established
that marked adverse effects due to compressibility may
occur on other parts of airplanes when the forward
speed of the airplane is approximately one-half the
speed of sound. Investigations conducted in both the
24-inch and the 8-foot high-speed tunnels have shown
that the compressibility burble results in a large energy
loss. A large increase in drag may therefore occur
when the flow about any part of the airplane produces
a local velocity equal to the speed of sound. A bluff
body and one having a high curvature produce high
induced velocities, and therefore the critical speed of
such bodies is low.
The results from an investigation in the 11-inch high¬
speed tunnel on the drag of circular and elliptical cyl¬
inders and prisms of triangular and square cross sec¬
tions show that the critical velocities or, in other words,
the forward speed at which compressibility effects be¬
come noticeable, may be as low as 0.4 the velocitv of
sound.
Similar results have been obtained in the 8-foot high¬
speed tunnel on a wing-nacelle combination. One-
fifth-scale models of a family of radial-engine cowlings
were tested on a nacelle with a wing of 2-foot chord.
18
REPORT NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
Five of the cowling shapes had previously been tested
in the propeller-research tunnel, and at the lower speed
possible in the propeller-research tunnel these cowlings
were considered satisfactory. One cowling shape was
found to have a critical speed between 280 and 350 miles
per hour, depending upon the attitude of the cowling
and nacelle. When the compressibility burble, or shock
wave, occurred at the critical speed the drag of the
combination was increased from 50 to 200 percent, with
only a slight increase in the tunnel speed.
During the investigation it had been found that if the
pressure distribution over the cowling was known, the
critical speed could be accurately predicted. Therefore,
two cowlings were designed with the nose curvatures
proportioned to reduce the peak negative pressure and
obtain a uniform negative pressure distribution
over the nose. By so changing the nose shape the
critical speed of the cowling was increased to more than
500 miles per hour and approached the critical speed
of the N. A. C. A. 23012 wing, which was used for the
investigation. It was found that when the critical speed
of the cowlings was increased other advantages were
obtained. The cowling with the highest critical speed
also had the lowest drag throughout the entire speed
range, and the drag remained substantially constant
over a larger range of angle of attack.
In order to determine at a large scale the possible
variation in pitching moment with speed, four wings
of 2-foot chord were tested in the 8-foot high-speed
wind tunnel through a range of speeds up to that at
which the compressibility burble was experienced. The
four wings tested had the following N. A. C. A. sec¬
tions : 0012, 23012, 23012-64, and 4412. The N. A. C. A.
23012 and 23012-64 airfoils were chosen as sections of
low pitching moment and the N. A. C. A. 4412 as a
section of high pitching moment. All the sections tested
showed an increase in pitching-moment coefficient with
increased speed, the increase amounting to as much as
45 percent at 500 miles per hour. This change in
pitching moment has little practical significance in the
case of an airplane on which a wing section having low
pitching moments is used, because the resulting abso¬
lute change in pitching moment at high speeds would
be of little importance in the design of the wing or tail
surfaces. In the case of an airplane with a wing sec¬
tion of high pitching moment the change may be very
important in high-speed dives.
BOUNDARY-LAYER CONTROL
The investigation of boundary-layer control has been
continued in the propeller-research tunnel, and tests
have been completed on a tapered wing of N. A. C. A.
8318 section with upper-surface suction slots to control
the boundary layer. Tapering the slot was found to be
very effective in producing an even distribution of con¬
trol over the span, and the suction power required was
intermediate between the low power required for a thick
wing and the high power required for a thin wing.
Measurements of boundary-layer thickness were made
both with and without the control in operation.
ICE PREVENTION
In view of the fact that several accidents during
the last year may be directly attributed to ice forma¬
tion on the airplanes, a survey has been made of the ice-
prevention investigations that have been conducted by
the various Government and commercial organizations.
A compilation of these data is being made so as to make
available to all concerned information that may be valu¬
able in preventing accidents due to ice formation.
In order to determine the effect of rubber de-icers on
the aerodynamic characteristics of a wing, a model of a
5-tube de-icer was tested on an N. A. C. A. 23012 wing
of 5-foot chord in the 8-foot high-speed tunnel. The
results show that for both the inflated and deflated con¬
ditions the de-icers did not appreciably affect the lift or
pitching moment for high-speed or cruising conditions,
but with either two or three tubes of the de-icer inflated
the drag of the wing was increased in the order of 80
percent. The conventional de-icer equipment deflated
increased the drag of the wing 16 percent at 200 miles
per hour. At air speeds greater than 200 miles per hour
the de-icer lifted from the wing and in some cases breaks
in the rubber were produced. In order to reduce the
drag of the de-icer in the deflated condition a flush
installation was made by the use of a metal attachment
strip, which on the full-scale airplane would be 1/32-
inch thick. With this installation the drag increment
was reduced from 16 to 9 percent, but the same difficulty
was experienced in the lifting of the de-icer from the
wing at speeds greater than 200 miles per hour.
ROTA riNG-WING AIRCRAFT
The development of the direct-control type of auto¬
giro has been delayed to some extent by the introduction
of certain secondary difficulties connected with the pro¬
vision of a satisfactory variation of control forces with
air speed and with the elimination of vibration. A
study of the effect on certain rotor characteristics of a
periodic variation in blade-pitch angle has been made,
and the results have been published in Technical Report
No. 591. The predicted value of the flapping motion of
the rotor blade was radically altered when the periodic
pitch variation was inserted in the rotor analysis, and
an appreciable influence of the periodic pitch on the
rotor thrust coefficient was indicated. An analysis has
been made of the factors involved and a method devel¬
oped of predicting the periodic variation of the pitch
angle. The results have been published in Technical
Report No. 600.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
19
An investigation lias recently been conducted both in
flight and in the full-scale wind tunnel on a direct-
control autogiro to determine the lift, drag, control
forces, flapping motion of the rotor blade, and periodic
variation in pitch angle. The tests in the full-scale wind
tunnel were made on the complete autogiro, on the rotor
alone, and on the machine without the rotor to deter¬
mine the interference effects bet ween various parts. The
data obtained from these tests are being analyzed for
use in the study of any desired variation of the location
of the center of pressure on the rotor.
An investigation has been started in the propeller-
research tunnel on a series of model autogiro rotors
having airfoil sections of different thickness and differ¬
ent mean camber lines, and will include two rotors that
differ only in plan form of the rotor blades. This work
is an extension of an investigation previously made in
which the effect of airfoil section and plan form on the
lift -drag ratio of an autogiro rotor was studied.
The analysis of the results obtained during the auto¬
giro jump take-off tests has been completed and pub¬
lished in Technical Note No. 582. The report covers a
theoretical study of the jump take-off without forward
speed and includes an experimental verification.
An analytical study of the rotor-blade oscillations in
the plane of the rotor disk has been made, and the results
have been published in Technical Note No. 581.
A study of the autogiro rotor-torque equation has
been made, and a report is in preparation which will
include a solution of the problem in chart form.
MISCELLANEOUS TESTS OF COMPLETE MODELS OF AIRPLANES
The improved aerodynamic efficiency of the modern
airplane has made it increasingly important to make
tests on a complete model of a projected airplane before
it is constructed. Consequently a large number of com¬
plete models have been tested in the 7- by 10-foot, the
20-foot, and the full-scale wind tunnels. Most of these
tests have been conducted at the request of the Army
and Navy, but several models have been tested for
manufacturers at their expense.
The models tested in the full-scale tunnel have been
y2 and 14 scale, and the tests have included considerable
development work that could be conveniently carried
out on these large-scale models at considerably less cost
than would be involved in doing the same work on the
actual airplane after it has been constructed. Although
this development work has restricted to some extent the
research programs in the tunnels, it is felt that the tests
have resulted in a large saving of money to the Govern¬
ment. It might also be pointed out that the develop¬
ment work in the wind tunnel will save much of the
time required to take an airplane through the experi¬
mental stages and place it in production.
NATIONAL BUREAU OF STANDARDS
WIND-TUNNEL INVESTIGATIONS
The aerodynamic activities of the National Bureau of
Standards have been conducted in cooperation with the
National Advisory Committee for Aeronautics.
Wind-tunnel turbulence. — Within the last few years
the equipment used in the study of wind-tunnel tur¬
bulence has been redesigned for use with an alternating-
current power supply instead of storage batteries. A
description of the new equipment and of its perform¬
ance has been published in Technical Report No. 598.
As mentioned in last year’s report, the investigation
of turbulence has been extended to include the measure¬
ment of the scale or eddy size of the turbulence as well
as the intensity. The most satisfactory method of in¬
troducing turbulence into the wind-tunnel stream was
found to be by means of screens placed across the
stream, the scale being controlled by the size of the
screen and the intensity by the distance downstream
from the screen. The measurements of scale and in¬
tensity have been made and the aerodynamic effect of
these two factors has been determined. The results of
this work have been published as Technical Report No.
581. The screens described in this report are now re¬
garded as standard equipment in the Bureau’s 414-foot
wind tunnel and are used to introduce turbulence of the
desired scale and intensity within the limits obtainable.
Preparations are being made to continue the study
of turbulence by measuring the distribution of energy
in turbulent motion with the wave length of (he turbu¬
lence. According to recent theories the spectral distri¬
bution of energy is a characteristic property of tur¬
bulence related to the intensity and scale.
Boundary layer near an elliptic cylinder. — During the
past year boundary-layer investigations have been in
progress with an elliptic cylinder of 12-inch major axis
and 4-inch minor axis, placed with the major axis
parallel to the wind. The laminar boundary layer
formed about the cylinder was previously studied and
the results were published as Technical Report No. 527.
The recent work has consisted of the measurement of
velocity distributions in the boundary layer with the
air speed in the tunnel high enough to produce transi¬
tion from laminar to turbulent flow in the layer before
separation occurred. Two cases were investigated: the
first with the low turbulence normally prevailing in the
wind tunnel and the second with the stream turbulence
raised to about 4 percent by means of the 1-inch screen
placed 18 inches ahead of the cylinder.
Marked differences were found between the types of
transition occurring in the two cases. Transition with
the low stream turbulence was the result of a laminar
separation, and occurred within a very short length of
the surface, about an inch ahead of the point of separa-
20
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
tion of the turbulent layer. Work with the higher
stream turbulence gave no evidence of a laminar sepa¬
ration, but showed a gradual transition extending over
about a third of the distance from the leading to the
trailing edge of the cylinder (i. e., over about 4 inches).
This latter type of transition was very difficult to detect
by any single means and was found only by careful
study of the velocity distributions in the layer. In
order to throw more light on the transition phenomena
at the higher stream turbulence measurements were
made of the fluctuations in velocity throughout the
layer at various points about the surface. These meas¬
urements also showed the gradual nature of the
transition.
Studies of transition. — The two different types of
transition found on the elliptic cylinder suggested an
extension of the work to cover the general effects of
turbulence and Reynolds Number on transition, the
purpose of the extension being to learn under what
conditions each type of transition exists and how the
region of transition shifts with changes in Reynolds
Number and changes in scale and intensity of the
stream turbulence.
As was pointed out previously, the location of the
transition region could be determined with the avail¬
able equipment only by extensive measurements of
the distribution of mean velocity or fluctuation of
velocity across the boundary layer. In order to facili¬
tate the investigation, a new device for quickly and
easily detecting transition was sought. Previous work
has shown that transition occurs in the neighborhood
of the point where the intensity of skin friction is a
minimum. This immediately suggested the use of some
device, such as the Stanton surface tube developed in
England, by which the surface friction may be meas¬
ured. However, the adaptation of the surface tube
was not considered feasible on the elliptic cylinder.
Instead a sliding steel band 6 inches wide and 0.002
inch in thickness was fitted about the cylinder so that
the heated element of a hot-wire anemometer, fixed at
the center of the band, could be moved around the con¬
tour of the ellipse at a small fixed distance from the
surface.
While an actual measurement of the velocity by this
means is not readily possible, the wire can be used to
detect where the speed is a minimum as the band is
slipped around the surface. In the tests already made
a platinum wire 0.016 millimeter in diameter and 13
millimeters long was mounted 0.21 millimeter from the
surface of the band. The device has proved quite sat¬
isfactory and shows sufficient promise to justify further
development. It may be possible to use a device of this
sort for locating transition on an airplane wing in
flight.
Investigation of boundary layer by diffusion of heat.—
The method of thermal diffusion described in Technical
Report No. 524 has been applied to the study of ve¬
locity fluctuations in a thick turbulent boundary layer
formed on the surface of a flat plate 10 feet wide and
24 feet long. The procedure consists of measuring
with a thermocouple the spread of the heated wake
downstream from a fine but long heated wire placed
transverse to the flow in the boundary layer. The
spread of the wake is caused by the components of
turbulent motion normal to the mean direction of flow,
and the purpose of the work is to compute the magni¬
tude of the components from the measured spread.
By this means the magnitude of the velocity fluctua¬
tions normal to the surface has been determined. In
a similar manner it is planned to determine the magni¬
tude of the component parallel to the surface. By the
usual hot-wire equipment the component in the direc¬
tion of the mean flow will be measured so that finally
a comparison between all three components of the
fluctuations will be possible.
AERONAUTIC-INSTRUMENT INVESTIGATIONS
The work on aeronautic instruments has been con¬
ducted in cooperation with the National Advisory
Committee for Aeronautics and the Bureau of Aero¬
nautics of the Navy Department.
Reports on aircraft instruments. — A report on the
pressure drop in tubing used to connect aircraft in¬
struments to vacuum pumps and pitot-static tubes has
been published as Technical Note No. 593, and a re¬
port on electrical thermometers is being published as
Technical Report No. 606.
An experimental investigation of the performance
characteristics of venturi tubes used in aircraft for
operating air-driven gyroscopic instruments has been
completed and a report prepared.
Progress has been made on reports on the effect of
vibration on service aircraft instruments and on gyro¬
scopic instruments for aircraft.
Tests and test methods. — It was originally planned to
measure humidity in the aerograph test apparatus by
the dew-point method. A simpler method has been
developed in which advantage is taken of the fact that
completely saturated salt solutions have a characteristic
vapor pressure so that a particular salt solution pro¬
duces a practically constant relative humidity when
placed in a closed chamber. Corrections can be ap¬
plied for the relatively small variation of the relative
humidity with temperature.
Altitude mercurial barometers for field use should
withstand shipment without breakage and should be
designed so that the accumulation of gas above the mer¬
cury column is easily removable. Principally for these
reasons it is advisable to fill the barometer tube in the
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
21
field. Experiments with the Barnes type, which meets
these requirements, indicate that the procedure to be
followed is too complicated. In cooperation with an
instrument manufacturer, the common-type altitude
barometer has been modified to make it possible for the
tube to be filled in the field by following a relatively
simple procedure. The barometer must be designed so
that the end of the tube is always well covered with
mercury while the barometer is tipped from the normal
to the upside-down position. The usual capillary re¬
striction in the end of the tube must be of such size that
the passage of gas is not impeded by mercury sticking
in the capillary.
Laboratory test methods have been developed, and
data on the performance obtained, on fuel-air-ratio in¬
dicators of the thermal conductivity type. In these
tests known mixtures of nitrogen and hydrogen and of
nitrogen and carbon dioxide were passed through the
instrument subject to various conditions, such as tem¬
perature, pressure, and voltage.
New instruments. — Instruments designed and con¬
structed for the Bureau of Aeronautics include : a
helium purity meter utilizing a porous plug of a type
recently developed commercially; a superheat meter of
the electrical-resistance type for a K airship; an ex¬
perimental pitot-static tube for installation on the wing
tip of monoplanes. Development of a fuel flowmeter of
the orifice type is in progress.
SUBCOMMITTEE ON AIRSHIPS
The Subcommittee on Airships formulates and rec¬
ommends programs of airship investigations to be un¬
dertaken at the Langley Memorial Aeronautical Labora¬
tory and maintains close contact with the work in
progress.
The Committee recently published as Technical Re-
port No. 604 the results of the investigation conducted
by the laboratory at the request of the Bureau of Aero¬
nautics of the Navy to determine the pressure distribu¬
tion at large angles of pitch on fins of different span-
chord ratios on a large model of the airship Akron.
This investigation was requested by the Bureau to pro¬
vide information particularly desired by the Special
Committee on Airships of the Science Advisory Board,
of which Dr. W. F. Durand, of Stanford University,
is chairman. Mention is made here of the publication
of the technical reports of this committee, which cover
certain phases of airship technical problems.
Models and apparatus are being prepared for the
investigation in the Committee’s 20-foot wind tunnel of
boundary-layer control on airship forms. This investi¬
gation will include a form with blower in the nose, and
also a form with propeller in the rear with control of
the boundary layer by both suction and discharge jets.
At a meeting of the Subcommittee on Airships held
in January 1937, plans were discussed for the extension
of the investigation of the forces acting on an airship
during ground handling, as published in Technical Re¬
port No. 566, to include a study of the effect of wind
gradient and also of the effect of fin angle. Considera¬
tion was also given to the desirability of conducting an
investigation at the Committee’s laboratory on the loads
on the tail surfaces of an airship in flight, and also an
investigation of the forces on a large airship model with
tail surfaces of the form used on the Hinderiburg .
SUBCOMMITTEE ON METEOROLOGICAL PROBLEMS
The Subcommittee on Meteorological Problems keeps
in contact with the progress of investigations being con¬
ducted by the various agencies on problems relating
to the atmospheric conditions which are of particular
importance in connection with aircraft design and
operation.
Atmospheric disturbances in relation to airplane acceler¬
ations. — Extensive measurements of gusts have been
made by the Langley Memorial Aeronautical Labora-
tory by means of flights to altitudes of 19,000 feet with
a large military-type airplane and flights with a small
light airplane. From partial analysis of the data ob¬
tained, it appears that it may be possible to correlate
the gust strength and gradient with the energy avail¬
able for turbulence in the atmosphere. The new re¬
sults do not invalidate the conclusions previously
reached tentatively that, in stable atmospheric condi¬
tions, with large wind gradients, vertical gust veloci¬
ties of the order of 30 feet per second are reached in a
horizontal distance of about 100 feet, and that the gust
gradient increases with decreasing gust intensity.
Surveys of clouds of cumulus type indicate, in gen¬
eral, stronger downward-acting than upward-acting
gusts. On one occasion a downward gust of 53 feet
per second, which reached maximum intensity in a dis¬
tance of 53 feet, was experienced.
The development of a special acceleration-altitude
recorder for installation at various Weather Bureau
stations throughout the country is nearing completion.
When available, these instruments will be used in con¬
junction with air-speed recorders to obtain data on the
relation between gust intensity and altitude.
The accumulation and analysis of records of accelera¬
tions on transport airplanes in regular operation is be¬
ing continued with the cooperation of a number of the
air transport operators. The records obtained repre¬
sent conditions encountered in operation over practi¬
cally every part of the United States, in transpacific
operation, and in operation over the Andes Mountains
in South America. Records from flying boats in the
transpacific service indicate effective gust velocities as
great as 33 feet per second, which is substantially equal
to the maximum recorded on flying boats in service
22
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
between Florida and the West Indies and South Amer¬
ica and on land transports.
Investigation of wind gustiness. — The study of wind
gustiness, including both atmospheric turbulence under
ordinary conditions and the fluctuations of wind ve¬
locity during the passage of cold fronts, conducted by
the Daniel Guggenheim Airship Institute at Akron,
Ohio, in cooperation with the Weather Bureau and the
Bureau of Aeronautics of the Navy, has been con¬
tinued. Additional measurements are being made by
means of instruments installed on the radio tower at
Akron and on movable towers placed at various posi¬
tions in relation to the radio tower and to each other,
with supplementary records obtained by the use of
balloons and theodolites.
Ice formation. — The problem of ice formation is re¬
ceiving considerable attention at the Langley Memorial
Aeronautical Laboratory, and a report has recently been
issued to American manufacturers giving the results
of a study of the prevention of ice formation on pro¬
pellers. In this report information is given as to the
conditions under which ice forms on propellers, and an
investigation conducted by the Committee on the pro¬
peller de-icer developed under the sponsorship of the
Bureau of Air Commerce in cooperation with the B. F.
Goodrich Company and Transcontinental and Western
Air, Incorporated, is described.
The problem of ice formation on wings and ailerons
is also being studied, and a report is being prepared
presenting all the information at present available. In
addition, a program is being formulated for the study
of the effect on the aerodynamic characteristics of a
wing, of ice particles that adhere after the de-icer has
acted. Data on the shape and location of such par¬
ticles for use in the preparation of this program have
been supplied through the cooperation of the Air
Transport Association of America.
Electrical phenomena.- — The question of the possible
effect of electrical phenomena on airplanes has been
brought to the Committee’s attention and will be dis¬
cussed at a meeting of the Subcommittee on Meteoro¬
logical Problems to be held in the near future. Observa¬
tions of pilots on the subject have been obtained from
a number of sources, and the question will be thor¬
oughly studied by the subcommittee.
SUBCOMMITTEE ON SEAPLANES
W oriel-wide interest in seaplanes has grown at an
accelerated rate and almost every month has brought
word of the launching of new craft of greater size and
speed. Designers are discussing with confidence the
construction of flying boats of magnitudes that would
have been considered impracticable a few years ago and
are looking forward to the construction of even larger
and faster flying boats within a relatively short time.
With the increases in size and range have come in-
creased get-away speeds and heavier loads on the hulls.
The power required for the take-off of such large flying
boats is sometimes 100 percent greater than that ordi¬
narily used in flight, and in such cases the designer is
confronted with the necessity of choosing between the
use of larger engines involving a serious increase in
weight and the possibility of shortened engine life as
a result of running at excessive power during take-off.
Idle cost of these large flying boats makes it essential
that the form of hull selected shall be the best possible
compromise between the requirements of low drag in
flight and good performance on the water. Research
in the N. A. C. A. tank has therefore been directed
toward the improvement of the over-all performance of
flying boats and seaplanes by the reduction of the re¬
sistance on the water and the general improvement of
the form of the hull. In contrast to previous work, the
aerodynamic improvement is being given consideration
at the same time.
Improvements to N. A. C. A. tank. — In anticipation of
the demand for tests of models of larger hulls at higher
take-off speeds, the Committee is enlarging the
N. A. C. A. tank and increasing the speed of the towing
carriage. When the work now under way is completed
the tank will have 2,880 feet of water at a depth of 12
feet, which is an increase of 900 feet. The extension
has been specially constructed to permit the generation
and propagation of waves for use in testing models in
waves and the simulation of operation in rough water.
The increase in length has been matched by an in¬
crease in the speed of the towing carriage. It is
expected that when the alterations are completed the
carriage will have a maximum speed of about 80 miles
per hour. The carriage will also be able to tow much
larger models.
At lower speeds, with models of the same size, it will
be possible to increase the amount of testing per day
because the ratio of the distance that can be used in
testing and obtaining readings to the distance required
for stopping and starting the carriage will be consider¬
ably increased.
A two-story office building has been built at the
southern end of the tank and the shop spaces have been
extended 100 feet.
Effect of variation in dimensions and form of hull on
take-off. — The result of incorporating longitudinal
steps on the forebody of a V-bottom hull was deter¬
mined by an investigation of a series of models in which
the form and number of steps were systematically varied-
In general, the longitudinal steps were found to de¬
crease resistance at high speeds by reducing the area in
contact with the water, but to increase resistance at
low speeds where the bottom is wetted out to the chines.
One longitudinal step on each side of the keel was
23
REPORT NATIONAL ADVISORY
superior to two longitudinal steps, except at high speeds
and very light loads. Spray strips fitted along the
steps reduced both the resistance and spray if they were
set at the proper angle. This investigation is described
in Technical Note No. 574.
Various methods of artificial ventilation of the step
were investigated on two typical hull forms, one having
straight V sections and one having chine flare on both
forebody and afterbody. In both cases the chines aft
of the step were clear of the water at the hump speed
and above. When the chines were clear the step was
ventilated by air flowing in from the sides and the in¬
troduction of additional air through ducts or slots
produced no further change in resistance or trim. In
the case of the form with chine flare, natural ventilation
was delayed at speeds below the hump speed and arti¬
ficial ventilation through ducts aft of the step resulted
in an appreciable reduction in resistance and trim.
The results of this investigation have been published
in Technical Note No. 594.
Tests of models of representative flying-boat hulls. — The
bull of the U. S. Navy PB-1 flying boat, which was
built by the Boeing Aircraft Company in 1925, had
two transverse steps very close together and a long ex¬
tension carrying the tail surfaces. The forebody was
much like that of the NC hull, from which it was
apparently derived. Comparisons of its water per¬
formance as obtained in the N. A. C. A. tank with that
of the NC hull and the Sikorsky S-40 hull are pre¬
sented in Technical Note No. 576.
A model of the hull of the British Singapore II-C
flying boat was investigated in the N. A. C. A. tank
in response to suggestion of the Director of Research,
British Air Ministry. This investigation made it pos¬
sible to determine the hydrodynamic characteristics of
a typical British hull form over an extensive range of
loadings and speeds. It was found that the Singapore
hull had higher resistance at the hump speed and lower
resistance at higher planing speeds than the American
hull with which it was compared. The results of this
investigation, together with a comparison with similar
results obtained in the British R. A. E. tank with the
same model, are presented in Technical Note No. 580.
A large model of the hull of the British Short Cal¬
cutta flying boat was made from lines supplied by the
British manufacturers and investigated in the N. A.
C. A. tank. The form is the immediate predecessor of
the Singapore hull, and is representative of British
flying-boat design in 1928. The results of these tests,
together with calculated comparisons of its take-off per¬
formance with that of typical American forms, are
published in Technical Note No. 590.
Trim-angle indicator.— The importance of holding a
seaplane at the trim angles that would give least resist¬
ance during the process of take-off was described in
38.r>48 — 3S - 3
COMMITTEE FOR AERONAUTICS
Technical Note No. 486, issued in 1934. In that publi¬
cation there is described and illustrated a trim indicator
for showing the pilot of a seaplane the trim angle at
which the craft is traveling. Several versions of this
type of trim-angle indicator have since been constructed
and tested in service. It has been found that if a pilot
has a trim-angle indicator and the information obtained
from tank tests of the hull as to the trim angles that
give least resistance during the take-off, it is possible for
him regularly to take off in much shorter time than he
requires when no such instrument and data are avail¬
able. The pilot of a heavily loaded amphibian operat¬
ing in the tropics reported that he attributed the uni¬
formly successful operation of his craft, especially the
ease with which it took off in smooth water, to (he use
of a trim-angle indicator that had been supplied by the
Committee. In another case the use of a trim-angle
indicator by a test pilot is credited with so greatly
improving the take-off characteristics that a seaplane
which at first appeared very unsatisfactory gave very
good performance.
REPORT OF COMMITTEE ON POWER PLANTS
FOR AIRCRAFT
LANGLEY MEMORIAL AERONAUTICAL LABORATORY
ENGINE POWER
The recent demand of aircraft designers for engines
of increased power output has been fulfilled by the sup¬
plying of radial air-cooled engines developing 1,500
horsepower during take-off. This large increase in
power has been obtained by increasing the number of
engine cylinders and by designing the engines to take
the greatest possible advantage of the antidetonating
quality of the improved fuels now available for aircraft
engines. These large engines will be used in aircraft
designed to transport greater loads at increased speeds
over present airways. The several investigations of the
Committee on the cooling of air-cooled engines have
indicated that it will be possible to cool satisfactorily
engines of even greater power.
Engine performance with high octane fuels. — The
greater percentage of the recent increase in power of
aircraft engines is due to the use of fuels having in¬
creased antidetonating quality. An investigation to
determine the maximum engine performance with fuels
having a range of octane numbers from 87 to somewhat
greater than 100 has been in progress at the Committee’s
laboratory during the past year, under the cognizance
of the Subcommittee on Aircraft Fuels and Lubricants,
and will be described in the report of that subcommittee.
Valve overlap. — The power of aircraft engines may be
increased by removing the exhaust gases from the cylin¬
der clearance volume. An efficient method of removing
the exhaust gas is to operate with a large valve overlap
24
REPORT NATIONAL ADVISORY (
and low boost pressure. At the request of the Bureau
of Aeronautics of the Navy Department, the Committee
is determining on a single-cylinder test engine the per¬
formance and optimum valve overlap to give efficient
scavenging of a radial air-cooled fuel-injection engine
operating at a maximum speed of 2,200 r. p. m.
The results indicate that satisfactory scavenging can
be obtained with a valve overlap of 130°. From the
tests on the single-cylinder engine it was found that as
the boost pressure was increased the gain in power with
the two-valve cylinder was slightly less than that ob¬
tained in previous tests with a cylinder having four
valves. The results showed that an engine operating
with valve overlap would develop 25 percent more
power at the same cylinder temperature than an engine
operating with normal valve timing. The tendency to
detonate was reduced so that the engine with valve
overlap, for the one fuel tested, showed an increase in
brake mean effective pressure of 25 percent without
detonation as compared with the normal valve timing.
The 2-stroke-cycle engine. — Increased power output
can be obtained from a given engine displacement by
operation on the 2-stroke cycle instead of on the 4-stroke
cycle. The availability of improved fuels having in¬
creased antiknock values has renewed the interest in the
2-stroke-cycle spark-ignition fuel-injection engine. An
investigation has been conducted to determine the opti¬
mum location of the fuel-injection valve and the best
arrangement of fuel-valve orifices for injecting the fuel
into the engine cylinder. Favorable results have been
obtained in a limited series of tests, and the research
program is being continued to obtain information on
the operating characteristics of this type of engine as
affected by speed, scavenging pressures, and induction
and exhaust conditions. With fuel of 100 octane num¬
ber, scavenging pressure of 3 pounds per square inch,
and a speed of 1.650 r. p. m., the single-cylinder engine
developed an indicated mean effective pressure of 166
pounds per square inch, the corresponding fuel con¬
sumption being 0.37 pound per horsepower-hour. A
maximum indicated mean effective pressure of 193
pounds per square inch has been developed with a fuel
consumption of 0.44 pound per horsepower-hour. A
positive valve-operating mechanism for this engine is
being developed that will permit the maximum engine
speed to lie increased from 1,800 to 2,500 r. p. m.
Air intercoolers. — An analysis has been made of data
from laboratory tests for the purpose of selecting the
most desirable intercooler for various operating condi¬
tions — the cooling, drag, pressure drop through cooler,
and weight of core being considered. On the basis of
this analysis, a program of tests for intercoolers has
been prepared that includes both full-scale tests in a
wind tunnel and tests of promising cores in the engine
laboratory.
'< EMM ITTEE FOR AERONAUTICS
COMBUSTION RESEARCH
A study of combustion both in spark-ignition and in
compression-ignition engines has been undertaken with
the object of obtaining new knowledge concerning the
combustion phenomena. The problem of detonation in
internal-combustion engines is being attacked with the
aid of high-speed schlieren photographs to indicate the
temperature variations in the front and rear of the
combustion zone following ignition.
Ignition lag in compression-ignition engines. — The in¬
vestigation of the effect of air temperature and density
on the auto-ignition and combustion of Diesel fuel with
a constant-volume bomb has been extended. Very little
reduction in ignition lag is possible for the particular
fuel under test, by the use of temperatures and pres¬
sures in excess of those attained in compression-ignition
engines. The combustion process, however, is more sat¬
isfactory at densities corresponding to considerable
boost. A concentration of combustion products several
times greater than that corresponding to the resid¬
uals in a compression-ignition engine is capable of
definitely increasing the ignition lag. Technical Re-
port No. 580 has been published giving the results of
this investigation.
Compression-ignition engine with air flow. — The in¬
vestigation of the fuel-spray and flame formation oc¬
curring in a compression-ignition engine having air
flow that was set up by a displacer on the piston crown
has been described in Technical Report No. 588.
Detonation in engines. — With a schlieren set-up and a
high-intensity electric spark as the light source, by
means of which 10 photographs are taken at rates up
to 2,000 pictures a second with an exposure interval
for each picture of approximately one-millionth sec¬
ond, photographs have been obtained that show clearly
the depth of the combustion zone and also the burning
of the end gases in normal combustion. No evidence
has been obtained of any sonic wave preceding the
combustion front. Such waves were artificially pro¬
duced in the chamber and, although their effect on the
combustion front was visible, they did not cause the
charge to detonate. Even with very severe detonation,
the combustion reaches all, or nearly all, the way across
the combustion chamber before the detonation occurs.
The results of this investigation are being prepared
for publication.
An apparatus has been constructed and is being used
for preliminary tests of the detonation of gasoline-air
mixtures. The combustible mixture is prepared in a
reservoir heated to a temperature below the auto-
ignition point but sufficiently high to vaporize all the
fuel. A portion of this mixture is then admitted by
means of a poppet-valve mechanism to an evacuated
tubular bomb heated to a temperature such that auto-
ignition of the charge will occur after a relatively long
25
REPORT NATIONAL ADVISORY
time. If this mixture is spark-ignitecl at one end in
such a way that the normal flame can traverse the tube
within this lag period, no detonation occurs. On the
other hand, when the spark is so applied to the mix¬
ture that the flame travels only a large portion of the
tube length, then severe vibrations, presumably due to
detonation, are set up in the optical pressure indicator
attached to the tube at the end opposite the sparking
end.
Analysis of engine cycle. — The calculated ideal engine
cycle does not include consideration of the actual com¬
bustion process, so that the results depart considerably
from those obtained from engine tests. In order to ob¬
tain better correlation between theoretical and experi¬
mental results, a study of the spark-ignition engine
cycle was made and a thermodynamic cycle set up
closely approximating the actual operating cycle.
From a consideration of this cycle, equations for the
cycle characteristics, such as indicated horsepower and
fuel consumption, maximum cylinder pressure, and
point at which the maximum cylinder pressure occurs
in the cycle, were written as functions of three com¬
bustion parameters that specify the rate, the complete¬
ness, and the position in the cycle at which combustion
occurs. The variation of the combustion parameters
with engine operating conditions was obtained from
indicator cards. The cycle characteristics calculated
from the combustion parameters agree closely with
those obtained in the engine tests.
Air flow in cylinders. — An investigation has been
started to determine the effect of air flow on combus¬
tion in spark-ignition engines. The air flow is set up
by shrouds placed on the inlet valves. Preliminary
tests have shown that with an orderly swirl in the
combustion chamber the entire combustion front is ro¬
tated, but that there is little apparent effect on the
combustion velocity.
FUEL CONSUMPTION
Any reduction in the fuel consumption of engines
used in long-range or transport aircraft can be utilized
to increase the useful load or the range of the aircraft.
Large savings in fuel have resulted from the use of
mixture indicators by commercial operators. The im¬
provement in cylinder cooling has progressed to such
a point that aircraft engines are capable of operating
at mixtures leaner than are accurately indicated by
commercial mixture indicators. The use of fuels of
high octane number has also resulted in an appreciable
reduction in fuel consumption.
Mixture distribution. — The results obtained from an
investigation of the distribution of fuel to each cylin¬
der of a single-row radial air-cooled engine by chem¬
ically analyzing the exhaust gases have been published
as Technical Note No. 583.
COMMITTEE FOR AERONAFTH'S
Fuel distribution. — The use of a fuel-injection system
instead of the conventional carburetor requires that ad¬
ditional air flow be set up within the cylinder to assist
in mixing the fuel and air. A study has been started to
determine the effect of air movement on the distribution
of the fuel spray during the suction and compression
strokes. The apparatus consists of a glass cylinder
clamped between the jacket and the cylinder head of an
N. A. C. A. single-cylinder test engine. The piston side
thrust is taken on the steel liner, and a dummy piston
screwed in the main piston moves in the glass cylinder
with very small clearance. The air flow is made visible
by goose down introduced with the inlet air and is re¬
corded by high-speed motion pictures taken at a rate
of 2,400 frames per second. Tests have been completed
with a pent-roof cylinder head in which the inlet valves
were shrouded to give different degrees of air move¬
ment. With the shrouds arranged to give a tangential
swirl, the photographs show that the tangential swirl
persists throughout the compression stroke. With the
shrouds arranged to direct the air parallel to the cyl¬
inder diameter, a decided vertical swirl is produced.
With the shrouds radially arranged, a general indis¬
criminate air movement similar to that obtained with¬
out shrouds is obtained. The data are being prepared
for publication.
Decreased fuel consumption. — A study of the fuel-con¬
sumption characteristics of modern air-cooled engine
cylinders at various values of engine speed and torque
has been completed. The determination of these char¬
acteristics was made on two single-cylinder air-cooled
test engines having compression ratios of 5.C and 6.9,
respectively. The results showed that to secure best fuel
economy an engine should be operated at high torque
and at 65 percent of rated speed. Increasing the com¬
pression ratio from 5.6 to 6.9 decreased the fuel con¬
sumption but did not change the air-fuel ratio that
produced maximum power or minimum fuel consump¬
tion. A report is being prepared giving the results of
this investigation.
Mixture-ratio indicators. — With transport aircraft
maximum range is obtained by operating the engines at
the air-fuel ratio giving minimum specific fuel con¬
sumption. The Committee is investigating the more
promising types of mixture-ratio indicators suitable for
aircraft. The use of these instruments is limited, how¬
ever, to air-fuel ratios from 15 to 9. Since aircraft en¬
gines under cruising conditions are already operating
at air-fuel ratios of approximately 18, there is need
for an improved instrument that will include the full-
range of mixture ratios. An investigation has been
started to determine possible methods of operating such
an instrument.
Exhaust-gas analysis. — As most commercial instru¬
ments for indicating air-fuel ratio depend upon one or
26
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
more constituents of the exhaust gases, it is important
in connection with the development of such an instru¬
ment to know the correlation of these constituents with
air-fuel ratio. The most reliable method of determin¬
ing this correlation is by chemical analysis of the ex¬
haust gases. An investigation to determine the correla¬
tion for a number of engines and a range of engine-
operating conditions has been completed, and the results
are in process of publication as Technical Report
No. G16.
ENGINE COWLINGS
The N. A. C. A. cowling’. — The results of the compre¬
hensive investigation carried out with full-scale models
of the N. A. C. A. cowlings in the N. A. C. A. 20-foot
wind tunnel have been published in Technical Reports
Nos. 592, 593, and 594. The effect of cowlings on the
cooling characteristics of a Pratt & Whitney Wasp
SlIIl-G engine is reported in Technical Report No. 596.
Nose-slot cowling. — The preliminary results obtained
with the nose-slot cowling in the wind tunnel have been
described in Technical Report No. 595. This cowling is
characterized by the fact that the exit opening dis¬
charging the cooling air is not, as usual, located behind
the engine but at the foremost extremity or nose of the
cowling. This nose-slot cowling is inherently capable
of producing two to three times the pressure head ob¬
tainable with the normal type of cowling, because the
exit opening is located in a low-pressure field. Thus
identical conditions of cooling can be obtained at corre¬
spondingly lower air speeds. In general, the efficiency
is found to be high, owing to the fact that higher
velocities may be used in the exit opening.
Investigation of the nose-slot cowling has been ex¬
tended to include flight tests on the XBFC-1 airplane.
A two-slot design with an adjustable nose section con¬
trollable from the cockpit has given very good results.
This cowling compares very favorably with the original
installation of the conventional N. xV. C. A. cowling.
Greater pressure is available for cooling on the ground,
while the top speed of the airplane is increased 8 miles
per hour. This investigation is being continued to
improve the ground cooling further and to eliminate
some conditions of local heating caused by the change
in direction of the air flow. In the second design of the
nose-slot cowling tightly fitting baffles were used. These
baffles were much superior to the service-type baffles,
lowering the temperature of the cylinder heads 40° and
requiring the expenditure of only one-fifth the power.
The in-line air-cooled engine. — With increase in the
power output of the air-cooled in-line engine the diffi¬
culties of obtaining satisfactory cooling and low drag
have increased. The Committee is investigating the
problems connected with the cowling and cooling of a
6-cylinder in-line air-cooled engine. In the in-line en¬
gine the opening available for the entrance of the cool¬
ing air is quite small, so that the air must enter at rela¬
tively high speed. The air must be turned through 90°
in order to flow over the engine cylinders. Owing to
the relatively high velocity, it was found that 30 per¬
cent of the available pressure was lost in turning the air
before it entered the cylinder baffles. The energy re¬
quired for cooling was therefore high compared to the
energy required in the radial engine.
A neve cowling has been constructed that will insure
a smooth flow of air over the cowling. Enlarged open¬
ings and passages on the air-entrance side of the cylin¬
ders will be used to reduce the turning loss of the air.
From the results obtained in the tests on this cowling a
supplementary investigation will be planned.
ENGINE COOLING
Aircraft engines must be operated at approximately
one-half the rated power and with lean mixtures to
obtain maximum range. Any improvement made in
the cooling of air-cooled engines can be utilized in oper¬
ating the engine at higher power output during take-off
and in cruising with leaner mixtures.
Fin dimensions. — An analysis has been made to de¬
termine the best proportions for metal fins for given
rates of heat flow, consideration being given to the mini¬
mum pressure drop across the fins, the minimum power
required for cooling, and the minimum weight of
the fins.
This investigation has shown that: A considerable
improvement in the heat transfer of conventional alu¬
minum fins is possible by the use of correctly propor¬
tioned fins; correctly proportioned aluminum fins will
transfer more than 2.25 times as much heat as steel fins
for the same weight and pressure drop ; the best fin pro¬
portions for maximum heat transfer for a given fin
weight and pressure drop are also best for obtaining a
high heat transfer for a given power expenditure in
cooling.
As a result of the investigation of fin dimensions it
was found that, for a given width of fin and velocity,
there was an optimum spacing below which the heat
transfer rapidly decreased. In order to determine the
cause of this decrease, an investigation has been started
in which the type of flow of air around large-scale model
cylinders is determined by means of smoke-flow pictures.
A hot-wire anemometer is also used to determine the
change from laminar to turbulent flow. The effect of
cylinder diameter, fin space, and fin width on the type
of flow is being determined.
Heat-transfer coefficients. — The calculation of the heat
flow from air-cooled finned surfaces depends upon the
experimentally determined heat-transfer coefficients.
An investigation to determine the surface heat-transfer
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
27
coefficients of closely spaced fins from wind-tunnel tests
with and without baffles and with blower cooling lias
been described in Technical Note G02.
An investigation has been made to determine the
heat-transfer coefficients of closely spaced aluminum-
alloy fins having a width of 1.22 inches and copper fins
having a width of 3 inches. The primary object of
these tests was to determine whether the heat transfer
as calculated from a theoretical equation checked the
experimental values for finned surfaces constructed of
metals having different thermal conductivities. The opti¬
mum fin spacing with wide fins ivas also investigated.
Cylinder baffles. — A study has been completed of the
aerodynamics of cooling air-cooled engine cylinders
with baffles. The air passage was recognized to be a
venturi and was studied from this point of view. The
use of a baffle approximating the best venturi possible
under the conditions imposed by a radial air-cooled
engine resulted in an improvement of 20 percent in
cooling on a model cylinder. When the results of this
study were applied in the baffling of a modern 2-row
radial engine the cooling on the head was improved
28 percent.
Further work is in progress on the problem of im¬
proving the cooling by changing the cylinder contour.
An attempt is being made to overcome some of the
difficulties in constructing a good venturi in the con¬
ventional circular engine cylinder. Although the study
is being made for convenience on a model simulating
the barrel of the cylinder, the results are applicable to
the head of the cylinder. Since 80 percent of the heat
is dissipated through the head, and since contour
changes are more easily made on the head than on the
barrel, the results will be applied to the head of the
cylinder.
Blower cooling. — The results of an investigation on a
cylinder with fins 1.22 inches in width and with spac-
ings varying from 0.022 to 0.21 inch have been pub¬
lished in Technical Report 587. The cylinders were
enclosed in jackets and cooled with air supplied by a
blower. The results showed that maximum cooling
was obtained with a fin spacing of 13 fins per inch and
that the heat-transfer coefficient was not sensitive to the
fin spacing for values near the maximum, whether more
or less. With 11 or 16 fins per inch the heat transfer
was 95 percent of that obtained with a fin spacing of 13
fins per inch.
The results of the investigation to determine the
effect of fin width, fin spacing, entrance and exit areas
of the jacket around the cylinder, separator plates, and
fillets on the pressure drop and power required to force
air around finned cylinders at air speeds from 15 to
230 miles per hour have been prepared for publication
and will be released as Technical Note 621. An analy¬
sis has been made of the losses occurring around the
cylinder. As a supplement to this work, some miscel¬
laneous tests are beiim made to determine the effect of
certain special jacket and baffle designs on the heat
transfer and pressure drop of finned cylinders.
Cylinder-temperature correction factors.— The results of
an investigation to determine the effect of engine power,
weight velocity of the cooling air, and atmospheric
temperature on the cylinder temperatures of a Pratt &
Whitney 1535 engine under flight conditions have been
published in Technical Note 584.
The study of the factors for correcting cylinder
temperatures of air-cooled engines to a standard atmos¬
pheric temperature has been extended to include the
correction factors for various flight and test conditions,
such as level flight, climb, take-off, airplane stationary
on ground, and conditions of constant mass flow of
cooling air and of constant velocity of cooling air.
The correction factors range from approximately a
change in cylinder temperature of 0.6° to 1.1° per
degree change in atmospheric temperature, the value of
the factor depending on the flight or test condition. A
report covering this work is being prepared.
Heat transfer. — The study of the cooling of air-cooled
engines has been continued. A report has been pre¬
pared and will be published as Technical Report 612,
presenting an analysis in which equations for the rate
of heat transfer from the engine gases to the cylinder
and from the cylinder to the cooling air, as well as
equat ions for the average head and barrel temperatures,
as functions of the important engine and cooling vari¬
ables, are obtained. Data obtained in tests of single-
cylinder engines of cylinders from Pratt & Whitney
1535 and 1340-H engines for checking the analysis and
for providing the empirical constants in the equations
for these cylinders are presented in the report. An
illustration of the application of the equations to the
correlation of cooling data obtained in flight tests of a
Grumman Scout (XSF-2) airplane is also given in the
report.
An investigation of the effect of turbulence in the
cooling air stream on the cooling of the Pratt & Whit¬
ney 1535 cylinder showed that in some cases the turbu¬
lence caused an increase of as much as 30 percent in the
heat-transfer coefficient of the fins for the same pressure
drop across the cylinder. These data are included in the
report.
Further cooling tests have been made on a cylinder
from a Wright 1820-G engine for obtaining the con¬
stants of the heat-transfer equations for this engine.
Radiators. — A study of radiator design has been un¬
dertaken. The entrance and exit conditions are being
studied with a view to improving their aerodynamic
performance. The study has revealed that 50 percent of
28
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the power required to cool a radiator is lost in the exit
of the air from the radiator tubes in the conventional
honeycomb tube radiator. The results show that an
important part of this loss can be avoided. Further, the
diameter and length of tubes for the minimum power to
cool is being determined. The results will give the
optimum dimensions for several operating conditions
and installations.
COMPRESSION-IGNITION ENGINES
The compression-ignition engine is of particular in¬
terest as a power plant for transport aircraft because
of its inherently low fuel consumption. The criticism
previously made of the compression-ignition engine was
that it could not produce the necessary high power out¬
puts for take-off and that the weight of the engine
would be excessive because of the high maximum cylin¬
der pressures. The results obtained by the Committee
in tests of single-cylinder engines with the N. A. C. A.
displacer-type combustion chamber showed that the
boosted performance of this compression-ignition en¬
gine was equal to that obtained from the latest type of
air-cooled engines operating with fuel of 100 octane
number. Under take-off conditions the maximum cylin¬
der pressures developed in conventional air-cooled en¬
gines have been found to equal those in the compres¬
sion-ignition engine. The two types of engines should
therefore weigh approximately the same.
Prechamber type of combustion chamber. — The results
of the investigation of the prechamber type of combus¬
tion chamber for compression-ignition engines have
been published in Technical Report 577.
Integral type of combustion chamber. — The investiga¬
tion of engine performance at 2,500 r. p. m. with a dis¬
placer piston and a vertical-disk form of combustion
chamber has been continued. In order to accommodate
the increase in the engine rotative speed from 2,000 to
2.500 r. p. m. the air induction and exhaust systems were
altered and development work conducted to determine
the proper air-flow passages and the arrangement of
fuel sprays in the combustion chamber. Test results
showed that with existing fuel-injection equipment the
injection period was too long, as evidenced by late burn¬
ing and a smoky exhaust. Even without the correct
rate of fuel injection an indicated mean effective pres¬
sure of 260 pounds per square inch was developed at
2.500 r. p. m. for a boost pressure of 10 pounds per
square inch. The corresponding specific fuel consump¬
tion was 0.42 pound per indicated horsepower-hour.
Altitude performance. — An investigation of the per¬
formance of a compression-ignition engine under alti¬
tude conditions has been completed, and the results
showed the Diesel engine to be under no handicap when
compared with the carburetor engine. Tests were con¬
ducted at pressure altitudes up to 30,000 feet and at
temperature and pressure conditions up to 14,000 feet.
Boosted performance was also determined at constant
inlet-air temperature from boost pressures of 0 to 10
pounds per square inch over a range of exhaust pres¬
sures corresponding to altitudes from 0 to 19,000 feet.
The scope of the research was expanded to include the
investigation of the effect of single variables of tem¬
perature and pressure of the inlet air and exhaust back
pressure. A report presenting the results of the work
is in process of publication.
Single-cylinder and multicylinder engines. — An air¬
cooled compression-ignition cylinder having a push-
rod-valve mechanism suitable for use on a radial en¬
gine has been designed by the Committee and is being
supplied by the Bureau of Aeronautics, Navy Depart¬
ment, for investigation. The cylinder has the displacer
form of combustion chamber developed by the Com¬
mittee and will be used to investigate its adaptation to
air-cooled cylinders. Information will also be obtained
on the factors of multicylinder compression -ignition
engine performance and the problem of air-cooling a
compression-ignition engine cylinder.
The 2-stroke-cycle engine. — The investigation of the
2-stroke-cycle compression-ignition engine has been
continued, and tests have been made to determine the
effect of the shape of the inlet ports on engine per¬
formance. A cylinder liner providing 62 iidet ports,
each of U^-bich diameter arranged in three stag¬
gered rows and drilled at an angle of 56° from the
radial, has been tested for several length-diameter
ratios of the ports. Best performance was obtained
when the length-diameter ratio was 0.7 and was ap¬
proximately equal to that with the eight large rec¬
tangular ports previously used. Work is in progress
to determine the effect of varying the timing and dura¬
tion of exhaust on engine performance.
Fuel-injection rates. — The results obtained from the
investigation of the rates of discharge from a single-
cylinder fuel-injection pump connected to two injec¬
tion valves have been published in Technical Note 600.
The increase in rotative speeds of the compression-
ignition engines has resulted in inferior performance
of the fuel-injection equipment. Special apparatus has
been constructed whereby accurate and convenient de¬
termination of injection rates has been made for a
group of available fuel pumps, plungers, and cams in
various combinations. The tests included variations of
engine speed and quantity of fuel injected for the sev¬
eral injection-system combinations. Results indicated
the unsuitability of any available injection equipment
to give satisfactory introduction of the fuel charge into
the cylinder at engine speeds in excess of 2,000 r. p. in.
and the urgent need for further injection-system tests
and development.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
29
Fuel-injection pumps. — An improvement in the per¬
formance of several compression-ignition engines lias
resulted from changes in the rate of fuel injection. A
knowledge of the rate of injection of the various fuel-
injection systems has been obtained only after investi¬
gation of their characteristics. A unit type of injection
system was investigated to obtain a direct control over
the injection rate by variation in the cam outline. A
cam-operated injection pump was closely coupled to
the injection valve, and the effect of changes in orifice
diameter, injection-tube length, throttle setting, pump
speed, type of injection valve, and cam outline was
studied.
The cam outline directly controlled the injection rate
during the first five pump degrees of injection for a
large orifice diameter and a differential-area valve.
After this time interval, leakage at the pump affected
the control. An open nozzle in combination with a
ball-check valve reduced the initial rate of discharge
to about half that of the differential-area valve. This
rate increased with fuel quantity to a maximum at cut¬
off. With the differential-area valve, the rate of in¬
jection reached a maximum a few degrees after the
beginning of injection and an increase in fuel quantity
did not increase this rate. An increase in pump speed
decreased the maximum rate and increased the period
in degrees. Increase in injection-tube length had less
effect on the open-nozzle valve. Secondary discharges
were not obtained under any operating conditions with
short injection tubes, but were obtained with increase
in tube length under operating conditions in which a
high initial pressure wave was obtained. The orifice
diameter materially affected the injection rate, owing
primarily to the high leakage rate at the injection
pump. The maximum rate decreased with decrease in
orifice diameter. With a suitable pressure seal at the
pump and a relatively large orifice diameter in a dif¬
ferential area valve, the rate of discharge should be
controllable by the cam outline for the unit-type
injector.
Fuel and combustion accelerators. — The efficiency of the
compression-ignition engine at increasing loads is re¬
duced by late burning during the power stroke. Some
evidence has been presented that the problem of elimi¬
nating the late burning may not be entirely the me¬
chanical process of fuel and air mixing but one also
of overcoming chemical retardants. The use of chemi¬
cal combustion accelerators in the fuel has been sug¬
gested as a possible means of overcoming this handicap.
A tetranitromethane Diesel oil dope has been obtained
and tested in various percentages in the standard labo¬
ratory fuel. The small improvement in performance
(2 to 3 percent) was considered economically undesir¬
able. A sample of a second combustion accelerator has
been ordered for test. A program is also under way
to determine the relative merits of combinations of fuel
oil and alcohol in various percentages, particularly with
respect to more complete utilization of the air charge.
Fuel investigation. — The correlation of engine-per¬
formance data requires a knowledge of the heat of com¬
bustion of the fuel used. The determination of this
factor and the distillation characteristics of the fuel
make possible the recognition of changes in fuels due to
aging or replacement. The heating values of five sam¬
ples of Diesel fuel used by the Committee for engine
testing have been determined. The values found vary
from 19,790 B. t. u. to 19,930 B. t. u. per pound.
The smoky exhaust obtained with compression-igni¬
tion engines operating at air-fuel ratios richer than the
theoretical (15 pounds of air to one pound of fuel)
indicates that considerable fuel is wasted in unburned
carbon. An investigation is being made to determine
the amount of this carbon and its variation with air-
fuel ratio. The method used is to determine the actual
hydrogen-carbon ratio of the fuel from complete com¬
bustion tests and the apparent hydrogen-carbon ratio
from exhaust-gas analysis, the difference in the two
values being the carbon in the exhaust. The actual
hydrogen -carbon ratio of five samples of Diesel fuel oil
representative of the fuels used during the past two
years by the Committee has been determined. The
values found varied from 0.160 to 0.161.
INSTRUMENTS
Fuel flowmeter. — Flight testing of the electrical type
of indicating fuel flowmeter which has been developed
by the Committee has been conducted by the Materiel
Division of the Army Air Corps. The fuel flowmeter
is being altered to incorporate desirable changes indi¬
cated as a result of the flight tests.
High-speed camera. — The design of a high-speed mo¬
tion-picture camera to photograph combustion at rates
up to 40,000 frames per second has been completed, and
construction of the camera has been started. The oper¬
ating principle of the camera has been checked by means
of a mock-up of the camera.
Fuel-injection pressure indicator. — A piezo-electric pick¬
up unit has been adapted to a fuel-injection valve to
obtain instantaneous values of the fuel pressure at the
discharge orifice. The pressures are shown on a
cathode-ray tube. Photographic records are made of
these instantaneous pressure traces. The rates of fuel
discharge calculated from the pressure records show a
very close agreement with the rates measured on the
rate-of-discharge apparatus. This unit allows a rapid
determination of rates of fuel discharge and of any
cyclic variations in the discharge.
30
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NATIONAL BUREAU OF STANDARDS
Phenomena of combustion. — A spherical explosion ves¬
sel with central ignition and auxiliary apparatus for
obtaining simultaneous records of flame travel and pres¬
sure development has been constructed. The bomb con¬
sists of two flanged hemispheres, about 10 inches in
diameter, clamped together on a short ring of glass
which affords a view of the flame in a narrow, vertical
center-section of the bomb.
The progress of the flame as it spreads from the cen¬
tral spark gap is photographed on a film which is car¬
ried on a drum rotating at a known speed on a vertical
axis. The movement of the film under the lengthening
image of the narrow flame section produces a time-
displacement record of the flame front.
Six diaphragm pressure indicators, designed with a
view to securing high accuracy throughout the pressure
range of the explosion, are mounted on the bomb.
Each indicator is set to close an electric contact the
instant some predetermined pressure is reached in the
bomb. When the contact is closed a neon lamp of high
intensity is lighted, which photographs on the rotating
film as a line beside the flame trace. In addition to the
six lamps corresponding to the six indicators, there is
a lamp which flashes 1,000 times a second under the
control of a tuning fork and a lamp which burns con¬
tinuous]}^ to provide a reference line for the measure¬
ment of flame displacements. The film thus contains
all the information necessary for plotting time-dis¬
placement and time-pressure curves for the explosion.
Formulas have been developed for calculating from
these curves (1) the “transformation velocity” or fun¬
damental speed at which the flame front advances into
and transforms the unburned charge; and (2) the “ex¬
pansion ratio” or ratio of the volume of burned gas to
the volume of the same mass of gas before explosion
at constant pressure. Experiments will be conducted
with this apparatus to investigate the separate effects
of charge composition, temperature, and pressure on
transformation velocity and expansion ratio.
Some experiments were made in which a cylindrical
glass bomb was used with no pressure indicator to
determine the effect of water vapor on the period of
subnormal flame velocity just after the occurrence of
the spark. In equivalent mixtures of carbon monoxide
and oxygen saturated with moisture at atmospheric
pressure this delay period is very short and high-film
speeds must be used to detect it. Constant flame ve¬
locity is attained much more slowly when the moisture
content is reduced below about one percent by volume.
The cause of the delay is not known and it is hoped
that new information concerning it will be obtained
with the spherical bomb.
A brief mimeographed circular outlining the com¬
bustion experiments which have been conducted at the
Bureau in engines, soap bubbles, and bombs, and con¬
taining a list of published reports on these experiments
has been prepared for distribution to visitors and to
others interested. A mimeographed bibliography con¬
taining 162 references on high-speed pressure indi¬
cators, classified according to type, is also available.
Investigation of piston cooling. — As the output of air¬
craft engines is raised the problem of heat dissipation
from the piston head becomes increasingly serious. A
program has been outlined for determining the heat
flow in suitable test specimens under conditions similar
to those encountered in service by aircraft-engine pis¬
tons. Preliminary static experiments showed greatly
improved heat transfer for a hollow steel specimen
with internal cooling over a solid aluminum specimen
of approximately equal strength, size, and weight.
SUBCOMMITTEE ON AIRCRAFT FUELS AND
LUBRICANTS
Engine performance with iso-octane fuels. — As men¬
tioned in the report of the Langley Memorial Aero¬
nautical Laboratory above, an investigation is being
conducted at that laboratory to determine the maximum
engine performance with fuels having octane numbers
ranging from 87 to somewhat greater than 100. In
this investigation the engine performance has been de¬
termined with the N. A. C. A. high-speed single-
cylinder test engine having a cylinder bore of 5 inches
and a stroke of 5.75 inches. The tests have been made
at an engine speed of 2,500 r. p. in. and a coolant tem¬
perature of 250° E. The desired octane number of the
fuel has been obtained by using commercial, iso-octane
blended with a gasoline having an octane number of 18.
For octane numbers greater than 100, tetraethyl lead
has been added to the iso-octane.
Tests have been completed with fuels of 87, 91. 95,
and 100 octane number as determined by the C. F. R.
method. In addition, tests are almost completed on
the iso-octane with 1 cubic centimeter of tetraethyl
lead. The limiting performance of these fuels has been
determined at maximum power and at best fuel econ¬
omy for both incipient and audible knock. The results
show that as the inlet-air temperature is increased for
any one compression ratio the effectiveness of the fuels
of higher octane number appreciably decreases. Only
at the lower inlet-air temperatures are the greatest in¬
creases in performance realized for the fuels of higher
octane number. The tests have shown that the power
of the engine does not vary as the inverse square root
of the inlet-air temperature, but as an approximately
lineal function.
Stability of aviation oils. — The investigation of the
stability of aircraft-engine lubricating oil, conducted by
the National Bureau of Standards in cooperation with
the Bureau of Aeronautics of the Navy, has been ex-
tended to include laboratory tests of the stability of oils
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
31
in an apparatus in which the oil flows in a thin film
clown the walls of a heated cylinder and thus simulates
engine conditions. The investigation of this method is
not yet completed, but the data obtained thus far indi¬
cate a correlation between the results of these tests and
the results of tests which have been made in a Pratt and
Whitney Hornet engine.
An investigation of the stability of compounded oils
has been initiated in cooperation with the Subcommittee
on Aircraft Fuels and Lubricants, and the effect of a
number of compounding materials on the stability of
the base oil has been studied. The results of this inves¬
tigation will serve as a basis for the choice of com¬
pounded oils to be used in connection with the study of
wear and oiliness characteristics of aviation engine
©
lubricating oils.
Oil acidity and bearing corrosion. — The investigation,
conducted by the National Bureau of Standards in
cooperation with the Bureau of Aeronautics of the
Navy, of the effect of increase in oil acidity during serv¬
ice on the corrosion of master-rod bearings has been
continued. Study of oils in the apparatus for forming-
acids in oils has indicated that this apparatus can be
used to produce changes in the acidity of oils similar to
changes which occur during service in aviation engines.
It has been found desirable to construct additional ap¬
paratus for use in this investigation and this apparatus
is being designed.
Aviation engine wear. — The investigation of the rel¬
ative wear with different oils in actual aircraft eno-ines,
carried out at the National Bureau of Standards in
cooperation with the Bureau of Aeronautics and certain
petroleum organizations, has been continued through¬
out the fiscal year. The assembly of the operating
equipment for engine control and absorption of power
is essentially completed. Considerable precautions have
been taken to insure reproducibility of operating con¬
ditions. Special fixtures for use with the precision
instruments required for measuring the engine parts are
under construction.
Wear and oiliness characteristics of aviation engine
lubricating oils. — The investigation of the oiliness and
wear characteristics of mineral and compounded lubri¬
cating oils, conducted by the National Bureau of Stand¬
ards in cooperation with the Army Air Corps and the
Bureau of Aeronautics, was continued throughout the
fiscal year. An apparatus for determining the differ¬
ences in piston-ring and cylinder-wall wear with vari¬
ous oils and compounding agents under conditions
approximating those of actual engine operation has
been completed, and preliminary tests are in progress.
Construction of a second wear apparatus of different
type has been begun. The design and construction of a
machine for the study of oiliness as related to friction
in master-rod bearings is under way.
REPORT OF COMMITTEE ON AIRCRAFT
MATERIALS
SUBCOMMITTEE ON METALS USED IN AIRCRAFT
Weathering of aircraft structural sheet metals — light
alloys. — The series of atmospheric exposure tests of
aluminum-alloy sheet materials was completed during
the spring of 1937 after four years’ duration at three
test sites, typical of conditions prevailing at a tropical
marine, a temperate marine, and an inland location.
The results amply confirm the tentative conclusions
announced in last year’s report concerning the most cor¬
rosion-resistant types of alloys and satisfactory coating
treatments for all alloys of this general kind. A report
intended for publication summarizing the essentials of
the test and the important facts established is in
progress.
Preparations are approaching completion for a new
series of tests. This series, which is on a somewhat
smaller scale than the two previous ones, will be con¬
ducted at only one location, a marine one. Hampton
Roads Naval Air Station is the site selected. Both
aluminum and magnesium alloys are included in the
program of tests scheduled, which are intended pri¬
marily for investigating the effects of riveting, weld¬
ing, and contact between unlike metals, as well as the
merits of newly developed protective surface treat¬
ments. The manufacturers of these materials are co¬
operating actively in the preparations, and this will
insure that the industrial aspects of the problem will
receive the careful consideration they deserve.
Corrosion-resistant steel. — The trend toward the use in
aircraft of corrosion-resistant steel in thin sheet form
has led to the inauguration of a similar program on
this type of material. Deterioration of this material,
if it occurs, takes place in a different manner from
that of the light alloys, and the inspection and testing
procedure must be correspondingly different. In both
programs the effect of continuous exposure to the
marine atmosphere as well as intermittent exposure to
sea-water (the so-called “tide-water” tests) is to be
determined.
Surface treatment for improving the durability of mag¬
nesium. — The ultimate aim in this investigation is to
produce a tightly adherent surface film, highly im¬
pervious to corrosive agents, particularly chlorides, to
which paint and other applied coatings will adhere
over long periods of time without peeling or flaking.
Anodic treatment in a dicliromate-phosphate bath by
the method developed in cooperation with the Bureau
of Aeronautics, according to repeated laboratory tests
at the National Bureau of Standards, continues to be
the preferred method for the surface treatment of
magnesium and its alloys. Studies on the improvement
of the anodic treatment have been continued, and the
38348—38 - 4
32
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
results have indicated certain modifications by which
further improvement appears possible. “Sealing” of
the pores in the anodic film after it has been formed
is important to produce a highly impervious film.
This may be accomplished either by chemical means
or by immersion in a hot oil or resin bath. Tests along
this line are continuing. Initial cleaning before anodic
treatment is also important in obtaining a film on the
treated specimen of superior resistance. Tests on paint
adherence as affected by the sealing treatment and
other surface characteristics are in progress in the
laboratory and on the outdoor exposure rack.
Sub-zero temperature and aircraft metals. — The original
program, undertaken in cooperation with the Bureau
of Aeronautics, has been completed and a report ren¬
dered, copies of which are available to all interested
Government agencies. The only important adverse
effect of low temperature, down to —80° C., is the de¬
creased impact resistance of ferritic steels, which is in
marked contrast to the aluminum alloys and the aus¬
tenitic steels. Study of the factors responsible for this
lowered impact resistance of ferritic steels is being
continued with the aim of reducing and possibly elimi¬
nating the effect by suitable initial heat treatment of
the steel. The investigation has been extended to in¬
clude a study of the impact resistance at low tempera¬
tures of welded joints in steel members.
Elastic properties of high-strength aircraft metals. — The
elastic properties of metals which owe their high-
strength properties to strengthening by cold working
are only nominal and vary greatly with the precision
of the method used for their determination. An out¬
standing example is austenitic steel, such as 18-8 stain¬
less steel, which because of its high corrosion resistance
is favored for many important uses in aircraft. The
method used in this work is essentially an “over-load”
or “proof-stress” method, consisting in the determina¬
tion of yield strength after various degrees of cold
working by stretching immediately prior to testing.
A rise in proof stress with increase in prior cold work
is indicative of an improvement in the material, and
vice versa for a decrease in proof stress. A report
summarizing this phase of the work will be forthcom¬
ing shortly. Hysteresis measurements, such as those
which may be obtained in the ordinary tensile-testing
machine, are now in progress.
Structural changes in aircraft metals occurring as a re¬
sult of service stressing. — The principal aim in this in¬
vestigation is expressed in the question, Does continued
fatigue-stressing below the endurance limit adversely
affect aircraft metals? The widely used aluminum pro¬
peller alloy, 25S, is the material used in this study. A
variety of approaches to the problem have been made,
some of which were abandoned at early stages for more
promising ones. The project is still in the stage of at¬
tempts to detect significant changes (other than crack
formation and propagation) in physical properties,
microstructure, and X-ray diffraction pattern as results
of continued repeated stressing in the range of maxi¬
mum fibre stress from 5.000 to 26,000 pounds per square
inch. Up to the present no nondestructive method of
inspection has been found which shows a significant
difference between the metal not stressed and the same
metal after it has been subjected to fatigue stressing.
Special mention may be made of the failure to detect a
lowering of impact resistance which could be attributed
to prior fatigue stressing.
Propeller materials. — The possible deleterious effect of
fabrication defects on the endurance properties of steel
used in hollow steel propellers merits serious study.
Also, the influence on the endurance of propellers of
surface coatings, such as chromium plating as a finish,
should not be overlooked.
The fatigue limit of such steel is approximately one-
half of the tensile strength, which is considered to be
normal for this material. Determinations of the fatigue
limit of sound weld metal showed this to be about 60
percent of that of the parent metal. Scaling and sur¬
face decarburizing, such as may be present accidentally
on the inside of the welded structure and cannot be
removed, reduced the fatigue limit to one-half that of
the polished steel, i. e., not much below that of the weld
metal. The effect of accidental defects in the weld is
variable; such defects may cause a very sharp reduction
in the fatigue limit of the weld metal.
The effect of chromium plating varies with the con¬
dition of the steel and thickness of the plating. Speci¬
mens of normalized steel (previously polished) bearing
relatively thick coatings showed no significant reduc¬
tion in fatigue limit and a thinner coating had only a
slightly greater effect. On specimens of the same steel
in quenched-and-tempered condition, however, a reduc¬
tion in fatigue limit was noted, which appeared to be of
more significance and was greater for a very thin coat¬
ing than for a coating ten times as thick, the plating in
each case being applied directly to the previously
polished steel. The use of a nickel “under coat,” in
accordance with commercial usage, prior to plating the
quenched-and-tempered steel, gave similar results. The
subject is receiving further study.
Further study of the unusual structural features
previously reported for aluminum-alloy propeller
blades has failed to show that any practical signifi¬
cance can be attached to them.
Miscellaneous. — The fact is well established that the
corrosion resistance of many of the aluminum alloys
which are strengthened by heat treatment is dependent
in large measure upon the control of the conditions of
heat treatment. A simple rapid test to determine in
advance of service whether structural materials of this
33
REPORT NATIONAL ADVISORY
kind have been suitably heat-treated so as to develop
maximum corrosion resistance should serve a very use¬
ful purpose. A study is being made of a proposed
method, the essential feature of which is a determina¬
tion of the solution potential of the material under
consideration.
A relatively inexpensive method of preparing small
fittings of unusual shape is to use transverse sections of
an extruded shape of the proper size and contour. A
study of extruded aluminum fittings made in this man¬
ner is under way, with a two-fold purpose, namely, (a)
the improvement of such fittings with respect to certain
features which have not proved entirely satisfactory
under all service conditions, and (b) the determination
of the practical significance of certain suspected struc¬
tural features.
The need for a certain degree of ductility in a struc¬
tural member, as in an aircraft assembly, is well recog¬
nized. The amount and the manner in which it is speci¬
fied are, however, matters on which difference of opin¬
ion exists. Determinations of the ductility of various
structural steels under various conditions of stress ap¬
plication have been continued, in cooperation with the
Bureau of Aeronautics of the Navy. Interpretations
as to the practical significance of differences in this
property observed under various conditions are yet to be
made.
SUBCOMMITTEE ON MISCELLANEOUS MATERIALS AND
ACCESSORIES
The problems under the cognizance of this subcom¬
mittee during the past year which are being investigated
at the National Bureau of Standards include the de¬
velopment of a flexible substitute for glass and the
development of substitutes for linen webbing and silk
shroud lines for parachutes. Consideration has also
been given to the possibilities of plastics as a material
for aircraft structures and to the adequacy of thermal
and acoustical insulation.
Development of flexible substitute for glass. — Commer¬
cial and experimental transparent plastics which have
been investigated to determine their suitability for air-
craft windshields and windows include cellulose ace¬
tate, acrylate resins, cellulose nitrate, ethylcellulose,
vinyl chloride-acetate, vinyl acetal, glyceryl-phthalate,
styrene, phenol-formaldehycle, and cellulose acetobuty-
rate.
The tests included light transmission, haziness, dis¬
tortion, resistance to weathering, scratch and indenta¬
tion hardnesses, impact strength, dimensional stability,
resistance to water and various cleaning fluids, burst¬
ing strength at normal and low temperatures, and flam¬
mability.
The two types of transparent plastics which are now
in use on aircraft, namely, cellulose acetate and acrylate
COMMITTEE FOR AERONAUTICS
resin, were found to have certain defects which, it is
believed, can be overcome in part by suitable modifica¬
tion of the composition and processing of the material.
Cellulose-acetate plastic was found to have excellent
impact strength, bursting strength, and flexibility, but
the commercial products tested varied considerably in
resistance to weathering and were all subject to marked
shrinkage in one year’s time. The shrinkage pro¬
duces warping and sets up strains in the plastic sheets,
which cause them to craze and crack. These strains
are believed to be the cause of the spontaneous crack¬
ing of cellulose-acetate windshields after they have
been in service for six months or longer. This is par¬
ticularly true of windshields which are exposed to low
temperatures, as by ascent to high altitudes, as addi¬
tional strains are thereby introduced in the windshield
because of thermal contraction. Considerable variation
was observed in the weathering resistance between cellu¬
lose-acetate sheets received from different manufac¬
turers and also between different lots of the material
from the same manufacturer.
The acrylate-resin plastic was found to be remark¬
ably transparent, more stable to light and weathering,
and more resistant to scratching than cellulose acetate,
but its impact strength and flexibility are much poorer.
Surface crazing of the acrylate resins was noted after
one year’s exposure on the roof and also after storage
for a similar period. It is claimed, however, that a
method of processing has been developed which elimi¬
nates this tendency to craze. Further tests on modified
samples of both cellulose acetate and acrylate resins are
in progress to determine whether more uniformly du¬
rable products than have been on the market to date can
be made available to the aircraft industry.
Certain of the other materials, which are not now
commercially available, appear very promising.
Tests for impact resistance were developed on a scale
commensurate with service conditions. Soft rubber
balls, five inches in diameter, loaded to weigh three
pounds, were fired from guns at the Naval Proving
Grounds. The muzzle velocity was approximately 300
feet per second. No material, whether plastic or lami¬
nated glass, was found able to withstand a direct hit
with such a projectile. The experimental pieces were,
of course, limited as to weight and thickness by prac¬
tical considerations of airplane design. It was there¬
fore concluded that the windshield alone cannot be re¬
garded as a protection against ducks.
Substitute for linen webbing. — An all-cotton webbing
- which meets the requirements for breaking strength,
weight, width, and thickness contained in U. S. Army
Specification No. 15-11-D for linen webbing has been
produced commercially. While the construction is not
identical with that of the Type-G webbing, the cotton
webbing appears to be a satisfactory substitute.
34
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Substitute for silk shroud lines. — Attempts to make
shroud lines from some material other than silk have
not been successful to date. Whether cotton or rayon
was used, the strength-weight ratio of the line lias not
equalled that obtainable with silk. Experiments are
being continued to obtain information on the effect of
variations in the construction of the line.
Development of plastic material for aircraft structures. —
A survey of the literature on this subject was com¬
pleted and a report presented to the Committee. The
report contains data on density, tensile and compressive
strengths, modulus of elasticity, fatigue, energy ab¬
sorption, corrosion, and methods of fabrication. The
Committee is now studying this report with a view to
deciding whether or not to go further into the matter.
Materials for acoustical and thermal insulation. — A re¬
port bringing together some of the information avail¬
able on this subject has been presented to the Com¬
mittee. Plans have been made to ascertain the practical
importance of this subject, and upon the answer to this
question will depend future developments.
REPORT OF COMMITTEE ON AIRCRAFT
STRUCTURES
LANGLEY MEMORIAL AERONAUTICAL LABORATORY
Applied loads on airplane structures — gust loads. — Co¬
ordinated measurements of acceleration and air speed
on transport airplanes have been continued during the
past year, and the total flying time represented on the
records has been extended to over 30,000 hours. The
maximum accelerations previously recorded have not,
however, been exceeded and the maximum effective gust
velocities for normal transport operations remain at
±35 feet per second.
Gust research. — The measurements of gust intensities
and gradients on light airplanes, begun last year, have
been continued and the data greatly extended. The
new results do not invalidate the previous tentative con¬
clusions, that in stable atmospheric conditions with
large wind gradients, vertical gust velocities of the
order of 30 feet per second are reached in a horizontal
distance of about 100 feet and that the gust gradient
increases with decreasing gust intensity.
Surveys of cumulus types of clouds indicate, in gen¬
eral, stronger downward-acting than upward-acting
gusts. On one occasion a downward gust of 53 feet per
second, which reached maximum intensity in a distance
of 53 feet, was experienced.
Gust tunnel. — During the past year an apparatus for
catapulting dynamically scaled models through artifi¬
cial gusts has been developed to the point of satisfac¬
tory operation. In this apparatus the model is
launched into a condition of steady glide, following
which it flies through an air jet whose angle relative to
the flight path can be controlled. The model carries
a small optically recording accelerometer, and as it
flies through the gust the acceleration is recorded ancl
synchronized with external photographic measurements
of the speed, path angle, and attitude angle.
Although this equipment is not ideally suited to the
investigation of some of the important fundamental
problems of unsteady flow, it can be used and was de¬
signed for the direct determination of the effects of
changes in the several airplane and gust variables on
the airplane motion and wing loads. This function is
justification for the equipment in view of the rapid
trend toward larger transport airplanes, to which the
statistical data obtained on past and present types of
airplanes do not apply.
Gust-relief devices. — A preliminary analytical study
of the merit of two devices for reducing accelerations
due to gusts has been made. The more effective ar¬
rangement appears to be a trai ling-edge flap operated
by a small vane located somewhat ahead of the wing.
This arrangement responds more quickly and reduces
the acceleration further than the other device studied,
which was simply a mass-overbalanced flap.
Load distribution. — The results of a previously re¬
ported investigation of the span-load distribution on
wings with partial-span flaps have been published as
Technical Report No. 585. This report includes a
simple set of computing forms for determining the
distribution by the Lotz method with sufficient har¬
monics retained for good precision. The work on
wings with partial-span flaps has been extended to
include the calculation of the angle of zero lift, the
pitching moment, and the induced drag. Wing models
are now being constructed for investigation to provide
data for comparison with the calculations.
Several pressure-distribution tests have been made in
the 7- by 10-foot wind tunnel of wings with various flap
arrangements, including Fowler flaps with chords 30
and 40 per cent of the wing chord.
Several reports describing investigations conducted
prior to this year have been issued and include a report
on pressure-distribution measurements on an 0-2H ob¬
servation airplane in flight (Technical Report No. 590),
a report presenting an empirical method for determin¬
ing tip corrections to the theoretical span-load distribu¬
tion (Technical Note No. 60(j), and a report on the
theoretical span loading and moments of tapered wings
produced by aileron deflection (Technical Note No.
589).
Fuel tank vents. — During a dive from high altitudes
the pressure changes rapidly on the outside of an air¬
plane. Unless the venting tubes to the fuel tanks and
plugs are of the correct size, a pressure difference may
be built up that will be sufficient to collapse the fuel
tanks or plugs.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The Committee has been requested by the Bureau of
Aeronautics, Navy Department, to investigate these
pressure differences for a range of diameters and lengths
of vent tubes. Apparatus has been assembled in the
laboratory that makes possible the rapid determination
of the pressure difference between a tank of given vol¬
ume and the atmosphere during a dive. The laboratory
tests have been made at constant temperature, as calcu¬
lations show that this does not introduce an appreciable
error.
Tests have been made for terminal velocities of 300,
400, and 500 miles per hour for dives starting at 10,000
to 40,000 feet altitude with float and tank volumes from
10 to 60 cubic feet. Several lengths of vent tubes 1.5
inches in diameter and 0.75 inch in diameter have been
investigated. Pressure differences of 10.5 pounds per
square inch have been recorded with a tube 0.5 inch in
diameter and 12 feet long.
Stressed-Skin Design — stress analysis of beams with shear
deformation of the flanges. — The rapidly increasing size
of aircraft structures is forcing designers to rely in¬
creasingly, for economic reasons, on mathematical stress
analysis rather than on static tests. It is well known
that the classic methods of analysis are not always suf¬
ficiently accurate and efforts are being made to correct
these methods.
As a step in this direction, the bending action of box
beams such as airplane wings has been examined. It
has been realized for some time that the flanges of such
beams deform sufficiently under shear stress to alter the
stress distribution materially. The mathematical theory
of this action has been developed to the point of practi¬
cal applicability and has been partially verified by tests.
Further tests are under way to determine under what
conditions the theory can be used without modification
and, for cases in which modifications are necessary, to
lead over into the range of the classic engineering theory
of bending.
Strength of stiffeners. — A theory for primary failure
of straight centrally loaded columns has been published
as Technical Report No. 582. In the report the theory
for twisting failure of open-section stiffeners, as pre¬
sented by Herbert Wagner (Technical Memorandums
Nos. 807 and 784), has been elaborated to include the
twisting failure of open-section stiffeners attached to a
skin, with stresses carried above the elastic range. An
illustrative computation of the column curve for the
twisting failure of an 1-section skin-stiffener combina¬
tion is also included.
Work is being continued on the twisting failure of
other types of stiffener sections, notably the Z section
and the U section, with and without flanged edges. Con¬
sideration is being given to the manner of shift of the
axis of rotation in twisting failure, both in and above
35
the elastic range, in order to establish the extent of
refinement necessary for practical application.
Besides the study of twisting failure, which is a
primary failure, the local failure of various types of
stiffener sections is being investigated, and the theo¬
retical strength curves are being compared with such
experimental data as become available from time to
time.
Stability of structural systems. — A report has been pre¬
pared and published as Technical Note No. 617 dealing
with the stability criterion for structural systems.
The Hardy Cross method of moment distribution is
employed. In order to simplify the application of the
stability criterion, detailed tables are given for the
read}7 evaluation of the stiffness and carry-over factors.
Sample problems are also included to illustrate the use
of the method.
NATIONAL BUREAU OF STANDARDS
Tubes under loads other than torsion. — Considerable
time has been spent during the year in revising and
bringing into conformity with latest Navy Department
specifications a report which has been written on the
fixation of struts; that is, the column strength of tub¬
ing elastically restrained at the ends. This report is
now completed and will be published by the National
Advisory Committee for Aeronautics as a technical
report. It gives the column strength of chromium-
molybdenum steel, 17ST aluminum alloy, stainless
steel, and heat-treated chromium-molybdenum-steel
tubing, and suggests a method by which planar trusses
that are continuous at the joints may be analyzed and
designed for stability. Two numerical examples are
given.
In order to determine the minimum ratio of slender¬
ness below which thin tubes fail by crinkling rather
than as columns, and to determine the crinkling
strength, tests of short tubes must be made under axial
load. The crinkling strength under axial load of rela¬
tively short specimens of round 17ST aluminum-alloy
tubing has been determined for values of the diameter-
thickness ratio approximately from 15 to 100. Work
is in progress and has been almost completed to deter¬
mine the crinkling strength of chromium-molybdenum-
steel tubing.
The modulus of rupture of round 17ST aluminum-
alloy tubing has been determined for values of the
diameter-thickness ratio approximately from 15 to 100.
This has been done under third-point loading with the
load applied (1) in such a way that failure occurred
in the free length between loads, and (2) in such a
way that failure occurred under a load. The latter
method of loading simulates practical conditions oc¬
casionally encountered under which the load is applied
36
REPORT NATIONAL ADVISORY
through a compression member tending to dent the
tube. Two empirical formulas involving the tensile
yield strength of the tube material and the dimensions
of the tube were derived to describe the modulus of
rupture for the two series of tests.
The modulus of rupture obtained with the first
method of loading does not depend to any marked ex¬
tent on the position of the loading points, and the em¬
pirical formula for this method of loading may be
used with safety whenever the maximum bending mo¬
ment occurs in the free length of tube between loading
points (including supports). The results are conserva¬
tive for all other cases except in those relatively few
instances in which the load is applied through a com¬
pression member tending to dent the tube. Under
these conditions the empirical formula obtained from
the tests with the second method of load should be
used. The results of the second series of tests can be
extended rationally to apply to other than third-point
loading.
Work is in progress and has almost been completed
to determine the modulus of rupture of round chro¬
mium-molybdenum-steel tubing under the same condi¬
tions of test as obtained for the 17ST aluminum-alloy
tubing.
Determination of elastic constants on stainless-steel sheet
material. — A study was made of the elastic properties
of stainless-steel sheet of three thicknesses (0.007,
0.01G, and 0.022 inch) in order to determine effective
values of Young’s modulus and of Poisson’s ratio
which could later be used in calculating stresses from
the deformation under load of a model structure of
this material.
The variation of Poisson’s ratio and of Young’s
modulus with stress, sheet thickness, direction of roll¬
ing. and prestressing was measured by cutting tensile
specimens in the direction of rolling and at right angles
to that direction and measuring the ratio of transverse
strain to axial strain with a set of four pairs of Tucker-
man optical strain gages suitably placed to eliminate
the effects of nonuniformity of stress distribution.
The values of Poisson’s ratio were found to range
from about 0.2 to 0.3. On the 0.007-inch specimen the
Poisson’s ratio in the direction of rolling was about
0.27. while at right angles to that direction it was only
about 0.21. In some cases a considerable difference in
values was found for the second run as compared to the
first, showing the effect of prestressing on the elastic
properties of the material.
Large variations in the value of Young’s modulus
with direction of rolling, sheet thickness, and stress
were also found. In the case of the 0.007-inch speci¬
mens tested in the direction of rolling the Young’s
modulus dropped from around 28.5 10a pounds per
square inch at a stress of around 5,000 pounds per
COMMITTEE FOR AERONAUTICS
square inch to a value less than 26.0 10'! pounds
per square inch at a stress of around 30,000 pounds
per square inch.
I he test results indicated the anisotropy of the
stainless-steel sheet material. Stresses determined
from strain measurements on a model constructed
from such material would be subject to a probable
error of several percent due to the variations in elastic
properties alone.
Flat plates under normal pressure. — Experimental work
was confined to tests of circular plates under normal
pressure. The stress-strain curve of the material in
the center of the plate was derived from the measured
strains and the measured contours under load for two
of the plates. In both cases the stress-strain curve ob¬
tained was found to differ from the tensile stress-strain
curve of a coupon cut from the plate in that the stress
continued to rise after passing the knee of the stress-
strain curve; the mechanism of yielding in bilateral
tension seemed to be different from that in straight
tension.
The experimental work was paralleled by an exten¬
sion of Stewart Way’s analysis of clamped circular
plates of medium thickness under normal pressure to
greater deflections than the deflections of 1.2 times the
thickness of the plate to which Way carried his tables.
The deflections in the present plates amounted to about
four times the plate thickness before yielding became
appreciable. With the derivation of the curves of
maximum stress and of deflection at the center of this
order it will be possible to make an instructive com¬
parison between the observed and the calculated defor¬
mation of circular flat plates, which it is hoped will
lead to an understanding of the yielding in the rectan¬
gular plates also.
Inelastic behavior of duralumin and alloy steels in ten¬
sion and compression. — The investigation of stress-strain
curves of sheet material in tension and compression has
been continued. A large number of tensile and “pack”
compressive tests have been made on specimens cut
with and across the direction of rolling from sheet
ranging in thickness from 0.032 to 0.081 inch. Stress-
strain curves have been obtained for aluminum alloys
17ST, 24ST, 24SRT, Alclad 17ST, and Alclad 24 ST.
The difference in yield strength in compression as com¬
pared to tension was found to be of the order of 10 to
15 percent. The data suggest that the compressive
yield strength of sheet material in the direction of
rolling can, in general, be approximated roughly by the
tensile yield strength at right angles to that direction,
and vice versa.
The accuracy of the pack compression test was in¬
vestigated by comparing the stress-strain curves ob¬
tained on solid specimens of cold-rolled steel, aluminum
alloy, and brass 0.7 by 0.7 inch in section, with stress-
37
REPORT NATIONAL ADVISORY
strain curves from pack compression tests on packs
built up from leaves cut from the same bar stock. The
two sets of stress-strain curves were found to agree
within ±2 percent.
The pack compression tests on 24SRT aluminum
alloy had shown a value of Young’s modulus which was
consistently higher by about 3 percent than the Young’s
modulus in tension. This difference could not be
ascribed to errors in the compression tests. Preliminary
tests indicated it to be due to a continuous increase in
the slope of the stress-strain curve in passing from small
tensile stresses through zero to small compressive
stresses.
Tubes with torsional loads. — The report on torsion tests
of 01 chromium-molybdenum-steel tubes and of 102
17ST aluminum-alloy tubes was completed and will be
published as Technical Report No. 601 of the National
Advisory Committee for Aeronautics.
A comparison of the empirical formulas proposed in
this report with the torsional strength of tubes of 17ST
and 51SW aluminum alloy as tested at the Aluminum
Research Laboratories showed close agreement, al¬
though the tubes tested by the Aluminum Research Lab¬
oratories were considerably shorter and in the case of
the 51SW material had considerably different mechani¬
cal properties than the tubes tested at this Bureau. The
agreement may be ascribed to the use in the empirical
formulas of ratios involving the tensile properties of
the tube material.
Beams and stressed-skin research. — The program on
wing beams has been continued with the completion of
tests under axial load, transverse load, combined axial
and transverse loads, of eight wing-beam specimens of
aluminum alloy with an I-type section having tilted
flanges. Failure in these beams occurred by local insta¬
bility of one of the flanges. The measured strains and
deflections are being analyzed with the help of com¬
pressive stress-strain curves for the flange material
which were obtained by the pack method. Failure of
the combined-load specimens occurred at a flange stress
calculated from the loads which ranged from 34,700 to
36.400 pounds per square inch.
The analysis of the data obtained on the two sheet-
stringer panels tested in end compression at the National
Bureau of Standards has been completed. Comparison
with the results of similar tests at the Navy Model
Basin on panels of the same design showed good agree¬
ment for the load carried by the sheet at failure. The
load carried by stringers at failure was found to be
about 10 to 20 percent lower for two of the specimens
tested at the Model Basin. This relative loss in strength
is probably due to the difference in end restraint, the
flat end condition used at the Model Basin providing
less restraint against buckling than the casting of the
COMMITTEE FOR AERONAUTICS
ends in Wood’s metal used at the National Bureau of
Standards.
The measured strain distribution in the sheet of the
two panels tested at the National Bureau of Standards
and the measured buckle shape were compared with the
deformation calculated from approximate theories de¬
veloped by S. Timoshenko, by J. M. Frankland, and by
K. Marguerre. None of the approximate theories was
found to agree accurately with observed deformations.
The deflections of the buckled sheet were best described
by Timoshenko’s theory, the axial strains were about
equally well described by all three theories, the trans¬
verse strains were best described by Frankland’s theory,
and the sheet load was best described by Marguerre’s
theory.
The analysis of the deformation of the stringers in
the sheet-stringer panels was confined to a series of plots
of deformation against deformation over load in accord¬
ance with Southwell’s method. If the deformation
plotted leads to an instability of the type to which
Southwell’s relation applies, all points will lie on a
straight line with a slope equal to the elastic buckling
load. Excellent straight lines could be obtained for
some of the stringer twists as measured by the rotation
of pointers mounted on the stringer, the slope of the
lines being in close agreement with the observed buck¬
ling load. The agreement was less satisfactory for plots
of other deformations. The lack of general agreement
is not surprising, since a proof for the validity of South¬
well’s method has been given so far only for the column
failure of beams under eccentric axial load and under
certain combinations of axial and transverse loads.
Eighteen sheet-stringer panels are being fabricated at
the Naval Aircraft Factory for the investigation of the
effect on the compressive strength of such panels of
rivet spacing and spot-spacing. The panels will be 12
and 18 inches long and will consist of three Z-type
stringers fastened to the sheet by rivets or spots spaced
an amount ranging from y2 to 4 inches. The spacing
between stringers, the sheet thickness, and the spacing
between rivets or spots will be varied to explore the
effect of rivet spacing on both the buckling of the sheet
between rivets and on the effective width of the sheet
between stringers.
Airplane vibration. — Close cooperation was main¬
tained with the Bureau of Aeronautics of the Navy
Department in its program on airplane vibration. The
National Bureau of Standards participated actively in
a number of conferences at which methods were dis¬
cussed for recording the readings of vibration pick-ups
and of strain pick-ups mounted on various portions of
an airplane in flight.
An important part of the program is the development
of dynamic-strain pick-ups suitable for attachment to
38
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the structural parts of an airplane. In connection with
this work a number of special strain pick-ups have been
built by the Sperry Gyroscope Company which em¬
bodied a principle of inertia compensation suggested by
William M. Bleakney, of the Engineering Mechanics
Section of this Bureau. A description of this principle
has appeared in the Journal of Research of the National
Bureau of Standards for June 1937 under the title
“Compensation of Strain Gages of Vibration and Im¬
pact,” by William M. Bleakney. Three of the experi¬
mental pick-ups built by the Sperry Gyroscope Com¬
pany were tested for compensation and for ruggedness
of construction on a device subjecting them to accelera¬
tions up to 50 times gravity with negligible strain.
Compensation for inertia forces adequate for present
applications was obtained on one of these after a num¬
ber of small adjustments had been made. The cali¬
brations also suggested a number of changes in the
design of the gage which would probably improve its
operation.
A second type of strain pick-up on which consider¬
able work was done at the Bureau is the strain pick-up
of the carbon-resistance type developed by A. V. de-
Forest. Static and dynamic calibrations were made on
20 carbon resistance strips, 5 of them of the “granular”
type used at the Hamilton Standard Propeller Com¬
pany, and the remaining 15 of the so-called “Ess-strip”
type. A report describing the results of these tests in
detail has been forwarded to the Bureau of Aeronautics
of the Navy Department. The report gives quantita¬
tive results for the effect of frequency, strain amplitude,
time under load, and temperature on the calibration of
a number of these strain pick-ups.
The best dynamic characteristics were found for the
gages of the “Ess-strip” type. These gages showed a
resistance amplitude that was nearly proportional to
the strain amplitude up to strains of 0.001 (correspond¬
ing to stresses of about 10.000 pounds per square inch in
aluminum alloy). The calibration factor calculated by
dividing the constant of proportionality by the direct-
current resistance of the gage was independent of fre¬
quency between 30 and 100 cycles per second within
±10 percent, independent of temperature between
-10° C. and 40° C. within ±10 percent, independent of
time for one day within ±5 percent and for 40 days
within ±9 percent.
The static Calibration tests, which were confined to
gages of the “Ess-strip” type, gave calibration fac¬
tors ranging from 40 percent below to 35 percent above
the dynamic calibration factors. The effect of tempera¬
ture variations and of time under load were found to be
sufficient to render this type of strain gage very much
inferior to accepted gages such as the Tuckerman opti¬
cal strain gage or the Huggenberger extensometer in
those cases where static strains on a large structure are
to be measured.
The dynamic calibrations of “Ess-strips,” which were
made by attaching the gage to a propeller blade and
then vibrating this blade in resonance, had indicated
the need for a calibrator that would subject the strips
to uniform sinusoidal strains of sufficient amplitude and
of a frequency that could be varied over a wider range
than the restricted number of resonance frequencies (30
to 100 cycles per second) that could be set up in the
propeller blades. A device was accordingly designed
for calibrating dynamic-strain gages up to 8 inches in
length by subjecting them to uniform sinusoidal strains
up to 0.001 at frequencies ranging from 10 to 200 cycles
per second. This device is now being constructed.
Strength of riveted joints in aluminum alloy. — The in¬
vestigation described in Technical Note 585 of the Na¬
tional Advisory Committee for Aeronautics has been
extended to joints in which combinations of the follow¬
ing alloys were used: rivets, A17ST, 53SW, 53ST, and
24ST : and sheet, 24ST, 24SRT, and Alclad 24ST.
In accordance with the suggestions of manufacturers,
tests have been made to determine whether the results
previously obtained on 0.25-inch rivets are applicable
to rivets of other sizes. Single shear and double shear
tests made so far on rivets ranging from %2 to 5/16
inch in diameter indicate that for practical purposes
there is no difference between the results obtained on
the various sizes. The driving stress required to form
a flat head of a given size was found to increase slightly
with the diameter of the rivet, but this tendency was
not observed for button heads.
Tests to determine the effect of aging upon the driving
stress required to form the head, the shearing strength
of rivets of the various alloys, and the mechanical prop¬
erties of rivet wire are being carried out.
To supply information needed by the industry on
riveted joints of the flush type, specifications for joints
to be made by manufacturers have been prepared and
distributed. Several sets of specimens have been re¬
ceived, and these are now being tested. Other flush
riveted specimens are being made at this Bureau.
A set of fixtures has been constructed for driving
rivets by means of a pneumatic hammer in a manner
which minimizes the personal element in the heading
process.
Investigation of fatigue resistance of fabricated struc¬
tural elements of aircraft. — The fatigue test on the rear
upper wing beam of a BF2C-1 airplane was followed
by a similar test on the front beam of the same wing
cell. The test was carried to failure at a nominal stress
amplitude of about 5,700 pounds per square inch, as
compared to a nominal stress amplitude of about 8,500
pounds per square inch for the first test. After about
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
39
2,900,000 cycles one flange parted with a sharp report
at a section where a rib attachment had been riveted
to the flange. Several other cracks were found in the
same flange, and a large crack was found in the web
just outside one terminal attachment. Comparison of
the stress history with the endurance curve of similar
material indicated a stress concentration factor of about
3.7. This is considerably higher than the stress con¬
centration factor of about 3 derived for the first test,
and indicates that the fatigue limit of the fabricated
structure may be well below one-third the fatigue limit
of the material, perhaps as low as a nominal stress of
4.000 pounds per square inch.
Two complete sets of BF2C— 1 wings have been sup¬
plied by the Navy Department for the fatigue tests.
The wing beams have been removed from these wings,
and a method of cutting them has been devised which
will give eight wing-beam specimens of sufficiently uni¬
form section for the tests. It is planned to test these
specimens at different amplitudes of nominal stress in
order to obtain a sufficient number of values of stress
against cycles to failure to draw a S-N curve for the
fabricated wing beam, which may then be compared
with the S-N curve of the wing-beam material. The
first of these eight specimens is being set up for test
in the fatigue machine.
PART II
ORGANIZATION ANT) GENERAL ACTIVITIES
ORGANIZATION
The National Advisory Committee for Aeronautics
was established by act of Congress approved March 3,
1915 (U. S. Code, title 50, sec. 151). The Committee
is composed of fifteen members appointed by the Presi¬
dent and serving as such without compensation. The
law provides that the members shall include two repre¬
sentatives each from the War and Navy Departments
and one each from the Smithsonian Institution, the
Weather Bureau, and the National Bureau of Stand¬
ards, together with not more than eight additional per¬
sons “who shall be acquainted with the needs of aero¬
nautical science, either civil or military, or skilled in
aeronautical engineering or its allied sciences.” One
of these eight is a representative of the Bureau of Air
Commerce of the Department of Commerce. Under
the rules and regulations governing the work of the
Committee as approved by the President the Chairman
and Vice Chairman of the Committee are elected an¬
nually. At the meeting held on October 21, 1937, Dr.
Joseph S. Ames was reelected Chairman for the ensu¬
ing year and Dr. David W. Taylor was reelected Vice
Chairman.
Dr. Joseph S. Ames resigned as Chairman of the
Executive Committee in April 1937, a position he had
filled continuously since October 9, 1919. At the meet¬
ing held on April 22, 1937, Dr. Willis Bay Gregg, Chief
of the Weather Bureau, was elected to fill out Dr.
Ames’ unexpired term as Chairman of the Executive
Committee. At the meeting held on October 21, 1937,
Dr. Gregg was elected Chairman of the Executive Com¬
mittee for the ensuing year and Dr. William P. Mac-
Cracken Vice Chairman of the Executive Committee.
Dr. David W. Taylor had served as Vice Chairman of
the Executive Committee since that position was cre¬
ated in 1927. He remains Vice Chairman of the main
Committee.
During the past year there was one change in the
membership of the main Committee. Dr. Fred D.
Fagg, Jr., who had succeeded Honorable Eugene L.
Vidal as Director of Air Commerce of the Department
of Commerce, was, on April 23, 1937, appointed by the
President to succeed Mr. Vidal as a member of the
National Advisory Committee for Aeronautics.
The executive offices of the Committee, including its
offices of aeronautical intelligence and aeronautical in¬
ventions, are located in the Navy Building, Washing¬
ton, D. C., in close proximity to the air organizations
of the Army and Navy.
The office of aeronautical intelligence was established
in the early part of 1918 as an integral branch of the
Committee’s activities. Scientific and technical data
on aeronautics secured from all parts of the world are
classified, catalogued, and disseminated by this office.
To assist in the collection of current scientific and
technical information and data, the Committee main¬
tains a technical assistant in Europe with headquarters
at the American Embassy in Paris.
CONSIDERATION OF AERONAUTICAL INVENTIONS
By act of Congress approved July 2, 1926, an Aero¬
nautical Patents and Design Board was established con¬
sisting of Assistant Secretaries of the Departments of
War, Navy, and Commerce. In accordance with that
act as amended by the act approved March 3, 1927, the
National Advisory Committee for Aeronautics passes
upon the merits of aeronautical inventions and designs
submitted to any aeronautical division of the Govern¬
ment and submits reports thereon to the Aeronautical
Patents and Design Board. That board is authorized,
upon the favorable recommendation of the Committee,
to “determine whether the use of the design by the
Government is desirable or necessary and evaluate the
design and fix its worth to the United States in an
amount not to exceed $75,000.”
During the past year the inventions section received
for consideration 1,475 new submissions. It conducted
the necessary correspondence and granted interviews as
requested by the inventors. Approximately six per¬
cent of the new submissions were received through the
Aeronautical Patents and Design Board. In those
cases reports on the merits of the submissions were
made to that board, and in all other cases replies were
submitted directly to the inventors.
40
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
41
AERONAUTICAL RESEARCH IN EDUCATIONAL
INSTITUTIONS
In continuation of the plan initiated as a result of
recommendation of the Federal Aviation Commission,
a special allotment of $25,000 was made available from
the Committee’s funds during the fiscal year 1937 for
aeronautical research in educational institutions. Un¬
der this allotment eleven contracts were made during
the year with five universities and technical schools, for
special investigations and reports on the basis of the
probable usefulness and value of the information to
aeronautics.
Several of the papers prepared under contracts made
the preceding year have been published by the Com¬
mittee, while others have supplied information of value
as a basis for further research either at the Committee’s
laboratory or elsewhere. The papers received under
contracts which have been published by the Committee
include one technical report and three technical notes.
In addition, one paper has been issued in advance con¬
fidential form to American manufacturers.
COOPERATION WITH THE AVIATION INDUSTRY
The Committee, in the preparation of its program of
research, makes provision for the requirements of
the aviation industry as to problems to be investi¬
gated, both in connection with design and opera¬
tion. The aircraft manufacturers and operators bring
their problems to the Committee’s attention as they
arise, either by correspondence or by personal contacts
and informal conferences. Advantage is taken by the
Committee of every opportunity to obtain suggestions
and recommendations from representatives of the in¬
dustry as to investigations which are of particular im¬
portance to them. When the need arises in connection
with any particular problem of the industry it is the
policy of the Committee to call a special conference, or,
as previously stated, to establish a special subcommittee,
including in either case representation from the
industry.
Realizing that frequently the value of information is
greatly enhanced by its prompt availability, every effort
is made to place in the hands of the industry at the
earliest possible date the results of researches that are
of particular interest to commercial aeronautics. It
sometimes appears, in the course of an extensive inves¬
tigation being conducted by the Committee, that the
results so far obtained will be of special interest and
value to the aircraft industry if made available
immediately. In such cases the Committee issues the
information in advance confidential form to American
manufacturers and the Government services.
Some of the subjects on which results have been re¬
leased in this manner during the past year are the pre¬
vention of ice formation on propellers; the characteris¬
tics of related forward camber airfoils, from tests in
the variable-density wind tunnel ; the characteristics of
tapered wings having X. A. C. A. mean lines; the char¬
acteristics of tandem air propellers, as investigated by
Stanford University under contract with the Commit¬
tee; wing-fuselage interference, including in the first
report a comparison of conventional and airfoil-type
fuselage combinations, and in the second report the
characteristics of thirty combinations, from tests in the
variable-density wind tunnel ; transparent plastics for
use on aircraft, as investigated by the National Bureau
of Standards for the Committee; tricycle-type landing
gears, including three phases of the subject — first, accel¬
erations in landing, second, factors affecting the geo¬
metrical arrangement ; and third, the stability of cas¬
tering wheels; and the characteristics of tapered wings
with ordinary ailerons and partial-span split flaps, as
determined in wind-tunnel investigation.
Annual research conference. — As an important aid in
keeping in close contact with the problems and needs
of the aviat ion industry, the Committee holds each May
at its laboratories at Langley Field an aircraft engi¬
neering research conference with representatives of
aircraft manufacturers and operators. This conference
was initiated in 1926, and has two principal purposes,
as follows: First, to enable representatives of the in¬
dustry to obtain first-hand information on the Com¬
mittee’s research facilities and the results obtained in
its investigations; and, second, to afford them an op¬
portunity to present to the Committee their suggestions
for investigations to be included in the Committee's
research program.
Owing to the large number of those who desired to
attend, the conference for the past two years has been
held on two days, the same program of discussions and
demonstrations being followed both days. The dates
of the 1937 conference were May 18 and 20.
Acting under authorization of Dr. Joseph S. Ames,
Chairman of the National Advisory Committee for
•j
Aeronautics, who was prevented by illness from being
present, Honorable Edward P. Warner, a member of
the Committee and Chairman of the Committee on
Aerodynamics, served as Chairman of the conference
on May 18; and on May 20 Dr. Willis Ray Gregg,
Chairman of the Executive Committee of the National
Advisory Committee for Aeronautics, was Chairman.
The Committee was represented on both days by officers
and members, and on May 18 also by its Committees on
Aerodynamics and Power Plants for Aircraft, and on
the 20th by its Committee on Aircraft Structures and
Materials and Subcommittee on Structural Loads and
Methods of Structural Analysis.
At the morning session each day the principal in¬
vestigations under way at the laboratory, both in aero-
42
REPORT NATIONAL ADVISORY
dynamics and power plants, were explained by the
engineers in charge of the work, and charts were ex¬
hibited showing some of the results obtained. The
guests were then conducted on a tour of inspection of
the laboratory and the research equipment was shown
in operation.
In the afternoon six simultaneous conferences were
held for the discussion of six different subjects, namely,
airplane performance and design characteristics, aero¬
dynamic efficiency and interference, cowling and cool¬
ing research, aircraft-engine research, seaplanes, and
rotorplanes. At these conferences the results of the
Committee’s researches were presented in further de¬
tail, and suggestions were submitted by the representa¬
tives of the industry for problems to be added to the
Committee’s program. Each of these suggestions, ac¬
cording to its nature, was referred to the Committee
on Aerodynamics, the Committee on Power Plants for
Aircraft, or the Subcommittee on Structural Loads
and Methods of Structural Analysis and was con¬
sidered by that committee in the preparation of the
research program being carried on under its cogni¬
zance.
SUBCOMMITTEES
The Advisory Committee has organized four main
standing technical committees, with subcommittees, for
the purpose of supervising its work in their respective
fields. The four main technical Committees on Aero¬
dynamics, Power Plants for Aircraft, Aircraft Mate¬
rials, and Aircraft Structures and their subcommittees
supervise and direct the aeronautical research con¬
ducted by the Advisory Committee and coordinate the
investigations conducted by other agencies.
As previously stated, during the past year there has
been a major change in the organization of the Com¬
mittee’s standing technical committees. The Commit¬
tee on Aircraft Structures and Materials, which was
one of the three principal technical committees, and
two of its subcommittees, the Subcommittee on Struc¬
tural Loads and Methods of Structural Analysis and
the Subcommittee on Research Program on Monocoque
Design, were discharged, and two new standing com¬
mittees, the Committee on Aircraft Materials and the
Committee on Aircraft Structures, were established,
each with a status coordinate with that of the Commit¬
tee on Aerodynamics and the Committee on Power
Plants for Aircraft. The Subcommittee on Metals
Used in Aircraft and the Subcommittee on Miscellane¬
ous Materials and Accessories were retained as subcom¬
mittees of the new Committee on Aircraft Materials.
The work of the standing technical committees and
subcommittees has been described in part I.
The organization of the committees and of the
standing subcommittees is as follows :
COMMITTEE FOR AERONAUTICS
COMMITTEE ON AERODYNAMICS
Hon. Edward P. Warner, Chairman.
Dr. George W. Lewis, National Advisory Committee for
Aeronautics, Vice Chairman.
Maj. II. Z. Bogert, Air Cox-ps, United States Army, Materiel
Division, Wright Field.
Dr. L. J. Briggs, National Bureau of Standards.
Theophile dePort, Matdriel Division, Army Air Corps,
Wright Field.
Lt. Comdr. W. S. Diehl, United States Navy.
Dr. II. L. Dryden, National Bureau of Standards.
Lt. Col. O. P. Echols, Air Corps, United States Army,
Materiel Division, Wright Field.
Richard C. Gazley, Bureau of Air Commerce, Department
of Commerce.
Lt. Comdr. L. M. Grant, United States Navy.
Dr. Willis Ray Gregg, United States Weather Bureau.
Lawrence V. Kerber, Bureau of Air Commerce, Department
of Commerce.
Delbert M. Little, United States Weather Bureau.
Elton W. Miller, National Advisory Committee for Aero¬
nautics.
Comdr. F. W. Pennoyer, Jr., United States Navy.
H. J. E. Reid, National Advisory Committee for Aero¬
nautics.
Dr. David W. Taylor.
Dr. A. F. Zahm, Division of Aeronautics, Library of Con¬
gress.
SUBCOMMITTEE ON AIRSHIPS
Hon. Edward P. Warner, Chairman.
Starr Truscott, National Advisory Committee for Aero¬
nautics, Vice Chairman.
Dr. Karl Arnstein, Goodyear-Zeppelin Corpox-ation.
Maj. H. Z. Bogert, Air Corps, United States Army, Materiel
Division, Wright Field.
Commander Garland Fulton, United States Navy.
Dr. Geoi’ge W. Lewis, National Advisory Committee for
Aeronautics (ex officio member).
Ralph H. Upson, Ann Arbor, Mich.
SUBCOMMITTEE ON METEOROLOGICAL PROBLEMS
Dr. Willis Ray Gregg, United States Weather Bureau,
Chairman.
Dr. W. .T. Humphreys, United States Weather Bureau.
Dr. J. C. Hunsaker, Massachusetts Institute of Technology.
Dr. George W. Lewis, National Advisory Committee for
Aeronautics (ex officio member).
Delbert M. Little, United States Weather Bureau.
Dr. Charles F. Marvin.
Lt. Comdr. F. W. Reiclielderfer, United States Navy, Naval
Air Station, Lakehurst.
Dr. C. G. Rossby, Massachusetts Institute of Technology.
Maj. B. J. Sherry, United States Army, Signal Corps, War
Department.
Eugene Sibley, Bureau of Air Commerce, Department of
Commerce.
SUBCOMMITTEE ON SEAPLANES
Capt. H. C. Richardson, United States Navy, Chairman.
Maj. II. Z. Bogert, Air Coi’ps, United States Army, Materiel
Division, Wright Field.
Theophile dePort, Matdriel Division, Army Air Corps, Wright
Field.
Lt. Comdr. W. S. Diehl, United States Navy-
43
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Richard C. Gazley, Bureau of Air Commerce, Department of
Commerce.
Jack T. Gray, Bureau of Air Commerce, Department of
Commerce.
Dr. George W. Lewis, National Advisory Committee for
Aeronautics (ex officio member).
Lt. Comdr. A. O. Rule, United States Navy.
Starr Truscott, National Advisory Committee for Aero¬
nautics.
COMMITTEE ON POWER PLANTS FOR AIRCRAFT
Dr. William P. MacCracken, Chairman.
r>r. George W. Lewis, National Advisory Committee for
Aeronautics, Vice Chairman.
Lt. Comdr. Rico Botta, United States Navy.
Dr. H. C. Dickinson, National Bureau of Standards.
John H. Geisse, Bureau of Air Commerce, Department of
Commerce.
Carlton Kemper, National Advisory Committee for Aero¬
nautics.
Gaylord W. Newton, Bureau of Air Commerce, Department
of Commerce.
Maj. E. R. Page, Air Corps, United States Army, Materiel
Division, Wright Field.
Prof. C. Fayette Taylor, Massachusetts Institute of Tech¬
nology.
SUBCOMMITTEE ON AIRCRAFT FUELS AND LUBRICANTS
Dr. H. C. Dickinson, National Bureau of Standards, Chair¬
man.
Lt. Comdr. Rico Botta, United States Navy.
Dr. O. C. Bridgeman, National Bureau of Standards.
Lt. Comdr. James V. Carney, United States Navy.
LI. K. Cummings, National Bureau of Standards.
L. S. Hobbs, The Pratt and Whitney Aircraft Company.
Robert V. Kerley, Materiel Division, Army Air Corps, Wright
Field.
Dr. George W. Lewis, National Advisory Committee for
Aeronautics (ex officio member).
Gaylord W. Newton, Bureau of Air Commerce, Department
of Commerce.
Arthur Nutt, Wright Aeronautical Corporation.
Maj. E. R. Page, Air Corps, United States Army, Materiel
Division, Wright Field.
Addison M. Rothrock, National Advisory Committee for
Aeronautics.
COMMITTEE ON AIRCRAFT MATERIALS
Dr. L. J. Briggs, National Bureau of Standards, Chairman.
Prof. H. L. Whittemore, National Bureau of Standards, Vice
Chairman.
Maj. H. Z. Bogert, Air Corps, United States Army, Materiel
Division, Wright Field.
S. Iv. Colby, Aluminum Co. of America.
Lt. Comdr. C. F. Cotton, United States Navy.
Edgar H. Dix, Jr., American Magnesium Corporation.
Warren E. Emley, National Bureau of Standards.
Comdr. Garland Fulton, United States Navy.
Richard C. Gazley, Bureau of Air Commerce, Department of
Commerce.
Jack T. Gray, Bureau of Air Commerce, Department of
Commerce.
C. H. Helms, National Advisory Committee for Aeronautics.
J. B. Johnson, Materiel Division, Army Air Corps, Wright
Field.
Dr. George W. Lewis, National Advisory Committee for Aero¬
nautics (ex officio member).
II. S. Rawdon, National Bureau of Standards.
E. C. Smith, Republic Steel Corporation.
Paul F. Voigt, Jr., Carnegie-Ulinois Steel Corporation.
Hon. Edward P. Warner.
SUBCOMMITTEE ON METALS USED IN AIRCRAFT
H. S. Rawdon, National Bureau of Standards, Chairman.
E. H. Dix, Jr., American Magnesium Corporation.
Comdr. Garland Fulton, United States Navy.
J. B. Johnson, Materiel Division, Army Air Corps, Wright
Field.
Dr. George W. Lewis, National Advisory Committee for Aero¬
nautics (ex officio member).
E. C. Smith, Republic Steel Corporation.
John Vitol, Bureau of Air Commerce, Department of Com¬
merce.
Prof. II. L. Whittemore, National Bureau of Standards.
SUBCOMMITTEE ON MISCELLANEOUS MATERIALS AND
ACCESSORIES
Warren E. Emley, National Bureau of Standards, Chairman.
C. J. Cleary, Materiel Division, Army Air Corps, Wright
Field.
John Easton, Bureau of Air Commerce, Department of Com¬
merce.
C. II. Helms, National Advisory Committee for Aeronautics.
E. F. Hickson, National Bureau of Standards.
Dr. George W. Lewis, National Advisory Committee for Aero¬
nautics (ex officio member).
J. E. Sullivan, Bureau of Aeronautics, Navy Department.
G. W. Trayer, Forest Service, Department of Agriculture.
COMMITTEE ON AIRCRAFT STRUCTURES
Dr. L. J. Briggs, National Bureau of Standards, Chairman.
Richard C. Gazley, Bureau of Air Commerce, Department of
Commerce.
Lt. Comdr. L. M. Grant, United States Navy.
Maj. C. F. Greene, Air Corps, United States Army, Materiel
Division, Wright Field.
Capt. Paul H. Kemmer, Air Corps, United States Army, Ma¬
teriel Division, Wright Field.
Dr. George W. Lewis, National Advisory Committee for Aero¬
nautics (ex officio member).
Eugene E. Lundquist, National Advisory Committee for Aero¬
nautics.
Lt. Comdr. R. D. MacCart, United States Navy.
Prof. Joseph S. Newell, Massachusetts Institute of Technology.
Dr. Walter Ramberg, National Bureau of Standards.
Richard V. Rhode, National Advisory Committee for Aero¬
nautics.
Edward I. Ryder, Bureau of Air Commerce, Department of
Commerce.
R. L. Templin, Aluminum Company of America.
Dr. L. B. Tuckerman, National Bureau of Standards.
Hon. Edward P. Warner.
COMMITTEE ON AIRCRAFT ACCIDENTS
Hon. Edward P. Warner, Chairman.
Lt. J. F. Greenslade, United States Navy.
Maj. E. V. Harbeck. Jr., Air Corps, United States Army.
J. W. Lankford, Bureau of Air Commerce, Department of
Commerce.
Dr. George W. Lewis, National Advisory Committee for
Aeronautics.
44
REPORT NATIONAL ADVISORY
Lt. Conitlr. A. O. Rule, United States Navy.
J. T. Shumate, Bureau of Air Commerce, Department of
Commerce.
Maj. Lowell H. Smith, Air Corps, United States Army.
COMMITTEE ON AERONAUTICAL INVENTIONS AND
DESIGNS
Dr. L. J. Briggs, National Bureau of Standards, Chairman.
Dr. Willis Ray Gregg, United States Weather Bureau.
Capt. S. M. Kraus, United States Navy.
Brig. Gen. A. W. Robins. Air Corps, United States Army.
Materiel Division, Wright Field.
Dr. David W. Taylor.
John F. Victory, Secretary.
COMMITTEE ON PUBLICATIONS AND INTELLIGENCE
Dr. Joseph S. Ames, Chairman.
Dr. Willis Ray Gregg, United States Weather Bureau, Vice
Chairman.
Miss M. M. Muller, Secretary.
COMMITTEE ON PERSONNEL, BUILDINGS, AND
EQUIPMENT
Dr. Joseph S. Ames, Chairman.
Dr. David W. Taylor, Vice Chairman.
Dr. Willis Ray Gregg, United States Weather Bureau.
John F. Victory, Secretary.
TECHNICAL PUBLICATIONS OF THE COMMITTEE
The Committee has four series of publications,
namely technical reports, technical notes, technical mem¬
orandums, and aircraft circulars.
The technical reports present the results of funda¬
mental research in aeronautics. The technical notes are
mimeographed and present the results of short research
investigations and the results of studies of specific de¬
tail problems which form parts of long investigations.
The technical memorandums are mimeographed and
contain translations and reproductions of important for¬
eign aeronautical articles. The aircraft circulars are
mimeographed and contain descriptions of new types of
foreign aircraft.
The following are lists of the publications issued :
LIST OF TECHNICAL REPORTS ISSUED DURING THE
PAST YEAR
No.
577. Prechamber Compression-Ignition Engine Performance.
By Charles S. Moore and John H. Collins, Jr., N. A. C. A.
57S. Flight Measurements of the Dynamic Longitudinal Sta¬
bility of Several Airplanes and a Correlation of the
Measurements with Pilots’ Observations of Handling
Characteristics. By Hartley A. Soule, N. A. C. A.
570. A Study of the Two-Control Operation of an Airplane.
By Robert T. Jones, N. A. C. A.
5S0. Heat Transfer to Fuel Sprays Injected into Heated
Gases. By Robert F. Selden and Robert C. Spencer,
N. A. C. A.
581. Measurements of Intensity and Scale of Wind-Tunnel
Turbulence and Their Relation to the Critical Reynolds
Number of Spheres. By Hugh L. Dryden, G. B. Schu-
bauer, W. C. Mock, Jr., and H. K. Skramstad, National
Bureau of Standards.
COMMITTEE FOR AERONAUTICS
582. A Theory for Primary Failure of Straight Centrally
Loaded Columns. By Eugene E. Lundquist and Claude
M. Fligg, N. A. C. A.
583. The Rolling Friction of Several Airplane Wheels and
Tires and the Effect of Rolling Friction on Take-Off,
By J. W. Wetmore, N. A. C. A.
584. Strength of Welded Aircraft Joints. By IV. C. Bruegge-
man, National Bureau of Standards.
585. Span Load Distribution for Tapered Wings with Partial-
Span Flaps. By II. A. Pearson, N. A. C. A.
556. Airfoil Section Characteristics as Affected by Variations
of the Reynolds Number. By Eastman N. Jacobs and
Albert Sherman, N. A. C. A.
557. Blower Cooling of Finned Cylinders. By Oscar W. Schey
and Herman II. Ellerbrock, Jr., N. A. C. A.
58S. Fuel Spray and Flame Formation in a Compression-
Ignition Engine Employing Air Flow. By A. M. Roth-
rock and C. D. Waldron, N. A. C. A.
5S9. An Analysis of Lateral Stability in Power-Off Flight with
Charts for Use in Design. By Charles II. Zimmerman,
N. A. C. A.
590. Pressure-Distribution Measurements on an 0-2II Airplane
in Flight. By H. A. Pearson, N. A. C. A.
591. An Analytical and Experimental Study of the Effect of
Periodic Blade Twist on the Thrust, Torque, and Flap¬
ping Motion of an Autogiro Rotor. By John B. Wheat-
ley, N. A. C. A.
592. Full-Scale Tests of N. A. C. A. Cowlings. By Theodore
Theodorsen, M. J. Brevoort, and George W. Stickle,
N. A. C. A.
593. Cooling of Airplane Engines at Low Air Speeds. By-
Theodore Theodorsen, M. J. Brevoort, and George W.
Stickle, N. A. C. A.
594. Characteristics of Six Propellers Including the High-
Speed Range. By Theodore Theodorsen, George W.
Stickle, and M. J. Brevoort, N. A. C. A.
595. Full-Scale Tests of a New Type N. A. C. A. Nose-Slot
Cowling. By Theodore Theodorsen, M. J. Brevoort,
George W. Stickle, and M. N. Gough, N. A. C. A.
596. Cooling Tests of a Single-Row Radial Engine with Sev¬
eral N. A. C. A. Cowlings. By M. .T. Brevoort, George
W. Stickle, and Herman II. Ellerbrock, Jr., N. A. C. A.
597. Air Propellers in Yaw. By E. P. Lesley, George F. Wor-
ley, and Stanley Moy, Stanford University.
598. Alternating-Current Equipment for the Measurement of
Fluctuations of Air Speed in Turbulent Flow. By
W. C. Mock, Jr., National Bureau of Standards.
599. Flight Tests of the Drag and Torque of the Propeller in
Terminal-Velocity Dives. By Richard V. Rhode and
Henry A. Pearson, N. A. C. A.
600. An Analysis of the Factors That Determine the Periodic
Twist of an Autogiro Rotor Blade, with a Comparison
of Predicted and Measured Results. By John B.
Wheatley, N. A. C. A.
601. Torsion Tests of Tubes. By Ambrose H. Stang, Walter
Ramberg, and Goldie Back, National Bureau of
Standards.
602. Wind-Tunnel and Flight Tests of Slot-Lip Ailerons. By
Joseph A. Shortal, N. A. C. A.
603. Wind-Tunnel Investigation of Wings with Ordinary Ailer¬
ons and Full-Span External-Airfoil Flaps. By Robert
C. Platt and Joseph A. Shortal, N. A. C. A.
604. Pressure-Distribution Measurements at Large Angles of
Pitch on Fins of Different Span-Chord Ratio on a 1/40-
Scale Model of the U. S. Airship “Akron.” By James G.
McHugh, N. A. C. A.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
45
605. Resume and Analysis of N. A. C. A. Lateral Control Re¬
search. By Fred E. Weick and Robert T. Jones, N. A.
C. A.
606. Electrical Thermometers for Aircraft. By John B. Peter-
son and S. H. J. Womack, National Bureau of Standards.
607. Spinning Characteristics of the NN2Y-1 Airplane Obtained
from the Spinning Balance and Compared with Results
from the Spinning Tunnel and from Flight Tests. By
M. J. Bamber and R. O. House, N. A. C. A.
60S. Stress Analysis of Beams with Shear Deformation of the
Flanges. By Paul Kuhn, N. A. C. A.
609. Experimental Investigation of Wind-Tunnel Interference
on the Downwash behind an Airfoil. By Abe Silverstein
and S. Katzoff, N. A. C. A.
610. Tests of Related Forward-Camber Airfoils in the Variable-
Density Wind Tunnel. By Eastman N. Jacobs, Robert
M. Pinkerton, and Harry Greenberg, N. A. C. A.
611. Wind-Tunnel Investigation of Tapered Wings with Or¬
dinary Ailerons and Partial-Span Split Flaps. By Carl
J. Wenzinger, N. A. C. A.
LIST OF TECHNICAL NOTES ISSUED DURING THE
PAST YEAR
No.
582. Analysis and Model Tests of Autogiro Jump Take-Off. By
John B. Wheatley and Carlton Bioletti, N. A. C. A.
5S3. Mixture Distribution in a Single-Row Radial Engine. By
Harold C. Gerrish and Fred Voss, N. A. C. A.
584. Effect of Several Factors on Cooling of a Radial Engine
in Flight. • By Oscar W. Schey and Benjamin Pinkel,
N. A. C. A.
585. Mechanical Properties of Aluminum-Alloy Rivets. By Wm.
C. Brueggeman, National Bureau of Standards.
556. The Reduction of Aileron Operating Force by Differential
Linkage. By Robert T. Jones and Albert I. Nerken,
N. A. C. A.
557. The Forces and Moments on Airplane Engine Mounts. By
Philip Donely, N. A. C. A.
588. Strain Measurements on Small Duralumin Box Beams in
Bending. By Paul Kuhn, N. A. C. A.
589. Theoretical Span Loading and Moments of Tapered Wings
Produced by Aileron Deflection. By H. A. Pearson,
N. A. C. A.
590. Hydrodynamic Tests in the N. A. C. A. Tank of a Model of
the Hull of the Short Calcutta Flying Boat. By Ken¬
neth E. Ward, N. A. C. A.
591. Full-Scale Span Load Distribution on a Tapered Wing
with Split Flaps of Various Spans. By John F. Parsons
and Abe Silverstein, N. A. C. A.
592. A Study of the Factors Affecting the Range of Airplanes.
By David Biermann, N. A. C. A.
593. Pressure Drop in Tubing in Aircraft Instrument Installa¬
tions. By W. A. Wiklhack, National Bureau of
Standards.
594. Tank Tests of Two Models of Flying-Boat Hulls to Deter¬
mine the Effect of Ventilating the Step. By John R.
Dawson, N. A. C. A.
595. Bending Tests of Circular Cylinders of Corrugated Alumi¬
num-Alloy Sheet. By Alfred S. Niles, John C. Buck-
waiter, and Warren D. Reed, Stanford University.
596. Full-Scale Wind-Tunnel and Flight Tests of a Fairchild 22
Airplane Equipped with a Zap Flap and Zap Ailerons.
By C. H. Dearborn and H. A. Soule, N. A. C. A.
597. Notes on the Calculation of the Minimum Horizontal Tail
Surface for Airplanes Equipped with Wing Flaps. By
Hartley A. Soule, N. A. C. A.
j
-Z598. Wind-Tunnel Tests of a Clark Y Wing with “Maxwell”
Leading-Edge Slots. By William E. Gauvain, N. A. C. A.
599. Charts Expressing the Time, Velocity, and Altitude Rela¬
tions for an Airplane Diving in a Standard Atmosphere.
By Id. A. Pearson, N. A. C. A.
600. Discharge Characteristics of a Double Injection- Valve Sin¬
gle-Pump Injection System. By Dana W. Lee and E. T.
Marsh, N. A. C. A.
601. The Lateral Instability of Deep Rectangular Beams. By
C. Dumont and H. N. Hill, Aluminum Company of
America.
602. Heat Transfer from Cylinders Having Closely Spaced Fins.
By Arnold E. Biermann, N. A. C. A.
003. A Preliminary Study of Flame Propagation in a Spark-
Ignition Engine. By A. M. Rothrock and R. C. Spencer,
N. A. C. A.
004. Full-Scale Wind-Tunnel and Flight Tests of a Fairchild
22 Airplane Equipped with External-Airfoil Flaps. By
Warren D. Reed and William C. Clay, N. A. C. A.
605. Noise from Propellers with Symmetrical Sections at Zero
Blade Angle. By A. F. Deming, N. A. C. A.
006. Empirical Corrections to the Span Load Distribution at
the Tip. By H. A. Pearson, N. A. C. A.
/ 607. The Behavior of Thin-Wall Monoeoque Cylinders Under
Torsional Vibration. By Robert E. Pekelsma, University
of Michigan.
608. Free-Spinning Wind-Tunnel Tests of a Low-Wing Mono¬
plane with Systematic Changes in Wings and Tails.
I — Basic Loading Condition. By Oscar Soidman and
A. I. Neihouse, N. A. C. A.
609. Considerations Affecting the Additional Weight Required
in Mass Balance of Ailerons. By W. S. Diehl, Bureau
of Aeronautics, Navy Department.
610. Effect of Air-Entry Angle on Performance of a 2-Stroke-
Cycle Compression-Ignition Engine. By Sherod L. Earle
and Francis J. Dutee, N. A. C. A.
611. The Sonic Altimeter for Aircraft. By C. S. Draper, Mas¬
sachusetts Institute of Technology.
612. Spinning Characteristics of Wings. Ill — A Rectangular
and a Tapered Clark Y Monoplane Wing with Rounded
Tips. By M. J. Bamber and R. O. House, N. A. C. A.
613. The Effect of Curvature on the Transition from Laminar
to Turbulent Boundary Layer. By Milton Clauser and
Francis Clauser, California Institute of Technology.
614. Fuselage-Drag Tests in the Variable-Density Wind Tunnel :
Streamline Bodies of Revolution, Fineness Ratio of 5.
By Ira II. Abbott, N. A. C. A.
615. Motion of the Two-Control Airplane in Rectilinear Flight
after Initial Disturbances with Introduction of Controls
Following an Exponential Law. By Alexander Klemin,
New York University.
LIST OF TECHNICAL MEMORANDUMS ISSUED DURING
THE PAST YEAR
No.
805. General Considerations on the Flow of Compressible Fluids.
By L. Prandtl. Paper presented at Volta meeting in
Italy, September 30 to October 6, 1935.
7806. The Question of Spontaneous Wing Oscillations (Deter¬
mination of Critical Velocity through Flight-Oscilla¬
tion Tests). By B. v. Scldippe. From Luftfalirtfors-
chung. February 20, 1936.
807. Torsion and Buckling of Open Sections. By Herbert Wag¬
ner. From the 25th anniversary number of the Tecli-
nische Hochscliule, Danzig 1904-1929.
46
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
808. High-Speed Wind Tunnels. By J. Ackeret. Paper pre¬
sented at the fifth convention of the Volta Congress,
Italy, September 30 to October 6, 1935.
S09. Tests for the Determination of the Stress Condition in
Tension Fields. By II. Lahde and H. Wagner. From
Luftfahrtforschung, August 20, 1936.
810. Impact of a Vee-Type Seaplane on Water with Refer¬
ence to Elasticity. By F. Weinig. From Luftfahrt¬
forschung. May 20, 1936.
811. The Impact on Floats or Hulls During Landing as Af¬
fected by Bottom Width. By E. Mewes. From Luft¬
fahrtforschung, May 20, 1936.
S12. The Horsepower of Aircraft Engines and Their Maximum
Frontal Area. By Michel Precoul. From L’Aeronau-
tique, No. 207, August 1936.
813. The Cetene Scale and the Induction Period Preceding the
Spontaneous Ignition of Diesel Fuels in Bombs. By M.
N. Michailova and M. B. Neumann. From Comptes
Rendus (Doklady) de l’Academie des Sciences de
PURSS, Vol. II (XI), No. 1 (90), 1936.
814. Experimental Studies of the Effective Width of Buckled
Sheets. By It. Lahde and H. Wagner. From Luftfahrt¬
forschung, July 20, 1936.
815. Automatic Stabilization. By Fr. Hans. From L’Aeronau-
tique, March 1936.
816. The Gyroplane — Its Principles and Its Possibilities. By
Louis Breguet. From Journees Techniques Internation¬
ales de l'Aeronautique, November 23-27, 1936.
817. The Stress Distribution in Shell Bodies and Wings as an
Equilibrium Problem. By H. Wagner. From Luftfahrt¬
forschung, September 20, 1936.
818. Valve-Spring Surge. By Willy Marti. Federal Polytech¬
nic Institute of Zurich. 1935.
819. Experimental Apparatus for the Study of Propellers. By
M. Panetti. From Experimental reports by the Aero¬
nautical Laboratory of the Royal Engineering Institute
of Turin, series 1.
820. Some Experiments on the Slipstream Effect. By C. Fer¬
rari. From Experimental reports by the Aeronautical
Laboratory of the Royal Engineering Institute of Turin,
series 2.
821. On the Actual Loads on Airplane Landing Gears. By S.
Shiskin. From Report No. 269, of the Central Aero-
Hydrodynamical Institute, Moscow, 1936.
822. Turbulent Boundary Layer of an Airfoil. By K. Fediaev-
sky. From Report No. 282, of the Central Aero-IIydro-
dynamical Institute, Moscow, 1936.
823. Experimental Investigation of the Problem of Surface
Roughness. By H. Schlichting. From Ingenieur-Ar-
cliiv, February 1936.
824. The Photoelastic Investigation of Three-Dimensional Stress
and Strain Conditions. By G. Oppel. From Forschung
auf dem Gebiete des Ingenieurwesens, September-October
1936.
825. The Source of Propeller Noise. By W. Ernsthausen. From
Luftfahrtforschung, December 20, 1936.
826. The Scale Effect in Towing Tests with Airplane-Float Sys¬
tems. By Rudolph Schmidt. From Luftfahrtforschung,
July 20. 1936.
827. Helicopter Problems. By H. G. Kiissner. From Luftfahrt¬
forschung, January 20, 1937.
828. Ground Effect — Theory and Practice. By E. Pistolesi.
From Pubblicazioni della R. Scuola dTngegneria di Pisa,
series 6, July 1935.
829.
S30.
831.
832.
v 833.
\j 834.
835.
836.
837.
838.
Method of Curved Models and Its Application to the Study
of Curvilinear Flight of Airships. Part I. By G. A.
Gourjienko. From Central Aero-Hydrodynamical In-
stitute, Moscow, Report No. 182, 1934.
Method of Curved Models and Its Application to the Study
of Curvilinear Flight of Airships. Part II. By G. A.
Gourjienko. From Central Aero-Hydrodynamical Insti¬
tute, Moscow, Report No. 182, 1934.
Contributions to the Theory of Incomplete Tension Bay,
By E. Scliapitz. From Luftfarhrtforschung, March 20,
1937.
The Critical Velocity of a Body Towed by a Cable from an
Airplane. By C. Ivoning and T. P. DeHaas. From
Rijks-Studiedienst voor de Luchtvaart, Amsterdam, Re¬
port A 367.
The Apparent Width of the Plate in Compression. By
Karl Marguerre. From Luftfahrtforschung, March 20,
1937.
The Stability of Orthotropic Elliptic Cylinders in Pure
Bending. By O. S. Heck. From Luftfahrtforschung,
March 20, 1937.
Pressure Distribution on a Wing Section with Slotted
Flap in Free Flight Tests. By Georg Kiel. From Luft¬
fahrtforschung, February 20, 1937.
The Ground Effect on Lifting Propellers. By A. Betz,
From Zeitsclirift fiir angewandte Mathematik und
Media nik, April 1937.
Charts for Checking the Stability of Plane Systems of
Rods. By K. Borkmann. From Luftfarhrtforschung,
February 20, 1937.
The Strength of Shell Bodies — Theory and Practice. By H,
Elmer. From Luftfahrtforschung, March 20. 1937.
LIST OF AIRCRAFT CIRCULARS ISSUED DURING THE
PAST YEAR
No.
205. The Ilafner A.R.III Gyroplane (British). From Flight,
February 18, 1937.
206. Armstrong Whitworth 27 “Ensign” Commercial Airplane
(British). An All-Metal Higli-Wing Monoplane. From
Flight, January 7, and April 1, 1937.
207. Baynes Bee Light Airplane (British). A Two-Seat High-
Wing Monoplane. From The Aeroplane, March 17,
1937 ; and Flight, March 11, and March IS, 1937.
208. The Airspeed “Oxford” Training Airplane (British). A
Two-Engine Cantilever Monoplane. From The Aero¬
plane, June 23, and July 28, 1937 ; and Flight, April 29.
and July 1, 1937.
FINANCIAL REPORT
The general appropriation for the National Advi¬
sory Committee for Aeronautics for the fiscal year
1937, as contained in the Independent Offices Appro¬
priation Act approved March 19, 1936, was $1,158,850.
A supplemental appropriation of $1,367,000 was made
available in the First Deficiency Appropriation Act,
fiscal year 1936, approved June 22, 1936, for the same
purposes specified in the Committee’s regular appro¬
priation act for 1936, to continue available until June
30, 1937, and providing for expenditure of not to
exceed $1,100,000 for the construction and equip¬
ment of an additional wind tunnel (19-foot pressure
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
47
tunnel), and not to exceed $267,000 for increasing the
length of the seaplane model testing tank and for
additional equipment therefor. The total amount
available for general expenditure during the fiscal
year 1937, therefore, was $2,525,850. The amount
expended and obligated was $2,337,638, itemized as
follows:
Personal services - $928, 337
Supplies and materials _ 71, 788
Communication service - 3, 053
Travel expenses - 14, 464
Transportation of things _ 2, 742
Furnishing of electricity - 36, 258
Repairs and alterations _ 4, 639
Special investigations and reports _ 80, 744
Equipment _ 381, 519
Structures _ 814, 094
Expended and obligated _ 2, 337, 638
Unobligated balance _ 188, 212
Total, general appropriation _ 2, 525, 850
The appropriation for printing and binding for
1937 was $18,700, of which $18,679 was expended.
The sum of $19,689 was received during the fiscal
year 1937 as special deposits to cover the estimated
cost of scientific services to be furnished private
parties. The total cost of investigations completed
for private parties during the fiscal year, amounting
to $12,073, was deposited in the Treasury to the credit
of Miscellaneous Receipts.
The amount of the regular appropriation for the fis¬
cal year 1938 is $1,259,850, as provided in the Inde¬
pendent Offices Appropriation Act approved June 28,
1937. A supplemental appropriation of $453,000 was
made available in the Second Deficiency Appropria¬
tion Act, fiscal year 1937, approved May 28, 1937, for
the same purposes specified in the Committee’s regular
appropriation act for 1937, to continue available until
June 30, 1938. and providing that $353,000 shall be
available only for the construction and equipment of
facilities and for the purchase of an airplane of the
light metal private type; and providing further, that
the unexpended balance of the supplemental appropria¬
tion of $1,367,000 for 1937 be continued available un¬
til June 30, 1938. That unexpended balance was $186.-
968. The total amount available for general expendi¬
ture during the fiscal year 1938, therefore, is $1,899,818.
In addition, the amount of $21,000 was appropriated for
printing and binding for the fiscal year 1938.
An allotment of $7,350 was received from the State
Department for payments during the fiscal year 1937
to employees stationed abroad, on account of exchange
losses due to appreciation of foreign currencies, and
of this amount $2,866 was paid during the fiscal year to
employees of the Committee stationed in the Paris
Office, leaving a balance of $4,484 turned back into the
Treasury.
Of the allotment of $2,000 for participation in the
Greater Texas and Pan American Exposition, which
opened at Dallas, Texas, June 12, 1937, the amount of
$404 was expended and obligated as at June 30, 1937.
CONCLUDING STATEMENT
The greatly extended use of aircraft for both mili¬
tary and civil purposes has been reflected in an in¬
creased activity on the part of progressive nations in
extending their aeronautical research facilities. The
demands made upon the Committee by the War, Navy,
and Commerce Departments for new information are
increasing in number and in difficulty with the increase
in the speed and size of aircraft. The Committee fully
recognizes its enlarged responsibility to make provision
not only to take care of research needs arising from
current problems, but also to look well into the future
and to anticipate the needs that will arise as a result
of the trend toward the construction of much larger
landplanes and seaplanes.
The Committee is grateful to the President and to
the Congress for the earnest consideration and support
that have been given to its needs, and urges the con¬
tinued support of this most fundamental activity of the
Federal Government in connection with aeronautics.
Respectfully submitted,
National Advisory Committee
for Aeronautics,
Joseph S. Ames, Chairman.
REPORT No. 577
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
By Charles S. Moore and John H. Collins, Jr.
SUMMARY
Single-cylinder compression-ignition engine tests were
made to investigate the performance characteristics of the
prechamber type of cylinder head. Certain fundamental
valuables influencing engine performance — clearance dis¬
tribution, size, shape, and direction of the passage con¬
necting the cylinder and prechamber, shape of prechamber ,
cylinder clearance, compression ratio, and boosting — were
independently tested. Results of motoring and of power
tests, including several typical indicator cards, are
presented.
Results of the investigation indicate that for maximum
performance of this 5- by 7 -inch engine at speeds up to
1,500 r. p. m., the compression ratio should be between
15.5 and 17.5 and the prechamber should be as large as
possible, disk-shaped, and connected to the cylinder by a
single passage. A strong rotational air flow should be
created in the prechamber by introducing the passage
tangentially. Flaring should be employed on the cylinder
end of the passage to spread the issuing gases over the flat
piston crown. At 1,500 r. p. m., the injection system
should deliver in approximately 20 crankshaft degrees the
full-load fuel in the shape of a narrow conical spray with
high penetration. This spray should be directed across
the disk chamber toward the mouth of the connecting
passage. Boosting the inlet-air pressure effectively raises
the power output. As the prechamber is inaccessible for
scavenging and the lack of clearance under the valves
prohibits the use of proper valve timing, the prechamber
type of cylinder head is judged to be incapable of developing
the high specific output required of aircraft engines.
INTRODUCTION
The general problem in the development of aircraft
compression-ignition engines is to obtain complete and
properly timed combustion in the engine cylinder at
high crankshaft speeds. A prime requirement for
complete combustion is that the fuel charge be inti¬
mately mixed with the air. Furthermore, combustion
must be so controlled that it is completed early in the
power stroke without combustion shock. In order to
accomplish these requirements, numerous chamber
designs and fuel-spray arrangements have been tried
by different designers with varying degrees of success.
Each has its own relative merits and its own field of
usefulness.
The prechamber, which may be classed as an auxil¬
iary-chamber type, has been extensively used. Its
popularity is no doubt due to the simplicity of the fuel-
spray arrangement which may be used and to the
variety of means which may be employed to control
the mixing and combustion of the fuel and air. The
auxiliary chamber may function as an air reservoir to
meter the air to the cylinder, or it may serve as a mixing
chamber in which the fuel charge is prepared for com¬
bustion before it passes into the cylinder. When
combustion starts and is partly completed in the auxil¬
iary chamber, this type becomes the usual precombustion
chamber.
For designs in which the auxiliary chamber acts as a
prechamber, or mixing chamber, the connecting passage
and chamber have two functions to perform: First, the
forced air flow is controlled by the size, shape, and
direction of the connecting passage, these factors being
selected to give the best mixing in the chamber with the
least loss by resistance to the flow; and second, the
mixing of the fuel and air is controlled by the size, shape,
and position of the prechamber, these factors being
designed to conserve and utilize the forced air flow as a
residual flow. After combustion starts, the passage
further functions to meter and direct the partly burned,
overrich mixture into the cylinder in such a way that
all the cylinder air is reached by the unburned fuel and
at such a rate as to control the pressures developed in
the cylinder.
As a part of a general research on aircraft-type com¬
pression-ignition engines, the Committee lias been in¬
vestigating the performance to be obtained with the
prechamber type of cylinder head. Most of the work
herein reported has been published as the several inves¬
tigations were completed; the purpose of the subject
report is to include the final and unreported work of the
investigation and to combine all the more important
results into a single publication.
APPARATUS AND TEST PROCEDURE
TEST ENGINE
The single-cylinder-engine test unit shown in figure 1
was used in this investigation. This figure shows the
assembly of equipment at the time the investigation
was completed; the original set-up, however, differed
only in minor details. The compression-ignition 4-
49
50
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
stroke-cycle engine had a 5-inch bore and 7-inch stroke.
Originally a single-cylinder Liberty test engine was
used (reference 1), in which the cast-iron head was
bolted to a special steel cylinder; the cylinder in turn
was bolted to the engine crankcase. Later a more
flexible unit was required, and an N. A. C. A. universal
engine crankcase (reference 2) and cylinder were sub¬
stituted for the Liberty crankcase and cylinder. Stand¬
ard liberty engine parts were used wherever possible.
Fuel, oil, and water temperatures were maintained at
80°, 140°, and 170° F., respectively, during all tests.
A 50-75 horsepower electric cradle-type dynamometer
measured the torque and absorbed the engine power.
CYLINDER HEADS
The several cylinder heads used in this investigation
will be described in the order of their use. In the first
design a pear-shaped auxiliary chamber was cast inte¬
grally with the head with a 1 -inch-diameter passage
connecting the chamber to the cylinder. With a
standard high-compression Liberty piston the com¬
pression ratio was 9.9. The first combustion-chamber
design was altered in order to increase the compression
ratio and to create a higher degree of turbulence within
the pear-shaped chamber on the compression stroke
and within the cylinder on the expansion stroke (fig. 2).
The turbulence was generated by locating the %6-inch-
diameter passage to produce tangential flow in both
the bulb and the cylinder. When the piston was a
top center, the ratio ol the volume of air in the peai
shaped chamber to the volume of air in the cylinder \va
approximately 1. Preliminary tests at a compressioi
ratio of 13.5 were made to determine the effect of pro
gressively altering the passage shape.
N. A. C. A. cylinder-head design 7 was made (see fig
3) to permit a wide range of changes in the connects
passage and auxiliary chamber without disturbing othe:
parts of the head. By the construction and assemble
of different chamber parts and adjustments of the uni¬
versal test engine, this cylinder head was readily adapted
to the investigation of a variety of combustion-chamber
forms and variables.
AUXILIARY TEST EQUIPMENT
Except for those tests in which the fuel-injection sys¬
tem was the variable, the same injection system was
used in all the tests. A speed-reduction and timing
mechanism, which operated the pump at camshaft
speed, allowed the injection advance angle to be varied
while the engine was running by changing the angular
relation of the fuel cam with respect to the crankshaft.
Varying the duration of the closure of a bypass valve
in the constant-stroke pump controlled the quantity of
fuel delivered to an automatic fuel-injection valve. A
single 0.050-inch-diameter orifice with a length-diameter
ratio of 2.5 was used in connection with a plain stem.
Figure l. — Single-cylinder engine and test equipment.
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
The Diesel fuel used in most of the tests had a specific
gravity of 0.847 and a viscosity of 41 seconds Saybolt
Universal at 80° F. Fuel input was measured by tim¬
ing electrically the consumption of / pound of fuel oil
while a synchronized revolution counter recorded the
number of engine revolutions. Air consumption was
measured by recording the time required for 80 cubic
feet to be displaced from a 100-cubic-foot gasometer.
Explosion pressures were indicated by the N. A. C. A.
balanced-diaphragm valve. Indicator cards were ob¬
tained with a Farnboro electric indicator. A strobo-
rama was used to determine the injection periods and
injection advance angles. From the indicator cards,
the ignition lags and rates of pressure rise were deter¬
mined. The ignition lag is considered as the time in
seconds from the start of injection of the fuel to the
start of pressure rise on the card.
TEST PROCEDURE
After the preliminary investigation was completed, a
more systematic study was undertaken. The most im¬
portant variables indicated by an analysis of the prob¬
lem were studied in the following order: clearance dis¬
tribution between cylinder and chamber, connecting-
passage diameter, prechamber shape, cylinder-clearance
51
shape, compression ratio, and boost pressure. Through¬
out the investigation, only one variable at a time was
changed; all other conditions were held constant insofar
as was conveniently possible. Although in some cases
(b) Spherical prechamber with tangential and radial (dotted) passage.
(c) Disk-shaped prechamber.
Figure 3.— Cylinder-head designs showing different prechambers.
a dependent factor changed when an attempt was made
to change a single variable, in no case was this condi¬
tion permitted if it was of major importance or if it
was economically possible to vary only the single vari¬
able. All pieces of apparatus were calibrated at inter¬
vals during the tests and corrections were applied to
the results. During the testing, the barometric pressure
varied from 29.49 to 30.40 inches of mercury ; no attempt
52
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
has been made, however, to correct the data to a stand¬
ard pressure, temperature, or humidity because there
is no generally recognized method of correcting com¬
pression-ignition data to standard conditions.
Figure 4.— Effect of fuel quantity on engine performance. Engine speed, 1,500
r. p. m.; cylinder head as shown in figure 2; compression ratio, 13.5; N. A. C. A.
7A fuel pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5.
TESTS AND RESULTS
PRELIMINARY INVESTIGATION
The curves showing the results of the preliminary
investigation of the prechamber type of cylinder head
are presented in reference 3. Owing to the low com¬
pression ratio of 9.9 the engine was difficult to start.
Acceptable operation, however, was obtained at 1,80
r. p. m. which, at the time these data were first put
lished, was considered an exceptionally high speed fo
compression-ignition engines.
According to the results obtained with the fir>
cylinder head, the N. A. C. A. combustion chamber
(fig. 2) was designed to cause a residual air flow fo
mixing the fuel and air (reference 3). This head hot'
improved the performance and reduced the maximuii
cylinder pressures A series of tests was made witl
this cylinder head, in which the location of the fue
nozzle with respect to the walls of the auxiliary chambe
was varied. With the fuel valve in location 1, the fue
nozzle was extended into the chamber by increment
from the flush position to a point 1% inches from tb
wall. Different orifices and spray types were tried
but no improvement in performance was obtained ove
that with the simple spray in the flush position.
With the cylinder head shown in figure 2, the greatea
improvement in performance (fig. 4) was obtained b
shortening the injection period from approximately
64 to 21 crankshaft degrees, although a small improve'
merit may have been due to flaring the cylinder end o:
the connecting passage.
CLEARANCE DISTRIBUTION
As maximum performance was not the first consider
ation, the shape of the combustion chamber was no
selected for best performance but to permit the study o!
chamber size without introducing a secondary variable.
For this reason, the chamber was made spherical]!
permit varying the allocation of the clearance betweer
cylinder and chamber with a minimum change in tht
shape of the combustion space. The spherical pro-
chambers plus one-half the connecting passage con
tained 20, 35, 50, and 70 percent of the total clearance
at a compression ratio of 13.5. For convenience ol
reference, these clearance distributions will be called
the 20-, 35-, 50-, and 70-percent chambers. Clearanct
in the cylinder was formed between the domed cylindei
head and the domed piston crown.
The connecting passages were circular in cross sec¬
tion, of constant length-diameter ratio, and were flared
at both ends. Each of the four passages was designee
to have a cross-sectional area proportional to the
prechamber volume. Thus, at the same engine speed
for each of the four clearance distributions, the calcu¬
lated air velocities through the passages were the same.
Passage diameters obtained by this method were
2/64, %, /i6, and 4%4 inch for the 20-, 35-, 50-, and 70-
percent chambers, respectively. The axis of the passage
included the center of the spherical chamber and inter¬
sected the cylinder axis at an angle of 45°.
The injection-advance-angle range from misfiring to
allowable knocking was negligibly affected by clearance
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
53
distribution. With the fuel valve in the lower hole of
the 20-percent chamber the operating range increased
from 12° to 27°, but the power decreased and the smoke
and flame of the exhaust increased. The injection
advance angle of 7° at 1,500 r. p. m. gave a start of
Figure 5 shows that, for the design of prechambers
used in these tests, the minimum volume in the chamber
for good performance is about 35 percent of the total
clearance volume. The inferior performance with the
20-percent, chamber cannot be attributed to the deposit
of fuel on the walls by the noncentrifugal spray because
the centrifugal spray that had insufficient penetration
to hit the walls gave slightly worse performance. More
power was obtained with the larger chambers because
of the greater quantity of air ready for initial combus¬
tion. Air in the cylinder, being distributed over the
piston crown, cannot be effectively reached by the
unburned gasses issuing from the chamber and there¬
fore does not materially assist the combustion process.
The motoring and combustion characteristics are
shown in figure 6. The motoring characteristics re¬
main nearly constant as the clearance distribution
varies. With the smaller chambers, less air is moved
through the passage and the friction mean effective
pressure should be less; the decrease in friction mean
effective pressure, however, is slight. Maximum indi¬
cated compression pressures are slightly higher in the
chambers than in the cylinder, probably owing to the
method used in measuring the pressures (reference 4).
Figure 6 also shows that clearance distribution does
not have an appreciable effect on ignition lag. This
result may be expected as the conditions of temperature,
pressure, and air speed were held constant during the
tests. For all clearance distributions the pressure rises
are straight lines and of such high rates that it is impos¬
sible to measure them accurately; the numerical values
are therefore only approximations. As the chamber pro¬
pressure rise that varied from T. C. to 3° A. T. C. for
all clearance distributions, as determined by inspection
of indicator cards.
Table I presents additional data on the engine-oper¬
ating characteristics.
portion increases, the chamber rate tends to decrease
and the cylinder rate to increase and then to decrease.
The larger chambers containing more air should give
a faster rate of pressure rise because the fuel and air
mixture would have more nearly the correct proportions
for complete combustion. The opposite occurs, how¬
ever, indicating that the passage size influences the rate
of pressure rise, the larger passages of the larger cham¬
bers allowing the gases to pass more freely into the
cylinder.
Improvement in exhaust conditions that occurs with
increase of chamber proportions is caused by the availa¬
bility of more air for combustion in the auxiliary cham¬
ber. Decrease in the rate of improvement with increased
allocation of clearance to the chamber of more than 35
percent is due to the combination of spray shape and
air flow as used in these combustion-chamber forms.
This combination allows a maximum of approximately
35 percent of the fuel to be mixed with air for efficient
combustion. The remaining fuel is burned either very
late or not at all.
An increase in chamber volume from 20 to 70 percent
causes the total heat loss to the cooling water to increase
from 21 to 29 percent, owing to the increased quantity
of fuel burned in the chamber and also to an increase
of approximately 10 percent in the total combustion-
chamber surface area (table II). The amount of heat
loss from the chamber increases with chamber volume
and surface, whereas the amount of heat loss from the
head decreases. As the combustion in the chamber
increases with increased chamber proportion, the cylin¬
der heat loss decreases.
TABLE I
GENERAL OPERATING CHARACTERISTICS— CLEARANCE DISTRIBUTION
[Engine speed, 1,500 r. p. in.; fuel consumption, 3.0X10-1 lb. /cycle; 12 percent excess air; cylinder head as shown in fig. 3 (a); compression ratio, 13.5; N. A. C. A. 7A
fuel pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5]
Operating characteristics
■
20-percent chamber
35-percent chamber
50-percent
chamber
Combustion knock _ _ _ _ _
Dull — Regular _.
Slight — Irregular
Hard — Irregular . _ .
Injection range, allowable knock to miss..
13° B. T. C. to 1° B. T. C _
10° B. T. CAo 2° B. T. C _
11° B. T. C. to 1° B. T. C _
Centrifugal spray compared to non¬
centrifugal spray.
Lower fuel-valve position compared
to upper position.
Optimum valve-opening pressure,
Ib./sq. in.
Knock and performance
slightly worse for centrifugal
spray.
Performance worse for lower
Knock and performance
worse for centrifugal spray.
No change . . . .
Knock and performance
worse for centrifugal spray.
Performance worse for lower
position i. a. a. range 27°.
3,500... _ _ _
5,000 _ .... _. _
position.
5.000 _
Carbon deposits
Chamber,
much
Cylinder,
little
Chamber, soot
and “cake”
Cylinder, soot
Chamber, soot
Cylinder, soot
Cyclic variation in maximum explosion
pressure, lb./sq. in.
300.. .
100 _
200 _
100 _
140. . .
130.... . .
70-percent chamber
Harder— Irregular.
10° B. T. C. to 1° A.
T. C.
Knock and perform¬
ance slightly better
for centrifugal spray.
Performance worse for
lower position.
3,500.
Chamber, soft
soot
90 _
Cylinder,
soft soot
110.
54
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE II
EFFECT OF CLEARANCE DISTRIBUTION ON HEAT
LOSS TO COOLING WATER
[Engine speed, 1,500 r. p. m.; fuel consumption, 3.0 X 10-< lb./cyele; 12 percent excess
air; cylinder head as shown in fig. 3 (a); compression ratio, 13.5; N. A. C. A.
7A fuel pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5.]
Chamber
volume in
percentage
of total
clearance
Distribution of heat loss to cooling
water
Percent¬
age of
total heat
in fuel
Cylinder
Percent
Head
Percent
Chamber
cap
Percent
20
50
44
6
21
35
46
34
20
22
50
44
20
36
26
70
43
17
40
29
0 ao 40 60 80 too
Clearance volume in chamber, percent
Figure 5— Effect of clearance distribution on engine performance. Engine speed,
1,500 r. p. m.; fuel consumption, 3.0 X 10~4 lb./cycle; 12 percent excess air; cylinder
head as shown in figure 3 (a); compression ratio, 13.5; N. A. C. A. 7A fuel pump
and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5.
Figure 7 shows tiie general effect of engine speed
and air-flow speed on mean effective pressure and fuel
consumption. The trend is nearly the same for all
the chambers with the optimum speed, based on maxi¬
mum i. m. e. p., at 1,200 r. p. m. The larger chambers
because of a more intimate mixture of a larger quantit;
of fuel and air, developed the most power with the bes
fuel economy. It is believed that the great different
in i. in. e. p. shown by the curves for the 20-perceu
chamber was caused by insufficient air in the smal
Figure 6. — Effect of clearance distribution on motoring and combustion characteris¬
tics. Engine speed, 1,500 r. p. m.; cylinder head as shown in figure 3 (a); com¬
pression ratio, 13.5; N. A. C. A. 7 A fuel pump and 13A fuel valve; 0.050-inch nozzle
length-diameter ratio, 2.5; injection advance angle, 7° B. T. C.
chamber. Explosion pressures of all the chambers in¬
crease with speed up to 1,200 r. p. m. because of the
better mixing of fuel and air and resultant faster
burning. As the engine speed increases above 1,200
r. p. m., most of the curves show a tendency to fall
off. The smaller chambers with small passage areas
confine the pressure, giving high chamber and low
cylinder pressures.
The 50-percent chamber was selected as being repre¬
sentative of all the chambers and the effect of speed on
combustion characteristics was investigated. Indi-
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
OO
cator cards from the other three combustion chambers
gave trends similar to those shown in figure 8, which
is for the 50-percent chamber. As the engine speed
increases, the velocity of air flow in the passage in-
Figure 7. — Effect of speed on engine performance. Fuel consumption, 3.0 X 10~f
lb./cycle; 12 percent excess air; cylinder head as shown in figure 3 (a); compression
ratio, 13.5; N. A. C. A. 7A fuel pump and 13A fuel valve; 0.050-inch nozzle; length-
diameter ratio, 2.5.
creases and the mixing of fuel and air in the chamber
is more complete with more rapid combustion and
higher rates of pressure rise. Successive engine cycles
varied, as the engine sound clearly indicated, so that
the points on the Farnboro indicator cards are widely
dispersed, especially at the pressure peaks. The rates
of pressure rise were obtained by considering the lead¬
ing points of the card. Apparently, rate of pressure
rise and knock do not vary together, inasmuch as the
rates of pressure rise were less at the lower speeds and
the combustion-knock audibility remained constant.
The starting point of the pressure rise was dependent
upon ignition lag and injection advance angle, the latter
Figure 8. — Effect of speed on compression pressure and combustion characteristics.
Fuel consumption, 3.0 X 10-' lb./cycle; 12 percent excess air; cylinder head as shown
in figure 3 (a); 50-percent chamber; compression ratio, 13.5; N. A. C. A. 7A fuel
pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5.
being the greatest permitted by allowable knock in¬
tensity. The start of pressure rise varied from ap¬
proximately 10° A. T. C. at 600 r. p. m. to 2° A. T. C.
at 1,800 r. p. m. The ignition lag measured in seconds
was reduced one-half by an increase in engine speed of
from 600 to 1,200 r. p. in., primarily because more heat
was brought to the fuel by the higher air-flow speed.
CONNECTING-PASSAGE DIAMETER
In order to investigate the effect of connecting-
passage diameter, the 50-percent prechamber was se¬
lected and the diameter of the connecting passage was
varied. As in former tests, the single passage used was
38548 — 38 - 5
REPORT NO. 577— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
56
circular in cross section. This shape was retained be¬
cause, with a circular passage, there is a minimum change
in clearance shape as the cross-sectional area of the
passage is increased. A connecting passage considered
too small for practical operation was selected and pro¬
gressively enlarged. (See table III.) The compression
ratio varied from 13.2 to 13.7 with change in passage
area. Air-flow speeds through the passages of different
size used were calculated by the method given in refer
ence 5 and the results are shown in figure 9.
The general operating and combustion characteristics
of the engine changed as the diameter of the connect¬
ing passage was varied and the data recorded dump
the tests are shown in table III.
TABLE III
GENERAL OPERATING CHARACTERISTICS— PASSAGE DIAMETER
[Engine speed, 1,500 r. p. m.; fuel consumption, 3.0 X 10_< lb./cycle; 12 percent excess air; cylinder head as shown in fig. 3 (a); compression ratio, 13.5; N. A. C. A. p
fuel pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5.]
Passage
diameter,
in.
Passage
area,
sq. in.
Idling
Injection range (allowable knock to
miss), Crank angle, degrees
Cyclic variation of
maximum explosion
pressure
Combustion sound inten¬
sity and regularity
Carbon deposits
Chamber,
lb./sq. in.
Cylinder,
Ib./sq. in.
Chamber
Cylinder
1 _
0. 028
Good
38 B. T. C. to 2 A. T. C _
Small. _
Quiet, regular _ _
None _ . .
Light.
1^4 1 _
. 055
do _
18 B. T. C. to 2 A. T. C _
___do_ _
. do.. . . _ _
_ .do _
Do.
% .
110
do
11 B. T. C. to 1 A. T. C _
80 .. ...
Light knock, regular _
Increasing car-
Increasing car-
bon.
bon.
2%4 _
. 161
. do _ _
11 B. T. C. to 1 A. T. C _
100 _
100 _
Medium knock, regular.. ..
_ do _ . _
Do.
1%2 ---
. 222
do - _.
10 B. T. C. to 1 A. T. C _
120 _
120. .
Hard knock, regular .....
_ do. . .
Do.
2 Ha
. 338
Fair
11 B. T. C. to 1 A. T. C
100_ .
160.
Dull knock, irregular
_ do _
Do.
% _
. 442
Poor
11 B. T. C. to 1 A. T. C _ _
120 _
130 _
. do _ ._ _ _
_ do _ _
Do.
.887
Bad
11 B. T. C. to 5 A. T. C .
Light knock, irregular. _
_ do _
Do.
1 Erosion of piston crown prevented complete power tests.
2 Excess heating of exhaust valve and manifold prevented complete tests.
Motoring characteristics shown in figure 10 indicate
that friction increases rapidly when passages of less
than 2%4-inch diameter are used. The large effect on
friction mean effective pressure in this range is due
mostly to passage throttling losses because the mechan¬
ical and induction losses remain nearly constant (refer¬
ence 6). The pressure difference between chamber
B.T.C. Crank angle, degrees B.T.C.
Figure 9. — Relationship of air-flow speed to crank position and passage diameter
during the compression stroke of a 5- by 7-inch engine with a 12-inch connecting
rod. Engine speed, 1,500 r. p. m.; cylinder head as shown in figure 3 (a); 50-percent
chamber.
and cylinder is greater with the smaller passages than
with the larger ones, which approach the integral
combustion chamber condition and show little pressure
difference. Figure 11 is a representative motoring
card and shows the lag of chamber pressure behind
cylinder pressure. The effect of speed on compression
pressures and friction mean effective pressure is shown
in figure 12. These curves illustrate the increasing
Figure 10. — Effect of passage diameter on motoring characteristics. Engine speed,
1,500 r. p. m.; cylinder head as shown in figure 3 (a); compression ratio, 13.5; 50,
percent chamber.
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
effect of the passage area on the different variables as
the engine speed is increased.
Figure 13 shows that, for the clearance shape used in
these tests, a connecting passage of approximately 2%4
inch in diameter will give nearly optimum performance
over the speed range investigated. Because the air¬
flow velocity through the passage depends on engine
speed, the consistent performance over a wide speed
range indicates that the longer time available for the
preparation of the mixture at low speeds compensates
500-1
0/
tling of the small passages. Throttling becomes less
important with decrease in engine speed and the result¬
ing performance curves at 1,000 and 500 r. p. m. are
quite flat. In the design of a prechamber, this lack of
sensitivity at low engine speeds is therefore advanta¬
geous because an optimum passage size for the maximum
engine speed can be selected and the performance at
lower speeds will not be adversely affected.
Figure 13 shows at 1,500 r. p. m. an increase in igni¬
tion lag and a decrease in the rate of pressure rise in
400"
,c
u
c
0)
<a
3
cr
W300-
L
0)
3.
w
"0
C
3
c
tx
0)
x 200 q
p
n
w
0)
x
(X,
100
Chamber -
Cylinder
->
B.T. C. 100
i. ■ . . i . .• .... -Vi . ... .. •
80 60 40 20 T.C. 20 40
Crank angle, degrees
.. j. _ _ • . . _
60 60 100 AT. C.
Figure II.— Motoring indicator card. Engine speed, 1,500 r. p. m.; cylinder head as shown in figure 3 (a); passage diameter, 29/64 inch; compression ratio, 13.5.
for the lower velocity of the air through the passage
and makes good performance with satisfactory engine-
operating conditions possible over a wide speed range.
In this instance, the criterions for satisfactory engine-
operating conditions are moderate cylinder pressures,
rates of pressure rise, and combustion sound. At
1,500 r. p. m., while the smallest passage was on test,
the pressure in the chamber could not be measured
because the engine-operating conditions caused the
repeated failure of the pressure-measuring apparatus.
Although the combustion is evidently better at high
speed and with small passage diameters, the perform¬
ance is not the optimum owing to the excessive tlirot-
both chamber and cylinder as the passage diameter is
increased. Increase in ignition lag in the tests of
passage sizes ranging from %-inch to Bib-inch diameter
was accompanied by an increase in combustion knock;
however, for the two larger passages the ignition lag
increased slightly, but the combustion knock became
less intense. (See knock rating of table 111.) In the
opinion of some investigators, combustion knock is
caused by a high rate of pressure rise. The results of
these tests indicate that this condition is not always
true because, at a speed of 1,500 r. p. m., the passage
giving the highest rate of pressure rise gave the quietest
engine operation.
Compression pressure, Ib./sq.in.
58
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 12.— Effect of speed on compression pressures and f. m. e. p. Cylinder head
as shown in figure 3 (a); compression ratio, 13.5.
A conclusion drawn from the results of these tests is
that combustion knock is more dependent upon ignition
lag than upon rate of pressure rise; however, the effect
of a small change in either condition is not consistent,
The tests made at 1,000 and 500 r. p. m. (fig. 13),
owing to the lesser velocities of air flow at these speeds,
do not show trends as sharply defined as those shown
at 1,500 r. p. m. At each speed, the injection advance
angle and rate of fuel injection were held constant for
the series of passage diameters tested.
The curves show that some combustion-pressure con¬
trol can be obtained by means of small passage diameters
because with the %-inch-diameter passage the rates of
pressure rise are higher in the chamber than in the
cylinder. The equivalent data could not be obtained
from either of the two smaller passages because, after
short power runs, the piston crown was dangerously
eroded by the impingement of the concentrated jet of
burning gases issuing from the small passage. Small
passages, however, do give good mixture control and
minimize the effects of irregularities of the fuel-injection
system, such as small variations in the start of injection.
This effect is shown by the small cyclic variations in
cylinder explosion pressure as measured with the bal¬
anced-diaphragm pressure indicator. The combustion
obtained using the largest passage tested was so slow
that the exhaust valve and exhaust manifold became
red hot after a few minutes of operation.
Supplementary tests made at maximum allowable
advance angle are represented in figure 13 by the
points that do not fall on the curves. These runs were
made because it was found that the explosion pressures
were decreasing with an increase in passage diameter
and it was considered advisable to determine whether
the best performance could be equaled by advancing the
injection and thereby raising the explosion pressures.
The results of these tests at maximum allowable advance
angle show that, although the maximum explosion pres¬
sures were considerably increased, the performance
was only slightly improved. The combustion knock
under these conditions was much worse than when
testing any passage and using optimum injection
advance angle.
COMBUSTION-CH AMBER SHAPE
Clearance distribution and connecting-passage diam¬
eter were considered the most important variables in
the design of a prechamber cylinder head and therefore
they were extensively investigated. Several lesser
variables that contribute to the performance character¬
istics of the combustion chamber were also investigated.
The prechamber was kept at 50 percent of the total
clearance for most of the tests, and the connecting
passage was maintained at %6-inch diameter or the
equivalent area. Although these proportions are not
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
59
the optimum for prechamber design, the sacrifice in
performance was sufficiently small to justify their use to
maintain continuity throughout the entire investigation.
The passage was brought into the chamber radially
and tangentially (fig. 3 (b)) by using inserts designed and
instructed to permit such variations. When the
tangential passage was used, the direction of the pas¬
sage to the cylinder was changed by rotating the chamber
cap and passage insert as a unit into positions as far as
72° to the right and to the left. The ends of the passage
were successively flared to determine the effect of
passage flaring.
The effect of prechamber shape was investigated for
a limited series of tests. Analysis and test results
indicated the advisability of confining the test shapes
to volumes of revolution in order to conserve the residual
air flow within the chamber. The spherical chamber
of the first tests was changed to a disk rounded at the
outer edge and arranged vertically so that the plane of
the disk was parallel to the axis of the engine cylinder.
The connecting passage was introduced tangentially to
the disk (fig. 3(c)). Three injection-valve locations
were provided as shown, and power tests were made
with the fuel valve in each.
The effect of increasing the quantity of air rotated
in the prechamber was investigated by changing the
volume of a spherical chamber from 50 to 70 percent
of the clearance volume. The tangential passage was
substituted for the radial passage and comparable tests
were made. The approximate direction of the air
flow for both the 50- and the 70-percent chambers
with radial and tangential passages was indicated by
air-flow patterns made by extending a number of copper
nibs into the auxiliary chamber from a gasket clamped
between the two parts of the chamber, as described in
reference 4. In order to take the air-flow patterns,
the engine was started from rest, motored up to 1,500
r. p. m. as quickly as possible, and then stopped. The
variation in performance when the engine was operated
with the fuel valve first in the central and then in the
top injection- valve location was determined for both
prechambers.
The general operating characteristics of the engine—
that is, starting and idling ability, cyclic regularity,
and combustion shock — were little affected by any
of the changes made during these tests. A change
from the Diesel fuel used in previous tests to Auto
Diesel fuel greatly reduced the combustion knock,
increased the injection-advance-angle range, and de¬
creased the cyclic variation in maximum cylinder pres¬
sure from ±75 to ±40 pounds per square inch. Some
combustion knock was present in all tests but was not
considered serious. The rates of pressure rise in the
cylinder and the prechamber were, respectively, 68 and
Figure 13. — Effect of passage diameter on engine performance. Fuel consumption,
3.25 X 10-< lb. /cycle; no excess air; cylinder head as shown in figure 3 (a) ; compression
ratio, 13.5; N. A. C. A. 7A fuel pump and 13A fuel valve; 0.050-incli nozzle; length-
diameter ratio, 2.5; injection advance angle, 11° B. T. C.
45 pounds per square inch per degree at 1,500 r. p. m.
with the best combination of variables covered in this
report. Rates of pressure rise for previous work, in
which the spherical chamber and the original fuel were
used, were in the order of 85 and 75 pounds per square
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
60
inch per degree at 1,500 r. p. m. for cylinder and
chamber, respectively.
The purpose of directing the passage tangentially to
the chamber instead of radially was to create a high-
velocity, rotational, residual air flow in the auxiliary
chamber to improve the fuel and air mixing. Table IV
shows the effects of flaring and of changes in the inten¬
sity of the rotational air swirls obtained by several
combinations of connecting passage. Flaring the
passage had very little effect on the performance.
Several other methods of spreading the gases over the
piston crown were tried, such as an elliptical passage
insert and a three-passage insert designed according to
the proportional-orifice principle (reference 7). The
effect of these changes on the performance was also
negligible.
As a rotational swirl was found to be effective in
the chamber, it was decided to determine the effect of
a swirl in the cylinder. This effect was produced by
changing the passage direction in the cylinder. Carbon
deposits showed that a swirl was produced, but there
was no appreciable improvement in engine performance,
TABLE IV
EFFECT OF PASSAGE DIRECTION AND FLARE ON ENGINE PERFORMANCE
[Fuel consumption, 3.25 X10_< Ib./cycle; no excess air; cylinder head as shown in fig. 3 (b); compression ratio, 13.5; N. A. C. A. 7A fuel pump and 13A fuel valve; 0.050-inch
nozzle; length-diameter ratio, 2.5)
1,000 r. p.
in.
1,500 r. p
m.
i. m.e. p.,
Ib./sq. in.
b.m.e.p.,
Ib./sq.in.
Explosion
pressure,
Ib./sq.in.
Fuel consumption
i. m.e. p.,
Ib./sq. in.
b. m. e. p.,
Ib./sq. in.
Explosion
pressure,
lb./sq. in.
Fuel consumption
lb/.i.hp.-hr.
lb./b.hp.-hr.
lb./i.hp.-hr.
lb./b.hp.-hr.
RADIAL PASSAGE
Slight rotational air flow. . _ _ _
137
109
795
0. 42
0. 52
133
98
750
0. 42
0.58
Strong rotational air flow. ... _ _
139
111
740
.41
.51
137
102
730
.41
.55
TANGENTIAL PASSAGE
Strong rotational air flow.. _
141
112
740
0.38
0- 48
142
104
720
0.38
0.53
Cylinder end of passage flared.. _
141
112
740
.39
.49
144
106
730
.38
.52
Both ends of passage flared _ _ _
140
113
800
.39
.49
141
105
770
.40
.54
Table V shows the effect of changing the prechamber
shape from a sphere to a disk of equal volume and also
the effect of fuel-valve location in the disk chamber.
Tangential passages were used in both cases. The disk
chamber with the injection valve in the central loca¬
tion gave an improvement in i. m. e. p. at 1,500 r. p. m.
over the spherical chamber under similar conditions,
which can be attributed to the fact that in the disk
chamber the low- velocity zones of the spherical chamber
were removed and the rotating mass of air was in the
zone of the single fuel spray and the connecting passage.
This relation of chamber shape and fuel spray evidently
resulted in better mixing in the prechamber with the
resultant improved performance.
TABLE V
EFFECT OF PRECHAMBER SHAPE AND FUEL-VALVE LOCATION ON ENGINE PERFORMANCE
Fuel consumption, 3.25X10-* lb./cycle; no excess air; cylinder head as shown in figs. 3 (b) and 3 (c); compression ratio, 13.5; N. A. C. A. 7A fuel pump and 13A fuel valve;
0.050-inch nozzle; length-diameter ratio, 2.5]
Fuel-
valve
loca¬
tion
1,000 r.
p. m.
1,500 r.
P. III.
i. m. e. p.,
lb./sq. in.
b. m. e. p.,
lb./sq. in.
Explosion
pressure,
lb./sq. in.
Fuel consumption
i. m. e. p.,
lb./sq. in.
b. m. e. p.,
lb./sq. in.
Explosion
pressure,
lb./sq. in.
Fuel consumption
lb./i. hp.-hr.
Ib./b. hp.-hr.
lb./i. hp.-hr.
lb./b.
hp.-hr.
Flame
Full
Flame
Full
Flame
Full
Flame
Full
Flame
Full
Flame
Full
Flame
Full
Flame
Full
Flame
Full
Flame
Full
start
load
start
load
start
load
start
load
start
load
start
load
start
load
start
load
start
load
start
load
SPHERICAL CHAMBER (FIG. 3 (b))
2 .
130
140
103
113
800
790
0. 36
0. 39
0. 46
0. 48
126
140
91
105
740
760
0. 33
0. 40
0. 45
0.54
DISK CHAMBER (FIG. 3 (c))
3 _
99
124
72
98
780
790
0. 40
0. 44
0. 55
0. 56
101
128
66
92
780
760
0. 37
0. 45
0. 57
0. 62
2 _
138
141
111
113
780
780
.38
.41
.47
.50
133
145
98
109
740
740
.35
.38
.48
.51
1 _
143
147
115
119
780
760
.37
.38
.47
.48
143
149
106
113
740
740
.36
.38
.48
.51
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
61
The effect of fuel-valve location is also shown in
table V ; the great difference in maximum power for the
three fuel-valve locations provided in the disk chamber
indicates the importance of the position of the fuel spray
relative to the air movement. The best performance
was obtained with the spray axis from the single-orifice
nozzle directed in the same plane with the air flow and
at only a small angle from the direction at right angles
to the air flow. The spray was also directed toward the
connecting passage. The worst performance was ob¬
tained with the fuel valve in the lowest position (see
fig. 3 (c)) in which the spray was injected counter to
the air flow and, with the injection timing used, should
have penetrated directly through the passage to the
cylinder. The fact that the fuel did penetrate at least
to the passage was indicated by carbon formation
around the mouth of the passage. This arrangement
was made to obtain a rich mixture adjacent to the pas¬
sage ready to be ejected into the cylinder by the pressure
resulting from the combustion in the chamber. The
chamber cap was rotated 180° so that the lower valve
position was in approximately the same location but the
spray was directed, not through the passage, but above
the entrance to the passage and at an angle to the air
flow, not counter to it. This condition increased the
brake mean effective pressure approximately 10 pounds
per square inch over that originally obtained with the
fuel valve in the lowest position.
An analysis of previous work indicated that the
greater the amount of air in motion the better would be
the mixing of the fuel and air and, consequently, the
better the performance. A tangential passage in con¬
junction with a chamber that contained a larger per¬
centage of the clearance volume was used to increase
the quantity of air in motion. Table VI shows that
this analysis was correct for spherical chambers be¬
cause, with the fuel valve in the central location, the
improvement in the performance with increase in cham¬
ber volume was greater when a tangential passage was
used than when a radial passage was used. Increase in
rotational, and probably residual, air-flow velocity due
to the tangential passage was sufficient to make an ap¬
preciable difference in the performance. The investiga¬
tion was made with spherical chambers although the
maximum performance would be less than with the disk
chambers; the indicated trend, however, should be the
same for both auxiliary-chamber shapes.
The tangential connecting passage was used because
introducing the air tangentially to a volume of revolu¬
tion assisted in setting up a rotational swirl in the
chamber, which should persist after the piston had
reached the upper limit of its travel. As this residual
air flow was believed to be the cause of the increased
power, every attempt was made to intensify and pre¬
serve the flow. This theory could not be definitely
proved because there are no means available for meas¬
uring the velocity of the flow; the predominating direc¬
tion of the air flow, however, was determined by means
of the air-flow patterns. The radial passage to the
same chamber also showed rotational air flow but of less
intensity and in the opposite direction. This condition
was probably caused by the short passage used, which
permitted some air from the cylinder to pass directly
into the prechamber without being directed by the
passage. (See fig. 3 (b).) The passage was as long as
the construction of the head would permit.
TABLE VI
EFFECT OF PASSAGE DIRECTION, PRECHAMBER
VOLUME, AND FUEL-VALVE LOCATION ON EN¬
GINE PERFORMANCE
Engine speed, 1,500 r. p. m.; fuel consumption, 3.25X10-4 lb. /cycle; no excess air;
cylinder head as shown in fig. 3 (b); compression ratio, 13.5; N. A. C. A. 7A
pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5]
Passage
i.m.e.p.,
lb./sq. in.
b. m. e. p.,
lb./sq. in.
Explosion
pressure,
lb./sq. in.
Fuel consumption
lb./i. bp. -hr.
lb./b. bp. -hr.
Flame start
Full load
Flame start
Full load
Flame start
Full load
Flame start
Full load
j Flame start
Full load
FUEL-VALVE LOCATION 2
50-percent radial.--
133
138
98
103
730
720
0. 35
0.41
0. 48
0. 56
50-percent tangen-
tial. . .
138
141
103
106
760
760
.33
.40
.46
.52
70-percent radial...
133
140
98
104
830
830
.34
.41
.48
.55
70-percent tangen-
tial .
139
144
104
109
800
790
.36
.38
. 48
.51
FUEL-VALVE LOCATION 1
50-percent radial...
131
141
99
109
790
800
0. 35
0.41
0.48
0. 52
50-percent tangen-
tial _ _
131
135
98
102
820
820
. 38
.42
. 51
. 55
70-percent radial...
141
147
108
112
880
880
.35
.39
. 47
.52
70-percent tangen-
tial _
132
138
98
104
800
780
.36
.42
. 49
. 55
As the air flow with either passage is rotational, the
differences in performance shown for the different fuel-
valve locations (table VI) are more readily understood.
It was found that with either passage in the spherical
chamber the performance was improved by injecting
the fuel at the point “upstream” on the circumference
of the chamber. Location 1 was better when using the
radial passage and location 2 better when using the
tangential passage. (See fig. 3 (b).) In the disk cham¬
ber, injecting the fuel near the passage mouth but
directly toward the passage gave the worst results.
CYLINDER-CLEARANCE SHAPE
In the tests of clearance distribution and passage size,
a domed piston crown was employed. At the conclu¬
sion of these tests, the performance with the domed
crown was compared with that using first a flat crown,
second a dished crown, and third a piston crown with
all the cylinder clearance concentrated in front of the
connecting passage. Extensive tests were made using
this latter type of piston crown, but the performance
was inferior to either of the other two piston crowns.
62
REPORT NO. 577 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
For the sake of convenience in testing, subsequent
tests were made using a flat piston crown since there was
little difference between the performance of the flat and
the domed crown piston.
INJECTION SYSTEMS
The 50-percent disk chamber with the tangential
passage was assembled with head 7 at a compression
ratio of 13.5 and, using fuel-valve location 1, the injec¬
tion system was varied to determine the effect on engine
performance. Three fuel pumps having widely differ¬
ent characteristics were selected and tested with differ¬
ent fuel- valve assemblies that gave a variety of injec¬
tion systems. The N. A. C. A. 7A and the commercial
fuel pump used were cam-operated and of constant
stroke but had different rates of displacement. The
third injection pump was the N. A. C. A. 12, a cam-
operated plunger type, but one in which injection is
caused by the release of pressure stored in a reservoir of
correct volume. This pump in combination with the
correct valve gives a fast rate of injection and was used
to obtain a shorter injection period than that of any
of the other pump and valve combinations. The
N. A. C. A. 7A fuel pump and the single 0.050-inch-
diameter orifice were used to determine the effect of the
orifice length-diameter ratio. Results obtained by
using multiple orifices to distribute the fuel by injec¬
tion as well as by air flow were also determined. Tests
of a pintle nozzle with two different fuel pumps were
included in the injection-system investigation. With
the injection system that gave the best engine per¬
formance, tests were made to determine the effect of
injection advance angle and fuel quantity on engine
performance.
In order to improve the inherently poor starting
characteristics of this type of combustion chamber, a
series of starting tests was made, injecting the fuel
directly into the cylinder instead of into the prechamber.
An 0.008-inch-diameter orifice nozzle was used with a
valve-opening pressure of 2,500 pounds per square inch.
The size of the orifice used limited the fuel injected to
very small quantities. The engine was motored at
gradually increasing speeds until the engine started
firing and the speed could be maintained under its own
power. For comparison, this procedure was repeated
with the same fuel nozzle in the prechamber.
Table VII shows the results of the injection-system
tests. The object of these tests was to obtain a fuel
spray the characteristics of which best suited the
50-percent vertical-disk chamber and tangential passage,
the arrangement that had given the best performance
for this size of chamber. Injection period was the only
spray characteristic accurately measured because in
this type of chamber with its high air-flow speed other
characteristics, such as distribution of fuel within the
spray and spray cone angle, should not be critical.
As shown in the table the optimum performance based
on the i. m. e. p. at flame start and full load was ob¬
tained using the N. A. C. A. 7A fuel pump, 13A fuel
valve, and 0. 050-inch nozzle with a length-diameter
ratio of 6. Multiple-orifice nozzles were tried but, as
they were definitely inferior, the performance is not
included.
TABLE VII
EFFECT OF INJECTION SYSTEMS ON ENGINE PERFORMANCE
[Engine speed, 1,500 r. p. m.; fuel consumption, 3.25X10-4 lb./cycle; no excess air: cylinder head as shown in fig. 3 (c); compression ratio, 13.5; fuel valve in location 1]
Injection system
i. m. e. p.
lb./sq. in.
b. m. e. p.
lb./sq. in.
Explosion
pressure
lb./sq. in.
Fuel con
lb./i. hp.-hr.
sumption
lb./b. hp.-hr.
Relation of injec¬
tion to top center,
crank angle,
degrees
Flame
start
Full
load
Flame
start
Full
load
Flame
start
Full
load
Flame
start
Full
load
Flame
start
Full
load
N. A. C. A. 7A pump:
13A valve:
0.050-inch-diameter orifice:
Length-diameter ratio, 2.5 _ _
145
149
109
112
700
700
0.35
0.38
0. 48
0. 49
7 R. T. C. to 14
A. T. C.
Length-diameter ratio, 4.0 _ _
143
148 .
107
111
710
700
.36
.38
.48
.50
Do.
Length-diameter ratio, 5.0
145
149
108
112
.35
.37
.47
.59
Do.
Length-diameter ratio, 6.0 _ _ .
146
150
109
113
700
700
.35
.37
.48
.49
Do.
0.040-inch-diameter orifice _ _ _
132
142
95
106
640
630
.35
.40
.49
.53
7 R. T. C. to 15
A. T. C.
0.070-inch-diameter orifice^ ___ _ __ - ...
145
148
108
112
740
730
.36
.38
.48
.49
7 R. T. C. to 12
A. T. C.
Commercial valve; pintle nozzle ... . _ ..
141
147
104
110
720
720
.35
.36
.47
.59
7 R. T. C. to 16
Commercial pump:
13A valve; 0.050-ineh-diamet,er orifice; 3,500 lb./sq. in.
140
150
103
113
760
740
.33
.38
.46
.59
7 R. T. C. to 14
valve-opening pressure.
A. T. C.
Commercial valve; pintle nozzle, 3,500 lb./sq. in. valve-
133
143
98
108
740
790
.35
.39
.48
.51
4 R. T. C. to 20
opening pressure.
A. T. C.
N. A. C. A. 12 pump:
13A valve; 0.050-inch-diameter orifice; 3,500 lb./sq. in.
141
147
104
111
800
870
.34
.38
.47
.59
7 R. T. C. to 27
valve-opening pressure.
A. T. C.
17— Me F. I. S. valve; 0.059-inch-diameter orifice; 6,000
128
144
92
108
720
720
.35
.39
.48
. 52
3 R. T. C. to 7
lb./sq. in. valve-opening pressure.
A. T. C.
17 — M 6 F. I. S. valve; 0.051-inch-diameter orifice, 3,500
150
112
730
.38
.50
4 R. T. C. to 11
lb./sq. in. valve-opening pressure.
A. T C.
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
63
Marked improvement in the capability of the engine
to start at a temperature of about 70° F. was obtained
by injecting the fuel into the cylinder. By the use of a
nozzle with a single 0.008-inch-diameter orifice and the
injection of only a small percentage of full-load fuel
quantity, the engine could be started by motoring the
engine at from 200 to 300 r. p. m.; whereas, when the
fuel was injected into the chamber with the same nozzle,
a speed of 600 to 700 r. p. in. was required. Improve¬
ment in starting is due to a higher temperature in the
cylinder.
Figure 14 shows the results of the variable-injection-
advance-angle tests. These curves are characteristic
Figure 14.— Effect of injection advance angle on engine performance. Engine
speed, 1,500 r. p. m.; fuel consumption, 3.0 X 10-i lb./cycle; 12 percent excess air;
cylinder head as shown in figure 3 (c); compression ratio, 13.5; N. A. ( . A. , A fuel
pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 2.5.
of the prechamber type of combustion chamber. lor
these tests the optimum advance angle was 7° before
top center because at this point increase in mean eflec-
tive pressure stopped while increase in maximum cylin¬
der pressure began.
The results of the variable-fuel-quantity test are
shown in figure 15. The curve of mean effective pres¬
sure against fuel quantity shows the characteristic
straight line at small fuel quantities but, for the com¬
bustion chamber under test, the curve continues straight
to comparatively large fuel quantities. The mean
Figure 15.— Effect of fuel quantity on engine performance. Engine speed, 1,500
r. p. m.; cylinder head as shown in figure 3 (c); compression ratio, 13.5; N. A. C. A.
7 A fuel pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 6.
effective pressure varies linearly with the quantity of
fuel injected up to a fuel quantity of 2.25X10 1 pound
per cycle (air-fuel ratio approximately 23) but the curve
begins to droop at this point ; when the fuel quantity is
increased to 2.90X10"4, flame appears in the exhaust.
With this type of combustion chamber, flame appears
in the exhaust before smoke. Both flame and smoke
can be seen in the exhaust at full-load fuel quantity.
The points of figure 15 that do not fall on the curve
represent the data obtained at a 4° increase of the
injection advance angle. It will be noted that the
explosion pressure increased out of proportion to the
increase in engine performance, and therefore the
38.548 — 38
6
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
64
800 i
„700j
o I
XI
o
a
©
600-
* 500-
P»
in
a
400
0)
§
« 300
IT
0)
u
o*
200-
100
100
B.T.C .
^ — - r
80 60 40
20 TC 20 40 60 80 100 A.T.C.
Crank angle, degrees
800-^
700'
X3
§
©600-
I
a
g500-|
p.
u
400
a
®
9
o 300 T
u
© «
n
a.
I
200-)
100
100
B.T.C .
80
60 40
20 TC 20 40
Crank angle, degrees
60
80 100 A.T.C.
Figure 16.— Typical power and motoring indicator cards. Engine speed, 1,500 r. p. in.; fuel consumption, 3.25 X KM lb./cycle; no excess air; cylinder head as
shown in figure 3 (c); N. A. C. A. 7A fuel pump and 13A fuel valve; 0.050-inch nozzle; length-diameter ratio, 6; injection advance angle, 7° B. T. C.
PRECHAMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
65
injection advance angle was not further increased. In
all except these tests the injection advance angle was
determined by the combustion sound. In these tests,
although the sound of combustion became more intense,
the condition was not considered dangerous.
At the full-load fuel quantity during the variable¬
load run, made with the best combustion-chamber
shape and fuel-injection system, indicator cards typical
of those obtained from this engine were taken from the
chamber and cylinder (fig. 16). The rates of pressure
rise determined from the indicator diagrams are 68
and 45 pounds per square inch per degree for the cylinder
and prechamber, respectively.
COMPRESSION RATIO
The lack of engine data concerning the influence of
compression ratio on engine operation and perform¬
ance made an investigation of compression ratio desira¬
ble (reference 8). An attempt was first made to follow
the usual procedure of changing only one variable at a
time. After some preliminary tests, however, this
procedure was found to be so expensive that it was
decided to permit variation of the clearance distribu¬
tion and to change the compression ratio by raising or
lowering the head, i. e., by varying the cylinder-clear¬
ance volume. Explosion pressures were kept nearly
constant by controlling the injection advance angle.
The results of the tests at different compression
ratios are shown in figure 17. The curves have been
plotted without correcting for the change in performance
due *o the increase in relative chamber size, which would
amount to about one-half the mean-effective-pressure
increase shown at the highest compression ratio.
When the chamber size is taken into account, there is
still a small but definite trend toward an increase in
indicated power with an increase in compression ratio.
This trend is in agreement with theoretical analysis,
which indicates higher cycle efficiencies at higher
compression ratios. The brake performance shows
very little change, possibly because the increased cycle
efficiency at the higher compression ratios was counter¬
acted by the decreased mechanical efficiency.
Starting and general operating characteristics im¬
proved with increasing compression ratio. At the
highest compression ratio, the increased compression
temperature reduced the ignition lag and caused the
combustion knock to soften and practically disappear.
As the compression ratio was increased, it was found
necessary to reduce the injection advance angle by
several degrees in order to hold the cylinder pressure
constant throughout the tests. Limitation of maxi¬
mum cylinder pressure, however, did not result in a
loss of power; in fact, short tests at higher cylinder pres¬
sures in some cases showed a slight impairment of
performance.
Indicator cards taken at each compression ratio
illustrated very clearly the decrease in allowable pres¬
sure rise as the compression pressure approached the
maximum cylinder pressure; the only gain in perform¬
ance was from the higher cycle efficiency. A decrease
in the rate of pressure rise is also shown on the cards, but
otherwise they have the same general shape as the cards
heretofore presented; therefore they are not included.
Figure 17.— Effect of compression ratio on engine performance. Engine speed,
l,500r. p. m.; fuel consumption, 3.25 X 10-< lb./eycle; noexcess air; cylinder as shown
in figure 3 (c); N. A. C. A. 7A' fuel pump and 13A fuel valve; 0. 050-inch nozzle;
length-diameter ratio, 6.
With the disk chamber, the greatest compression
ratio that could be obtained was 17.5. The trend of the
curves indicates, however, that there would be no im¬
provement in brake performance at higher compression
ratios. Although an optimum compression ratio is not
clearly defined, the b. m. e. p. at flame start, the easier
starting, and the quieter operation favor the use of a
high compression ratio in this type of engine.
BOOSTING OF AIR CHARGES
Boosting tests were conducted on the engine assem¬
bled with the optimum combination of variables. For
continuity throughout the investigation, the compression
66
REPORT NO. 577 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ratio was retained at 13.5. A DePalma supercharger
with a 12-cubic-foot surge tank was connected to the
engine and variable-load runs made at boost pressures
Figure 18. — Effect of fuel quantity on engine performance at several boost pressures.
Engine speed, 1,500 r. p. m.; cylinder head as shown in figure 3 (c); compression
ratio, 13.5; N. A. C. A. 7A fuel pump and 13A fuel valve; 0.050-inch nozzle; length-
diameter, 6.
of 0, 2.5, 5, 7.5, and 10 inches of mercury at 900, 1,200,
and 1,500 r. p. m. At 1,500 r. p. m. one point was
taken at the highest boost pressure obtainable with the
supercharger used, about 13 K inches of mercury.
Explosion pressures were kept nearly constant by retard¬
ing the injection advance angle as the boost pressure
was increased. At 1,800 r. p. m. power tests were made
at each of the test pressures at the flame-start fuel
quantity and at one larger fuel quantity. Friction
tests were made by motoring the engine after each power
run at the different boost pressures and engine speeds.
The effect of boosting a prechamber type of cylinder
head was rather thoroughly investigated because the
authors could find no references to previous tests by
other investigators. However, only the data at 1 ,500
r. p. m., which are representative of the entire family ol
curves, are presented (fig. 18). The m. e. p. curves are
quite conventional in shape and, at an air-fuel ratio of
14.5, show a constant increase of from 3 to 4 pounds per
square inch per inch of boost pressure.
The objective of holding the explosion pressure con¬
stant while the boost pressure was varied during the
tests was not exactly accomplished, but the increase
in explosion pressure shown was within the limitations
of the equipment used. Explosion pressures were
controlled by varying the injection advance angle,
which was 7° at zero boost pressure and was progres¬
sively retarded until at 10 inches of mercury the injec¬
tion advance angle was only 2°. Since the compres¬
sion pressure increases with boost pressure and the
maximum cylinder pressure was kept constant, the
amount of fuel that could be burned at or near top
center was decreased by retarding the injection. If it
had not been necessary to decrease the injection
advance angle, the gain in power with increased boost
pressure would have been slightly greater because
more fuel could have been burned at or near top center
with a resulting greater efficiency. Because of the
higher compression pressures with the consequent
reduction in ignition lag, however, the power loss was
not nearly so great as if the injection advance angle
had been reduced the same amount at zero boost
pressure.
In view of these facts, it is possible that it might be
advantageous to use a compression ratio lower than
13.5 for boosting because the compression pressure
would be lower and a greater useful pressure rise could
be used. The influence of boost pressure on the com¬
bustion shock would permit a lower compression ratio
to be used because the combustion shock is diminished
with increased inlet pressure, although a lower com¬
pression ratio alone would increase it. At the boost
pressure of 7.5 inches of mercury, the sound of the
engine was very satisfactory at all loads and at each
test speed.
An examination of the curves presented herein shows
that the friction mean effective pressure, neglecting
supercharger friction mean effective pressure, did not
decrease with increase in boost pressure. This observa¬
tion applies for all test speeds. With the integral
combustion-chamber type of cylinder head, the friction
mean effective pressure, also neglecting the power
required by the supercharger, was found to decrease
PRECII AMBER COMPRESSION-IGNITION ENGINE PERFORMANCE
(57
slightly with increase in boost pressure. This condi¬
tion did not exist with the type of cylinder head under
test, probably because of the increase in pumping
loss as the weight of air forced through the connecting
passage is increased. At large boost pressures the
higher pumping losses more than offset the work done
on the piston during the intake stroke, which resulted
in a slight increase in friction mean effective pressure.
In these tests the connecting passage was maintained
at a fixed diameter, which is probably not the best con¬
dition. The ideal way of conducting the tests would
have been to determine and use the correct passage
size for each boost pressure. The injection period was
too long at high boost pressures, as the injection system
is designed to deliver, in approximately 20 crankshaft
degrees, a fuel quantity of 3.25 X10-4 pounds per
cycle, which is full load at zero boost. The full-load
fuel quantity and consequently the injection period,
however, increase with boost. At high boost pressures,
therefore, the injection period continued too long after
top center for efficient combustion. It is believed that
the performance at the optimum boost pressure would
be improved if the correct passage area and injection
period were used ; however, the scope of these tests did
not include the determination and application of each
of these conditions. With this type of combustion
chamber improvement in engine performance by scav¬
enging the clearance volume is practically impossible
because all the clearance should be in the prechamber
away from the valves. Furthermore, owing to lack
of mechanical clearance when the piston is on top
center, both valves must be closed. This condition is
improper for the best exhausting and air charging,
which limits the specific output.
CONCLUSIONS
The following specific conclusions are presented:
1. Clearance distribution:
(a) For maximum performance the prechamber
should be relatively as large as is practicable; however,
lower cylinder pressures, less combustion knock, and
less heat loss to the cooling water occur with the smaller
chamber sizes.
( b ) The size of the prechamber has a negligible effect
on friction mean effective pressure and compression
pressures.
(c) Variation of clearance distribution only, for a
fixed ratio of prechamber volume to connecting passage
area, does not sufficiently control combustion or elimi¬
nate combustion knock.
2. Connecting-passage diameter:
(a) For the engine size and combustion-chamber
design used in this investigation, the connecting-pas¬
sage diameter should be between 2%4 and Vh inch, or
the equivalent area; the i. m. e. p., the fuel economy,
and combustion knock at 1,500 r. p. m. favoring the
smaller passage size.
(6) The size of the connecting passage becomes less
critical as the engine speed is decreased. It is therefore
possible to select a passage size for maximum operating
speed and still have good performance at the lower
speeds.
(c) The friction mean effective pressure due largely
to throttling losses was excessive when a passage diam¬
eter of less than 2964 inch was employed; however, for a
passage diameter equal to 2%4 inch, the friction mean
effective pressure was acceptable and the rate of de¬
crease with increase in passage area became much less.
(d) It was impossible to obtain both high perform¬
ance and combustion-pressure control with any com¬
bination of variables tried in this investigation.
The general conclusions are:
From the results of this investigation of the pre¬
chamber type of cylinder head, several optimum con¬
ditions are evident. For maximum performance of
this engine, which has a 5-inch bore and a 7 -inch stroke,
the compression ratio should be between 15.5 and 17.5,
the prechamber should be relatively as large as possible,
disk-shaped, and connected to the cylinder clearance
by a single passage the area of which is determined by
the highest engine speed. Entering the chamber
tangentially, the passage should cause a strong rota¬
tional air flow and, upon entering the cylinder, should
be flared to spread the issuing gases over the piston
crown. The injection system should deliver full-load
fuel with atmospheric induction in the shape of a
narrow conical spray of high penetration requiring
approximately 20 crankshaft degrees for injection.
This spray should be directed across the disk chamber,
with the air flow, toward the mouth of the connecting
passage. The spray direction greatly affects the
engine performance. Considerable improvement in
engine performance and combustion knock can be
obtained by boosting.
As all of the clearance should be in the prechamber,
proper valve timing and scavenging are prohibited, a
condition which limits the specific output.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Ya., July 7, 1936.
REFERENCES
1. Reichle, W. A.: Report of One Cylinder Liberty Engine
Tests. Serial No. 55, Bur. Aircraft Production, Airplane
Eng. Div., McCook Field, Dayton, Ohio, June 10, 1918.
2. Ware, Marsden: Description of the N. A. C. A. Universal
Test Engine and Some Test Results. T. R. No. 250,
N. A. C. A., 1927.
3. Joachim, William F., and Kemper, Carlton: The Perform¬
ance of Several Combustion Chambers Designed for Air¬
craft Oil Engines. T. R. No. 282, N. A. C. A., 1928.
68
REPORT NO. 577 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
4. Spanogle, J. A., and Moore, C. S.: Performance of a Com¬
pression-Ignition Engine with a Precombustion Chamber
Having High-Velocity Air Flow. T. N. No. 396, N. A.
C. A., 1931.
5. Moore, C. S., and Foster, H. H.: Performance Tests of a
Single-Cylinder Compression-Ignition Engine with a Dis¬
placer Piston. T. N. No. 518, N. A. C. A., 1935.
6. Moore, Charles S., and Collins, John H., Jr.: Friction of
Compression-Ignition Engines. T. N. No. 577, N. A. C. A.,
1936.
7. Spanogle, J. A., and Foster, H. H.: Basic Requirements of
Fuel-Injection Nozzles for Quiescent Combustion Cham¬
bers. T. N. No. 382, N. A. C. A., 1931.
8. Pye, D. R.: The Limits of Compression Ratio in Diesel
Engines. R. & M. No. 1365, British A. R. C., 1931.
BIBLIOGRAPHY
Loschge, A.: Vergleichende Druckindizierversuche an einem
Luftspeicherund an einem Vorkammerdieselmotor. Auto,
tech. Zeitsclir., Jahrg. 35, Nr. 23, 10. Dezember, 1932, S.
562-568.
Mehlig, Hans: Die Vorkammergrosse und ihr Einfluss auf das
Arbeitsverfahren der Vorkammer-Dieselmaschinen. Auto,
tech. Zeitsclir., Jahrg. 32, Nr. 32, 20. November, 1929, S.
723-725, und Jahrg. 32, Nr. 34, 10. Dezember 1929, S. 783-785.
Moore, C. S., and Collins, J. H., Jr.: The Effect of Clearanc-
Distribution on the Performance of a Compression-Ignitioi
Engine with a Precombustion Chamber. T. N. No. 435
N. A. C. A., 1932.
Moore, C. S., and Collins, J. H., Jr.: The Effect of Connecting
Passage Diameter on the Performance of a Compression
Ignition Engine with a Precombustion Chamber. T. N. No,
436, N. A. C. A., 1932.
Moore, C. S., and Collins, J. H., Jr.: Effect of Combustion
Chamber Shape on the Performance of a Prechamber Con.
pression-Ignition Engine. T. N. No. 514, N. A. C. A., 1931
Neumann, Kurt: Diesel-Engine Investigations. Ignition Chan,
ber Engines. T. M. No. 589, N. A. C. A., 1930.
Ritz, G.: Beitrag zur Verbrennungstechnik des schnellaufende:
Vorkammer-Dieselmotors. Auto. tech. Zeitsclir., Jahrg. 36
Nr. 8, 25. April 1933, S. 197-203.
Ruble, Hans: Der Druckverlauf im Ziindkamniermotor. Zeit-
sclir. f. tech. Physik, Bd., Zehnter Jahrg., Nr. 10, 1929, §,
465-472.
Sclilaefke, K.: Vorgange beim Verdichtungshub von Vorkam.
mer-Dieselmaschinen. Z. V. D. I., Bd. 75, Nr. 33, 15. August
1931, S. 1043-1046.
Scliwaiger, Iv.: Einzelheiten iiber das Vorkammerverfahrea
Auto. tech. Zeitsclir., Jahrg. 37, Nr. 16, 25. August 1934, S
422-424.
REPORT No. 578
FLIGHT MEASUREMENTS OF THE DYNAMIC LONGITUDINAL STABILITY OF
SEVERAL AIRPLANES AND A CORRELATION OF THE MEASUREMENTS WITH
PILOTS’ OBSERVATIONS OF HANDLING CHARACTERISTICS
By Hartley A. Soul£
SUMMARY
The dynamic longitudinal stability characteristics of
eight airplanes as defined by the period and damping of
the longitudinal oscillations were measured in flight to
determine the degree of stability that may be expected in
conventional airplanes. An attempt was made to cor¬
relate the measured stability with pilots’ opinions of the
general handling characteristics of the airplanes in order
to obtain an indication of the most desirable degree of
dynamic stability. The results of the measurements show
that the period of oscillation increases with speed. At
low speeds a range of periods from 11 to 23 seconds was
recorded for the different airplanes. At high speeds the
periods ranged from 28 to 64. seconds. The damping
showed no definite trend with speed. A general tendency
for airplanes that were stable with power off to become
unstable with power on was noted. The maximum damp¬
ing recorded was sufficient to reduce the amplitude of
oscillation by one-half in 9 seconds, or approximately
one-fourth cycle. The opinions of two pilots concerning
the handling characteristics of the airplanes apparently
were not influenced by the stability characteristics as
defined by the period and damping of the longitudinal
oscillations.
INTRODUCTION
The theory of dynamic longitudinal stability of air¬
planes, although not complete for power-on flight owing
to a lack of knowledge of the effect of the propeller
slipstream on certain of the stability derivatives, has
been developed to the point where it is possible to
predict the power-off stability characteristics of an
airplane from its dimensions. (See reference 1.) The
longitudinal motion of an airplane following a disturb¬
ance may consist either of a continuous divergence, i. e.,
static instability, or of two superimposed oscillations
of different periods and damping. In the present case
consideration is given only to the oscillatory motion
since no statically unstable airplane should be regarded
as satisfactory. The periods and damping of both
oscillations are given by the theory but, as the short-
period oscillation is so heavily damped that there is
no probability of instability of the oscillation for con¬
ventional airplanes, it is usual to consider the dynamic
longitudinal stability characteristics to be defined by
the period and damping of only the long-period, or
phugoid, oscillation. With the aid of the charts of
reference 1, the areas and dimensions of airplanes can
be adjusted during design to produce, within limits,
any length of the period and magnitude of damping
desired for this oscillation. Aside from the desirability
of having the airplane stable for all normal-flight condi¬
tions, little is known as to the length of the period and
the magnitude of the damping that constitute satis¬
factory stability. Pilots express opinions of an air¬
plane’s longitudinal stability in terms of such factors
as “stiffness” and of pitching or unsteadiness in flight
through rough air, but the relation between these
observed characteristics and the degree of stability as
defined by the period and damping of the phugoid
oscillation is unknown.
In the present tests, the period and damping of the
phugoid oscillations of several airplanes were measured
and, in addition, the general handling characteristics
as related to longitudinal motions were observed. The
measurements were made to obtain information on
the degree of stability to be expected in conventional
airplanes. The observations of the handling charac¬
teristics were made to determine whether there is any
definite relationship between the stability as defined
by period and damping of oscillations and the pilot’s
impression of handling characteristics. It was hoped
that the tests would provide an indication of the
degree of dynamic stability desired.
The theory of stability indicates that the period
and damping of the phugoid oscillations are affected
by engine power and elevator restraint as well as by
speed. It was therefore desirable to make the measure¬
ments for several conditions. The tests were made
with eight single-engine airplanes of different types:
69
70
REPORT NO. 578 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
two high-wing monoplanes and six biplanes. The
weights ranged from 1,440 to 6,100 pounds and the
engine powers from 95 to 575 horsepower. Where
feasible, the measurements of period and damping
were made for a speed range extending from 10 miles
per hour above the minimum speed to the maximum
speed in level lliglit for the following conditions:
1. Elevator fixed with throttle closed.
2. Elevator fixed with full throttle.
3. Elevator free with throttle closed.
4. Elevator free with full throttle.
The handling characteristics of each airplane were
rated by each of two test pilots.
APPARATUS AND METHOD
The eight airplanes tested were the Fairchild 22,
the Martin XBM-1, the Verville AT, the Martin
T4M-1, the Fairchild FC2-W2, the Boeing F4B-2,
the Consolidated NY-2, and the Douglas 0-2H. The
dimensions of these airplanes pertinent to their longi¬
tudinal-stability characteristics are given in table I.
The weights and center-of-gravity locations given are
for the airplanes as flown in the tests and do not repre¬
sent full-load conditions. The NY-2 airplane has a
fixed stabilizer that limited the elevator-free runs to
one air speed.
The following procedure was employed in the tests:
All runs were made at a mean pressure altitude of
approximately 3,000 feet. Steady conditions were
first obtained at a given speed. For the elevator-free
runs the stabilizer was adjusted to obtain trim at this
speed. The oscillations were induced by depressing
the nose of the airplane with the elevator until a
steady speed of approximately 5 miles per hour above
the initial flight speed was obtained. The elevator
was then immediately returned to the original setting
for the elevator-fixed runs or freed for the elevator-free
runs. Adjustable stops were provided for the elevator-
fixed runs to assist the pilot in resetting the elevator
to the original position and in holding it fixed during
the oscillations.
The air speed was used for the determination of the
period and damping of the oscillations. The variation
of air speed with time was obtained by means of a
recording air-speed meter and timer started prior to
the start of the oscillations. The record of air speed
was obtained for at least two complete cycles of oscilla¬
tion. The period of the oscillation was, of course, the
time between successive peaks on the air-speed record.
The damping factor f was computed by the equation
f=7)lo gevr — 17 (from reference 2)
where P is the period in seconds, Iff and V3 are the
true air speeds in feet per second at successive maxi-
mums, and V2 the air speed at the intervening mini¬
mum. The time T required for an oscillation to damp
to one-half amplitude was obtained by the equation
T_- 0.693
r
The period and the time to damp to one-half amplitude
were plotted as functions of the mean air speed during
the oscillation.
RESULTS AND DISCUSSION
The results of the measurements are given in figures
1 to 4. The figures show that the period and the damp¬
ing vary considerably with speed for a given condition,
between different conditions, and among different
airplanes. The condition with the elevator fixed with
throttle closed (fig. 1) is the only one which is com¬
pletely covered by the theory at the present time and
for which the stability derivatives may be readily com¬
puted. For this condition, all the airplanes were stable
in the speed ranges covered by the tests. The curves
show an almost linear increase of period with the
velocity of flight and, with the exception of the results
for the 0-2H airplane, there is very little difference
between the curves for the different airplanes. Longi¬
tudinal-stability theory indicates that the period may
be approximated by the equation
P=0.142(2+a)V2F
where V is the velocity in miles per hour, and a is a
variable dependent on the aerodynamic characteristics
but which does not change greatly for conventional
airplanes. Computations made on the basis of figure
1 show that a constant value of 1.4 for a is satisfactory
for approximating the period of conventional airplanes
for the speed range of the tests for the power-off eleva¬
tor fixed condition. The equation would then reduce
to
P= 0.262F
The damping is a more critical stability characteris¬
tic than the period and, consequently, the damping
curves show more dispersion than those for the period.
The times for an oscillation to damp to one-lialf am¬
plitude show a slight general tendency to decrease with
increasing velocity. In general, the number of cycles
required to damp to one-half amplitude varies inversely
as the period.
The effect of power on the stability characteristics is
shown by a comparison of the curves of figure 2, for
the elevator fixed with full throttle, with the curves of
figure 1. The periods of the oscillations are generally
longer with full throttle than with the throttle closed.
The damping is less, that is, the time required to damp
to one-half amplitude is longer. The power effects are
greatest at low speeds where the propeller thrust and
the ratio of slipstream velocity to forward speed are
greatest. All of the airplanes with the exception of the
FLIGHT MEASUREMENTS OF THE STABILITY OF SEVERAL AIRPLANES
71
T4M-1 showed a tendency toward dynamic instability
at low speeds with power on. Four airplanes, the
0-211, the F4B-2, the AT, and the NY-2, actually
became unstable within the speed range covered by the
tests. The instability existed in the form of an increase
in the amplitude of the oscillations with time. No case
of instability in the form of continuous divergence from
steady conditions, corresponding to a positive slope of
the pitching-moment curve or static instability, was
encountered in the tests.
Figures 3 and 4 present the results for the elevator-
free tests. A comparison of figures 1, 2, and 3 shows
Figure 1. — Period and damping of longitudinal oscillations with elevator fixed and
power off.
that the stability characteristics are considerably less
affected by freeing the elevator than by applying power.
The periods are slightly shorter with free elevator than
with the elevator fixed. The damping is decreased, but
only the results for the 0-2H airplane show instability.
All the airplanes had statically unbalanced elevators.
For elevators equipped with mass balances, as is usual
with more modern airplanes, the differences between
the elevator-fixed and elevator-free stability would
probably be less than that recorded.
For most cases power has the same general effect of
decreasing the period and damping with the elevator
free as with it fixed. The 0-2H airplane is an excep¬
tion. This airplane with the elevator fixed was stable
with the throttle closed and unstable with the throttle
open. With elevator free, it was unstable with the
throttle closed and stable with the throttle open.
Table II has been prepared to show the test condi¬
tions for which instability was recorded for the various
airplanes. As will be noted, only the F-22 and the
T4M-1 were stable for all test conditions and speeds.
The FC2-W2 and the XBM-1 were stable for three of
the four test conditions. The F4B-2, AT, and 0-2H
airplanes were completely stable for only two condi¬
tions. The NY-2 airplane was unstable for only one
condition but, since this airplane had a fixed stabilizer,
the elevator-free runs were made at only one speed.
Figure 2.— Period and damping of longitudinal oscillations with elevator fixed and
power on.
The range for periods of oscillations given by the
results for all test conditions extends from 1 1 seconds,
for the F-22 airplane at 60 miles per hour in gliding
flight with the elevator free, to 64 seconds, for the 0-2II
airplane at 102 miles per hour with the elevator fixed
and power on. It has been noted previously that, for
the power-off elevator-fixed condition, all airplanes
except the 0-2H had approximately the same period at
any given speed. If all test conditions are taken into
consideration, however, fairly large variations of the
periods at a given speed are noted. At 60 miles per
hour, the shortest period is 11 seconds and the longest
23 seconds. At 102 miles per hour, the shortest period
is 23 seconds and the longest 64 seconds. It is of
72
REPORT NO. 578 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
interest to note that for most airplanes and test condi¬
tions the maximum period is about 45 seconds.
The times for the oscillation to subside to one-half
amplitude vary from infinity for the cases of instability
previously discussed to 9 seconds for the FC2-W2 air¬
plane in gliding flight at 118 miles per hour with the
elevator fixed. On the basis of the number of cycles,
this damping corresponds to a reduction of the ampli¬
tude to one-half in approximately one-fourth cycle.
The damping shows no definite trend with speed of
flight, so ranges at different speeds are of no importance.
Table III shows alphabetical ratings of the airplanes
based on measured stability characteristics as compared
with pilots’ ratings based on observed longitudinal
Figure 3.— Period and damping of longitudinal oscillations with elevator free and
power off.
control and handling qualities. It will be appreciated
that any ratings made on the basis of the measurements
for comparison with the pilots’ ratings can only be
approximate and represent average conditions. The
ratings for the period given in table III consider the
entire speed range. The shortest period is designated
A. The periods increase in alphabetical order. The
ratings for damping consider primarily the higher por¬
tion of the speed range where most flying is done and
where most of the airplanes are stable. The greatest
damping is designated A.
The magnitude of the elevator forces and movements
required for normal operation of an airplane, through
their partial dependence on the slope of the pitching,
moment curve, are indirectly related to the stability a;
defined by the period and damping of the longitudinal
oscillation. The relationship has resulted in the use o!
the loosely defined piloting term “stiffness” to describe
the combined longitudinal stability and control char¬
acteristics. The general usage of the term has made it
desirable to make it one of the bases for rating the air¬
planes, although it is appreciated that the ratings given
depend on the interpretation of only two pilots and
might be somewhat different from those that would
have been obtained had more pilots been consulted.
In table III, the stiff est airplane has been designated A.
Figure 4.— Period and damping of longitudinal oscillations with elevator free and
power on.
Because stiffness does include the elevator force and
movements, pilots prepared separate ratings on the
basis of these two items. The airplane with the heaviest
elevator control and the one requiring the greatest
elevator movements are designated A. A rating was
also prepared on the basis of the amount of pitching
occurring during flight in rough air. In this case, A
designated the airplane doing the most pitching or
being the unsteadiest in flight in rough air.
A comparison of the different ratings prepared by the
pilots shows that the ratings for stiffness are almost
identical with those for elevator force. Aside from the
fact that stiffness is given in four gradations and the
elevator force in three, the T4M-1 airplane is the only
FLIGHT MEASUREMENTS OF THE STABILITY OF SEVERAL AIRPLANES
73
one for which there is actual disagreement. This air¬
plane was the largest of the group tested and had a
wheel control. The pilots associate heavier forces with
a wheel than with stick control and rate airplanes for
stiffness accordingly. Apparently, at least for the
Committee’s pilots, stiffness refers primarily to elevator
force with consideration taken of the size of the air¬
plane and type of control. The ratings for elevator
movement show that there is a tendency for large
elevator forces to be associated with large elevator
movements. The ratings for pitching in rough air show
no correlation with those for any other item.
In the vibration of springs, the period of oscillation
varies in an inverse ratio to the spring stiffness. By
analogy the airplane having the shortest period may be
considered the stillest. From the listings on table III,
it will be noted that the pilots’ ratings for stiffness are
in almost direct opposition to the stiffness as indicated
by the period. There are too many variables involved
to determine the reason for the reverse order for the
two ratings, but the conclusions cannot be drawn that
this reverse order will occur for all airplanes. The
disagreement, however, indicates that elevator forces
and period are not closely enough related to the slope
of the pitching-moment curve to assume that high
forces and a short period will result from a large nega¬
tive slope to the curve. Neither can the ratings for
damping be correlated with the pilots’ observations of
stiffness. Likewise, there is no apparent correlation
between the pilots’ ratings for pitching or unsteadiness
in rough air and either the measured periods or the
damping. It is also of interest to note, in connection
with the lack of correlation of the measured dynamic
stability characteristics and the characteristics observed
by the pilots, that the instability of the oscillations for
the power-on conditions for several of the airplanes
had no appreciable effect on their flying characteristics
and was not noted by the pilots prior to the tests.
It is evident from the foregoing comparisons that
the dynamic longitudinal stability characteristics, as
defined by the period and damping of the phugoid
oscillation, are not apparent to the pilot and, therefore,
cannot be taken as an indication of the handling
characteristics of airplanes. If the most desirable
degree of dynamic stability is to be determined, factors
other than the handling characteristics will have to be
considered. The reaction of the airplane to rough-air
conditions appears to offer a possible basis. The pitch¬
ing in rough air, from the present tests, does not appear
to be related to the phugoid oscillation. It may,
however, be related to the short-period oscillation, and
this possibility should perhaps be investigated. Fisher
(reference 3) shows that the structural loads imposed
by gusts are influenced by the stability derivatives.
CONCLUSIONS
1. The period of the phugoid longitudinal oscillations
for the eight airplanes tested varied from 11 seconds at
low speeds to 64 seconds at high speeds. For the
elevator-fixed power-off condition the period for con¬
ventional airplanes may be approximated by the
equation
P= 0.262F
2. The maximum damping encountered in the tests
was sufficient to reduce the amplitude of oscillation to
one-half in 9 seconds, or in approximately one-fourth
cycle.
3. Four of the eight airplanes were dynamically
unstable with power on although all were stable with
power off and the elevator fixed and only one was
unstable with power off and the elevator free, indicating
the importance of the effect of power upon the stability
characteristics.
4. The dynamic longitudinal stability of airplanes,
as defined by the period and damping of the phugoid
oscillation, has no apparent bearing on the factors from
which pilots judge the handling characteristics.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., July 15, 1936.
REFERENCES
1. Zimmerman, Charles H.: An Analysis of Longitudinal
Stability in Power-Off Flight with Charts for Use in Deisgn.
T. It. No. 521, N. A. C. A., 1935.
2. Soule, Hartley A., and Wheatley, John B.: A Comparison
between the Theoretical and Measured Longitudinal
Stability Characteristics of an Airplane. T. R. No. 442,
N. A. C. A., 1932.
3. Fisher, H. R.: The Normal Acceleration Experienced by Aero¬
planes Flying through Vertical Air Currents. Part I. The
Calculation of the Acceleration Experienced by an Aeroplane
Flying through a Given Gust. R. & M. No. 1463, British
A. R. C., 1932.
74
REPORT NO. 578 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I
CHARACTERISTICS OF AIRPLANES TESTED
Airplane.
Type
Wing area (sq. ft.) - - - -
Weight (lb.) _
Engine horsepower - - -
Wing loading (lb./sq. ft.) - - - .
Power loading (lb./hp.) - - - ---
Wing dimensions:
Span upper (ft.) . . .. . . . . .
Span lower (ft.) - - - -
Chord upper (ft.) - - - - -
Chord lower (ft.) - - - - -
Gap (ft.) _ _ - _ _
Stagger (ft.) - : - - -
Wing setting (deg.) _ _
Airfoil section _ _ _ _ _
Mean aerodynamic chord (ft.) _ _ _ _
Leading edge to leading edge of lower wing {horizontal^dt.j"
Tail dimensions:
Span (ft.).. . ... . - - -
Stabilizer area (sq. ft.) _
Elevator area (sq. ft.) . . . . . . . . .
Elevator hinge to leading edge of lower wing {hoGzonta/ fft!)
c. g. location:
Relative to M. A. C. {^wntd} percent of M' A‘ C . .
Relative to thrust axis (ft.) . - . . . . . .
Fairchild
22
Martin
XBM-1
Verville
AT
Martin
T4M-1
Fairchild
FC2-W2
Boeing
F4B-2
Consoli¬
dated
NY-2
Douglas
0-2H
Parasol
Biplane
Biplane
Biplane
High-wing
Biplane
Biplane
Biplane
mono-
mono-
plane
plane
171
412
242
656
336
236
370
368
1, 440
6, 100
2,300
5,824
4,510
2, 875
2, 769
4, 960
95
575
165
525
450
500
220
400
8.4
14.8
9.5
8.9
13.4
12.2
7.5
13.5
15.2
10.6
13.9
11. 1
10. 0
5. 75
18.2
12.4
32. 83
41.0
31.0
53.0
50.0
30.0
40.0
40. 1”
40.0
31.0
53.0
26. 33
40. 0
28 f,;
5.5
6. 17
4. 17
6. 58
7.0
5.0
5.0
5.0
5.42
4. 17
6. 58
3.75
5. 0
5.0
6. 17
5. 0
7. 5
4.87
4. 96
6.0
2. 58
2. 13
0
2. 67
2.33
1 85
1.0
0
0
2.0
2.6
0
2.0
2.0
N 92
N 22
/ Clark
Clark
Gottingen
Boeing
Clark
Gottingen
{ Y-15
Y-15
387
106
Y
398
5. 50
5. 66
4. 17
6. 58
7.0
4.60
5. 00
5.00
. 13
3.60
2.92
4. 03
.25
3.30
2. 83
3.48
0
.92
1. 18
0
0
2.05
1.33
.98
10.0
14.0
10.0
18. 92
11. 6
12. 17
12. 27
13.92
15.8
28.4
16.6
54. 5
28.6
19.9
17.3
23, S
10.4
25. 6
13.3
30. 0
17.6
17.9
17.6
23.1
-2.0
3.0
2.3
5.5
. 7
2. 17
4. 25
4.00
14. 69
18. 20
15.4
24.0
25. 34
12. 53
18. 18
20.71
/ -52. 3
-35. 8
-21.6
-21.7
-29.0
-32.8
-18. 2
1.2
t 28. 0
29. 7
33. 1
30.9
30.6
38.5
28.6
36.6
-.30
-.38
.08
-.40
.83
. 12
-.08
1. 4!
TABLE II
SUMMARY OF DYNAMICALLY STABLE AND
UNSTABLE CONDITIONS OF AIRPLANES
TESTED
[S, stable; U, unstable]
Airplane
Ele¬
vator
fixed
throt¬
tle
closed
Elevator fixed
full throttle
Elevator free
throttle closed
Elevator free
full throttle
1 Fairchild 22 _
s
S _
S _ _ _
S.
Martin T4M-1...
s
S _
S _
s.
Con solidated
s
U below 49
s _
s.
NY-2
m. p. h.
Boeing F4B-2 _
s
U below 58
s _ _
U below 56
m. p. h.
m. p. h.
Verville AT _
s
U below 58
s _
U below 57
m. p. h.
m. p. h.
Douglas 0-2H _
s
U below 83
U below 91
S.
m. p. h.
m. p. h.
Fairchild FC2-W2.
s
S _
S _
U below 61
m. p. h.
Martin XBM-1
s
S — - - _
s _
U below 70
m. p. h.
TABLE III
RATING OF LONGITUDINAL STABILITY AND
HANDLING QUALITIES OF AIRPLANES TESTED
Airplane
Obs
Stiff¬
ness
erved characteristics
Factors affecting stiffness
Measured char¬
acteristics
Eleva¬
tor
force
Eleva¬
tor
move¬
ment
Pitch¬
ing in
rough
air
Period
Damp-'
mg
Fairchild 22 _ _
D
C
B
A
A
A
Martin T4M-1 _
C
A
A
B
B
B
Consolidated N Y-2 _
C
B
B
A
B
B
Boeing F4B-2 _ ...
D
C
C
C
A
C
Verville AT. . . .
C
C
B
B
D
B
Douglas 0-2H _
A
A
A
A
D
I)
Fairchild FC2-W2 _ .
B
B
B
B
C
A
Martin XBM-1 _ _
A
A
C
D
C
I)
A is used to designate airplanes that are stiffest, require the greatest elevate:
forces and movement, do most pitching in rough air, and have the shortest period;
and the greatest damping.
REPORT No. 579
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
Bv Robert T. Jones
SUMMARY
The two-control operation of a conventional airplane
is treated by means of the theory of disturbed motions.
The consequences of this method of control are studied with
regard to the stability of the airplane in its unconstrained
components of motion and the movements set up during
turn maneuvers .
It is found that the motion of a conventional airplane
is more stable when an arbitrary kinematic constraint is
imposed in banking than when such constraint is imposed
in yawing. Several hypothetical assumptions of piloting
procedure, each of which is considered to represent a
component of the actual procedure, are studied. Different
means of two-control operation are also discussed and it is
concluded that a reliable rolling-moment control that does
not give the usual adverse secondary yauying moment
should be most satisfactory . Several special modifications
intended to make the airplane more suitable for two-control
operation are also discussed, and it is found that relatively
great weathercock stability (Nv) would be desirable.
INTRODUCTION
A number of flights have been made with airplanes
utilizing both the aileron-elevator and the elevator-
rudder combinations for two-control operation. Some
question exists as to which of these modes of operation
is likely to prove the better and also whether either of
them is capable of affording the controllability requisite
to safety in flight. Such questions must, of course, be
eventually decided by experience, no mathematical
analysis being sufficiently broad to deal with all aspects
of the problem. It is believed, nevertheless, that cer¬
tain conceptions gained from an analysis of the problem
may be useful in furthering development along these
lines.
One of the purposes of the present work was to
ascertain on theoretical grounds which of the two
possible modes of operation was more likely to prove
satisfactory. It was also desired to find what changes
might be effected in a conventional airplane to make it
more suitable for two-control operation.
The analysis of the various dynamical problems that
arise makes use of many concepts that are discussed
at length in reference 1. The treatment of airplane
motion as a problem of dynamics is based primarily on
the assumptions of the theory of airplane stability as
developed by Bryan and others; for the elucidation of
this theory the reader is referred to text books on
aeronautics.
MATHEMATICAL TREATMENT OF CONTROLLED
MOTION
The motion of an airplane with adequate control
about its three axes may, in one sense, be regarded as a
purely constrained motion. From this point of view,
the act of piloting the airplane must be considered to be
the use of the available control means for overcoming
the inherent aerodynamic and inertial reactions of the
airplane, causing it to follow a more or less definitely
constrained motion induced by the controls. The
natural oscillation and damping of the free motion of
the airplane do not appear, then, in the controlled
motion because the pilot has accommodated his use
of the available control to the governing of these
inherent tendencies. Accordingly the stability or insta¬
bility of the airplane will be apparent only in the requi¬
site use of the controls to perform a given maneuver.
It has been found by experience that the lateral-
stability characteristics of an ordinary airplane are
such that it is feasible to abandon one of the direct
constraints of the lateral motion in ordinary flight
maneuvers. All lateral maneuvers that are to be
performed with a minimum of sideslipping or sidewise
acceleration require a definite coordination between
the banking and yawing motions; it appears that a
conventional airplane will naturally tend to fulfill this
requisite relation in greater or less degree, on account
of the inherent stability, even when one of the lateral
controls is abandoned.
Under the conditions of two-control operation the
motion of the airplane cannot be considered as an en¬
tirely constrained motion. The pilot of such a machine
can exercise direct constraint in only one of the three
components of lateral movement and must depend on
the natural tendencies of the airplane for the requisite
coordination of the other motions. In order to show
this coordination the airplane need not be entirely
stable with all controls released, but it is imperative
that there be satisfactory stability in those components
in which the machine is unconstrained. Thus, if an
75
76
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
airplane is to be controlled by the ailerons and elevator
alone, it must be satisfactorily stable in combined
yawing and sideslipping, in which it is free; if control
is by rudder and elevator, corresponding stability in
combined banking and sideslipping is necessary.
If the controls are considered to impress constraints
in those components of motion in which they operate
directly, the movements of a two-con trol airplane may
be studied by the method of forced oscillations. Thus,
if the airplane controlled by ailerons is caused to follow
a definite course in banking, in which it is considered
to be constrained, this motion will impress disturbing
forces and couples leading indirectly to yawing and
sideslipping motions. The yawing and sideslipping
motions must, however, be considered to be uncon¬
strained and to be conditioned by the natural stability
of the machine as well as by the impressed disturbances.
The disturbing forces or couples impressed in those
components in which the airplane is unconstrained
are caused by the constrained movements and are
considered proportional to them. The factors of
proportionality are simply the appropriate stability
derivatives of the airplane. Thus, if the machine is
constrained to follow a definite sequence of rolling
motions by the application of a suitable control moment,
a disturbing acceleration in yawing that is propor¬
tional to the given rate of rolling at each instant will
be impressed, namely:
impressed
dr v y ,,
s=J,xiV'
In order to express the foregoing ideas definitely it
will be necessary to resort to mathematical treatment
of the motions. It is convenient for this purpose to
choose a set of axes rigidly fixed in the airplane at its
center of gravity and inclined at the angle of attack a,
so that the X axis points into the direction of the
relative wind in steady flight at the specified lift co¬
efficient. The following notation and diagram define
the quantities used in the subsequent equations.
U0, forward (A"- wise) velocity in steady
flight.
p, rolling component of angular veloc¬
ity.
<P}
yawing component of angular veloc.
ity.
component of flight velocity along ]
axis (sideslip).
angle of bank (relative to gravity),
d, angle of sideslip v/U0, approximately
<5, angle of rudder or aileron deflection.
Y , force component along the direction
of the Y axis.
L , rolling-moment component.
N, yawing-moment component.
8Li—L\mk: y2, [Control moments per unit moment ol
8N&= N/mkz2,\ inertia of airplane.
Stability derivatives in terms of unit
mass or moment of inertia of air¬
plane, thus:
dY
dv
5 L
Y
L
jp
Lr
Lv
NP
Nr
Nv
Yv=^ I™
Lr= dr lmkx2> etc-
A number of secondary considerations will be neg¬
lected in the mathematical analysis of the problems
to make the mathematical expressions as simple as
possible and because it is not considered important to
secure exact numerical results for studying the general
problem. For these approximate calculations the
lateral and longitudinal motions of the airplane will be
considered separable during turning flight. A check
of the maximum gyroscopic couples encountered shows
that they are negligible for the present study, although
it is probable that the longitudinal and lateral oscilla¬
tions in turning flight can be separated for only &
relatively short time after the passing of a disturbance.
Another assumption made is that the effect of a com¬
ponent torque applied to the airplane is an angulai
acceleration about the axis of the torque. In general,
the angular acceleration does not have the same axis
as the applied torque but in the present case the refer¬
ence axes chosen lie near the assumed principal axes ol
inertia, and the difference of moments of inertia taken
about various axes is not great. In addition, the
flight of the airplane is assumed to be horizontal and
the speed not to vaiy appreciably from the average
(U0) in a given case.
According to the previously outlined treatment, the
movement of the airplane in at least one of the lateral
coordinates will be modified by a constraint. The
complete set of three degrees of freedom is not in this
case expressed in the usual three simultaneous equa¬
tions of motion, for this procedure would imply that
each component of the motion was affected by the
other two, whereas the present problem calls for an
independent expression of one of them. Thus, it is
assumed that the available control is sufficiently
powerful to force any desired motion in the controlled
component. When setting up the equations, this
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
motion will be considered to be given as a function of
the time.
It is important to emphasize in the interpretation
of the mathematical analysis the practical significance
of the assumptions used. The solution of the equa¬
tions requires that the complete history of the variation
of one of the components of the motion (or the control
setting) be known beforehand. This variation is not
subsequently altered to accommodate the variation of
the other motions as would be the case if an intelligent
pilot were at the controls. It may be imagined that
the pilot has only one degree of attention. Having fixed
on a procedure of rolling the airplane, he concentrates on
the execution of this alone, paying no attention to the
consequences in yawing or sideslipping. It would be
feasible to assume that the pilot concentrated his
attention on carrying out a predetermined manipu¬
lation of the controls, without regard to any of the
motions set up. This assumption is, however, con¬
sidered to be too far removed from actuality to be of
much use in analyzing the problem. It would be of
more practical interest to assume that the pilot had
sufficient skill to enforce a desired motion in every
respect, taking no account of the control manipulations.
The control manipulations required could then be
calculated and an idea of the degree of skill necessary
to attain a perfect result could be derived therefrom.
With two-control operation a perfect coordination
of the motions is, of course, not possible. If the pilot
enforces complete control over one component of the
airplane’s motion, he must do so at the expense of
control in some other component. The residual com¬
ponent is then considered to be free. In practice the
pilot can exercise an indirect influence on all lateral
motions with only a single lateral control. Hence, it
is possible to assume that a skilled pilot could enforce
complete control over the yawing motion even though
his available control exerted only rolling moments
directly. Then the rolling motion must be considered
free and not subject to the pilot’s attention although
his available control operates directly on this motion.
Such an assumption obviously cannot give an accurate
description of anything occurring in practice. The
same is true in some degree of any other assumed pro¬
cedure that can be mathematically treated. The actual
procedure of a pilot is undoubtedly an indeterminate
and variable synthesis of such elementary procedures.
The study of a single assumption of this nature is
therefore incomplete, constituting simply a part in the
analysis of the problem.
In order to illustrate the variety of assumptions
that may be treated, four equations, containing
movements both of the airplane and of the control
surface, will be set down:
i {
dv , T J -T /-
■^—gv+rUu—vl „
= 0
dp
dt
dr
dt
—pLp—rLT—vLv—bLi =0
~pNv— rNT — vNv — 8 Ns =0
= 0
dip
iirv
a)
These equations are to be satisfied simultaneously and,
since there are more variables than equations, one of
the variables must be given in terms of the time to
effect a solution. Any assumption of the kind con¬
sidered may be applied by setting one of the variables
equal to a function of t. Thus the equations of motion
with an arbitrarily prescribed course in rolling are:
jf+rU,-vY,
=g<p(t)
d
-rL-vL-hU =Lpp(t)-^p(t)
dr
dt
-rNT-vNv-5N6=Npp(t)
(2)
Similarly, if the pilot uses the control to enforce
some given motion in yawing, the equations are:
dv
dt
dp
dt
-g<p—vY
— U0r(t)
—pLP—vLt—8L&=Lrr(t)
d
- pNp-vN-M = Nrr (<) - Jfr it)
d<p
dt
—p— 0
(3)
Solutions of the foregoing differential equations have
the general form
v,p,8, or r=iCieXltJrC2eMt-)r • • + f (0 (4)
This type of solution has two significant components;
the part enclosed by parentheses represents the oc¬
currence of the natural oscillations and damping in the
resultant motion. If the natural modes of motion are
stable, this component will disappear with time and
the solution will be represented by f(0- If the im_
pressed disturbance is periodic, the motion will at first
be conditioned by the natural period but, if this is
damped, will later follow the impressed period in ac¬
cordance with Herschel’s theorem. In these cases
the term f(rf) may be called the “steady-state solution.”
Under the assumed conditions of two-control opera¬
tion the pilot enforces one component of the motion
and relies on the reaction of this motion on the un¬
controlled component to induce an appropiiate
78
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
motion there. As seen in equation (4), this accom¬
panying motion is at first conditioned by the natural
oscillations. Obviously for satisfactory two-control
operation it is desirable that the natural oscillations
in the uncontrolled components quickly die away. It
also appears that if any reasonable coordination of the
motions is to be obtained the period of the free oscil¬
lation must be short compared with the duration of
the maneuver.
STABILITY OF A CONVENTIONAL AIRPLANE
OPERATED WITH TWO CONTROLS
From the foregoing considerations it is apparent
that the airplane must have certain degrees of stability
for satisfactory two-control operation. Operation
with constraint in yawing calls for stability in combined
rolling and sideslipping, whereas operation with rolling
constraint requires stability in combined yawing and
sideslipping, as indicated by equations (2) and (3).
In order to illustrate the degree of stability of a con¬
ventional airplane in these motions, data from an
assumed average airplane (described in reference 2)
have been used and several calculations made for the
two cases. The principal characteristics of the as¬
sumed airplane are given in the table I.
TABLE I
CHARACTERISTICS OF ASSUMED AVERAGE
AIRPLANE
Type - Monoplane, 2-passenger.
Gross weight _ 1,600 lb.
Wing area - 171 sq. ft.
Wing span _ 32 ft.
mkx2 - 1,216 slug-ft.2
mkz 2 - 1,700 slug-ft.2
Stability derivatives at various lift coefficients:
Cl
Lp
Lr
«L,
NP
Nr
N,
Y,
0. 35
1.0
b 1.8
-5.44
-3. 23
-2. 46
1. 11
1.88
2.51
-0. 0544
-.041.5
-.0461
-0. 207
-.301
-.310
-0.913
-.663
-.977
0. 0368
.0231
.0221
-0. 172
-. 145
-.224
a 5° dihedral.
6 Flaps down.
STABILITY WHEN CONSTRAINED IN ROLLING
The stability of the motion of the airplane (or of the
movement of the control, 5) when the rolling compo¬
nent is arbitrarily constrained may be calculated from
the complementary equations of (2):
Ji+rUo— vYv =0
—rLT—vLe—8Ls = 0
dr
—rNT— vNv — 5 Ns = 0
(5)
The complementary equations express only a part of
the complete motion. They show the influence of sta¬
bility on the manipulations of the control required
to enforce the desired constraint in bank as well as the
stability of the free yawing and sideslipping oscilla¬
tions. Whatever rolling motion is assumed, a solution
of the complementary equations will appear as a com.
ponent of the final solution.
The third equation of (5) may be solved for v and the
resulting expression substituted into the first equation,
etc. The same procedure may be carried out for r or 5;
in either case the so-called “auxiliary” equation is:
U[\2- (Nr+ Yv)\+NrYv+ UoN, }
(6)
+Ns[LT\-LrY-U0Lv]=0
The equation is conveniently divided into two parts
to show the effects of control rolling and yawing mo¬
ments. If the rolling motion is constrained by a direct
rolling-moment control, the second part of the equation
(containing Ns) is eliminated. Since the first poly¬
nomial is a quadratic, its roots are:
X = rT Y v) T V (N rT F8)~ — 4 ( Nr Yv -f- Nv U o) ^
If the airplane shows an average degree of weathercock
stability (A77>0), the roots will be conjugate complex
numbers and the terms
of equation (4) will represent a damped oscillation.
If \i=a-fT& and X2=a— ib, the period of this oscillation
is
(8)
and the time to damp to one-half amplitude:
(9)
a a w
provided that a is negative.
Neglecting the first part of equation (6) (containing
Ls) amounts to the assumption that the banking
motion is constrained by the application of a rudder
control. The solution of this part of the equation
alone is:
X (10)
The auxiliary equation thus has only one real root and
it is negative, indicating stability. The assumption
is that a sidewise disturbance (v) causes the pilot to give
the airplane a rate of yawing such that
rLr= —vLv (11)
As Lr is positive, this yawing reduces the sideslip and
must then itself be reduced in proportion to prevent
rolling, thus resulting in a convergence. This control
procedure, although stable and nonoscillatory, rep¬
resents a more artificial assumption than the control of
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
79
the rolling motion by direct rolling moments, for here
the pilot in order to check a sudden disturbance must
move the airplane as a whole with equal suddenness
while with direct control he is only called upon to de¬
flect the control surface suddenly.
Although the motion that occurs when the rolling
is controlled — either directly by a variable rolling
moment alone or indirectly by a yawing moment —
is stable, a control device that gives both rolling and
yawing moments in combination may cause instability.
Inasmuch as conventional ailerons do give secondary
yawing moments, this case is of considerable interest.
Denoting the ratio:
where each <5 denotes aileron deflection, the following
resolution of equation (6) is obtained
X2- [(N-kLt) + FJX+ (. N-kLt ) Yw
Uo(Nv — kLv) =0
The solution of this equation differs from that of the
first component of equation (6) in that the quantities
Nv and Nr are replaced by ( Nv—kLv ) and (N t—kLt),
respectively. Thus it is concluded that an effect of a
secondary adverse yawing moment in an attempted
rolling maneuver will be an apparent reduction of both
the weathercock stability (Nv) and the damping in
yawing (2Vr).
Calculation shows that the motion becomes unstable
when
or when
*>
Nr+Yv
Lr
yvnt+ u0nv
YvLt+U0Lv
(13)
(14)
in negative magnitude. Such instability would indi¬
cate that an arbitrary constraint in rolling (such as
attempted level flight) could not be maintained by the
ailerons alone.
Conventional ailerons give rise to adverse yawing
moments in an amount approximately independent of
the speed of flight while the rolling moments and
stabilizing factors are much reduced at the lower speeds.
The result is that the ratio k approaches the foregoing
undesirable magnitude at the highest lift coefficients.
It is therefore considered that ordinary ailerons work¬
ing on a part of the wing surface that sustains a high
lift would not be desirable for two-control operation.
Table II lists the residts of calculations of the stabil¬
ity indexes of the average airplane in free yawing and
sideslipping motions at several lift coefficients. Since
these calculations were to be used later in investigating
the motions set up during turning maneuvers, a certain
increase in the steady-flight speed at a given lift coeffi¬
cient was assumed. The increase amounted to 7J4
percent and the stability derivatives at each lift coeffi¬
cient were multiplied by this factor.
TABLE II
INDEXES OF STABILITY OF MOTION WITH CON¬
STRAINT IN ROLLING
Cl
Roots of
stability
equation
Period of
oscilla¬
tion
Time to
damp Yi
( 0.35
-0. 583±2. 50 i
Seconds
2.51
Seconds
1. 18
K=0 _ _ _ _
1 1.0
— . 435±1. 51 i
4. 16
1.60
1 1.8
— . 645:4=1. 23 i
5. 10
1.08
Adverse yaw *= — 0.15, . .
1.0
— . 283±1. 31 i
4.80
2.5
Favorable yaw *=0.15 _ _
1.0
-. 585±1. 67 i
3. 76
1.2
The combined yawing and sideslipping motion under
consideration is, in general, very stable. Further
calculations have shown that the stability of the
motion when free only in yawing and sideslipping is
much greater than the stability of the completely free
motion. The oscillations have, in general, a shorter
period and greater damping.
STABILITY WHEN CONSTRAINED IN YAWING
Calculation of the stability of the rolling and side¬
slipping motions when the airplane is constrained in
yawing is similar to that given for constraint in banking.
Here the complementary equations of (3) are used.
The corresponding auxiliary equation is
Ns[\3 — (.Lp-j-I v)\2-\-Lpl ,,X yLv 1 , r.
+Ls[-Np\2+NpYv\-gNv}= 0
The complementary part of the general solution (4)
will be of the form
p, v, or 5= Ciex,t + C2eMt + C3eMv (16)
since there are now three roots. In case the yawing
motion is constrained directly by the application of
control yawing moments, only the first part of the
equation will be in force. Calculation shows that two
of the roots will then be of the conjugate complex type
previously discussed and that the third root will be very
nearly equal to Lp. Table III gives these roots as
calculated for the average airplane under conditions
similar to those assumed in table II.
TABLE III
STABILITY OF MOTION OF AVERAGE AIRPLANE
WITH CONSTRAINT IN YAWING
CL
Real
root
Complex roots
Period of
oscillation
Time to
damp Yi
(complex
roots)
0. 35
1.0
1.8
-5.90
-3.59
-2. 67
-0. 064 ±0. 562 i
— . 019± .636 i
— . 015=fc .716 i
Seconds
11.2
9.9
8.8
Seconds
10.8
36.6
46.3
80
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The fact that the auxiliary equation for the case of
free rolling and sideslipping motion with yawing control
has roots of such widely different magnitude is an
indication that the motion may be separated into
distinct modes. The large real root (nearly equal to
Lp) indicates the sharp damping of an initial rolling
motion and is of such magnitude that the wings may
be considered to be in a measure constrained against
rolling relatively to the air. A possible rolling motion,
however, that will not be appreciably damped consists
in rolling about an instantaneous center some distance
above the center of gravity of the airplane. For
rotation of the airplane as a rigid body about this
point the rolling moment due to sideslip will balance
the damping of the rolling.1 The height, zL, of the
instantaneous center above the center of gravity is
found from:
vLv=—pLp
where
v— —pz
whence
- _Lv
L L, (17)
The mode of motion represented by the small complex
roots (table III) thus consists in a swinging oscillation
of the airplane about the metacenter i as a pendulum
suspended from that point. The characteristic roots
for the pendulum motion would be
±V-!-±V^r (,8)
which are seen to be approximate roots of equation
(15) (Z, = 0).
From these considerations it appears that the two-
control airplane constrained in yawing with the rudder
would be subject to swinging oscillations of long period
and slight damping. If the airplane is given an initial
angle of sideslip, it will be restrained against banking
directly by the relatively great damping in rolling Lp
and the banking that occurs will conform nearly to a
rotation of the airplane about the metacenter zL. It
will be of interest to calculate this height, using the
stability derivatives given in table I:
CL
Feet
0. 35
100
1.0
92.5
1.8
53
Physical considerations indicate that the damping of
this mode of motion is almost entirely dependent on
Ye; hence, for two-control operation with the rudder, it
should be desirable to have a large value of this
derivative.
It is possible for the pilot to apply a yawing moment
either through the secondary influence of an aileron
control or indirectly by rolling the airplane as a whole.
If the latter effect were used to constrain the yawing,
the resulting motion would be excessively unstable,
Thus, in order to prevent a sidewise disturbance from
yawing the airplane (r=0), the pilot must execute a roll
such that the forward wing is depressed (pNp— —vNt).
This roll provides the occasion for an increase of side¬
slip due to the bank and requires, in turn, more rapid
rolling so that the motion diverges quickly. Secondary
aileron yawing moments of either sign moderate this
instability and the motion may become stable if the
yawing moment is favorable.
These considerations indicate that the pilot could
not maintain an exact yawing constraint by the use of
ailerons alone. On the other hand, this inability is
probably not of great importance since the assumption
of piloting procedure is obviously artificial and since
the former calculations (stability with constraint in
rolling) indicated that, if the ailerons were used to
hold the wings level, the free yawing oscillations would
be short and quickly damped. (See table II.) Thus
it appears that, in order to prevent any yawing whatever
during a disturbance, the pilot would have to execute a
divergent bank whereas if he merely held the wings
level the yawing motion might be unnoticeable. The
divergent bank consists in a rotation of the airplane
about the metacenter
zN —
Np
Nv
(19)
which is now situated below the airplane. The motion
is like that of a pendulum placed at this height above
its point of support.
TWO-CONTROL OPERATION IN STEADY TURNS
The two-control average airplane, showing stability
both in combined yawing and sideslipping (rolling
control) and in combined rolling and sideslipping
(yawing control), should reach a definite condition of
equilibrium with some fixed setting of the lateral con¬
trol. In general, the equilibrium condition corre¬
sponding to a definite rudder or aileron setting will be
a steady turn at a definite angle of bank. If the
components of rolling and yawing angular acceleration
produced by the deflected controls are 8L5 and 8 Ns,
as before, the equations of lateral equilibrium at a
fixed angle of bank may be written:
g<p— rU0+vYv =0
vLr -\-vL v -f- 8 Lb =0 >
vNr T vNv A 8 Ns = 0 ,
(20)
In case control is by ailerons giving secondary (adverse
or favorable) yawing moments, the term N$ is re¬
placed by kLs] and, in case control is by rudder alone,
L5 is dropped from the equations. In any case it has
1 This mode of oscillation has been discussed by Lanehester.
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
81
to be assumed that the longitudinal control is properly
manipulated for maintaining altitude and speed while
turning.
Two special conditions of equilibrium are of interest.
Solving the equations for the angle of bank
_ ( 1 vLr -f- LvJj o) 5 A/'s ( YvNt -}- Nt U0) 8L& /n 1 N
' g(LrN-LvNr ) ~ (21)
The necessary condition for the bank angle to be zero
with deflected controls is:
1 L$ / Y vLr-\- LVU0\
K Ns \YvNr+N,Uo) {JJ)
(See equation (14).)
In case the applied control rolling and yawing
moments are in this ratio, the steady state of motion
of the airplane will be a flat turn without bank. This
limiting ratio may be compared with the ratio of the
secondary aileron yawing moments to the rolling
moments. If the secondary moment is adverse and
exceeds a certain proportion of the rolling moment,
an equilibrium condition in which the ailerons do not
produce a bank of the airplane becomes possible. In
this condition a gradual deflection of the ailerons would
merely cause the airplane to assume a yawed attitude,
turning slowly under the influence of the side pressure
vYv. Such a condition should be especially avoided
in a two-control airplane utilizing aileron operation.
Another simpler condition of equilibrium that is also
of interest is the condition for zero rate of yawing
with deflected controls. The resolution of the equa¬
tions in this case is:
/ L „N 5 ATVLA _ „
\LrN-LvNT)
(23)
This is the condition for an ordinary sideslip and the
ratio of yawing to rolling moment requisite to this
condition is simply
_ L*s _ L v
K~NTW,
(24)
Obviously it should be considered undesirable to allow
the secondary adverse yawing moment of the ailerons
to approach this proportion of the rolling moment.
By a similar resolution of the equations another
condition, namely,
■Ls
K Nf, N T
(25)
is obtained for the case of steady turning without side¬
slipping. This equilibrium is possible with aileron
control alone in the case of secondary adverse yawing
moments and furnishes another criterion for the mag¬
nitude of these secondary moments. In this case it
would be expected that a gradual application of the
rolling control would lead to turning at a progressively
greater rate with the angle of bank opposite in sense to
the applied rolling moment.
The main point of interest in the condition of steady
turning with two-control operation is the angle of side¬
slip incident to the turn at various angles of bank.
The resolution of the equations for v results in:
V=g,PK(Y,L,+ UM ~(Y.N,+ UoN „) (20)
In the case of rudder control, where 0 the
expression for v reduces to:
_ -Z9V _
(f.+ E/ojj) (27)
while in the case of pure rolling-moment control
(ailerons giving no secondary yawing moments)
v
-g<p
(28)
Thus the sideslip incident to turning with only rudder
control is mainly dependent on the ratio of LJLr while
with rolling-moment control the important factor is
A'
Figure 1. — Diagram illustrating combined yawing and sideslipping motion during a
steady two-control turn. Metacenter for yawing moment r v =^1 metacenter for
- L »
rolling momentxL = £—
Nv/Nr. In both cases the sideslip will ordinarily be
positive (toward the center of the turn) although the
airplane does not necessarily lose altitude on this
account.
Figure 1 illustrates the combined sideslipping and
yawing of a two-control airplane during a steady turn.
82
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
In the case of rudder control the inward sideslip must
be such that vLv——rLr to prevent rolling. This
combined sideslipping and yawing motion may be
ascribed to a rotation of the airplane about some point
aft of the center of gravity. If the distance of this
point behind the center of gravity is denoted by xL
rxhLv——rLT
or xh=—h- (29)
for the case of rudder-controlled turns. For rotation
of the airplane about this point the rolling moment
vanishes, lienee the point is a metacenter for the rolling
moment. The X axis will be tangent to the flight
path at this point in rounding a turn, as shown in
figure 1.
Similar considerations apply in the case of operation
with a rolling-moment control with fixed rudder.
Here the metacenter is for a vanishing yawing moment,
the amount of sideslip being that necessary for
vNv=~rNr. The distance of the metacenter aft of
the center of gravity is found from
rxNNv— —rNr
or (30)
- _ Nr
AT
i\ g
An interesting point arises in connection with the
relation of the two metacenters (xL and xN). For
positive rotation of the airplane about a point nearer
the center of gravity than xN the residual yawing
moment will be negative; hence if the metacenter
xL is nearer the center of gravity than xN, steady
turning with rudder operation will require a positive
setting of the rudder, i. e., in a direction to aid the turn.
Conversely, if control is by rolling moments, the steady
motion will be a rotation about xN and, if the residual
rolling moment for rotation about this point is negative
( xL<CxN ), the rolling control setting will be positive,
also in a sense aiding the turn. Obviously, the con¬
dition xN<^xL corresponds to instability since in this
case with either mode of two-control operation the
control setting during a steady turn would be one
appropriate to recovery from the turn. This condition
is analogous to the spiral instability discussed by Lan-
chester. The following table gives the metacenters
xL and xN for the average airplane at various lift
coefficients:
Cl
XL
Xs
Fed
Feet
0. 35
20
25
1. 0
45
29
1.8
1
55
44
At the lowest speeds (C7z = 1.0 and 1.8) xN is le$.
than xL, indicating that negative rudder and aileron
settings will be required during steady positive turn?
Figure 2 shows results of calculations of the control,
moment coefficients for equilibrium in turning at
Figure 2.— Moment coefficients indicating control settings during steady turns si
various angles of bank.
various angles of bank that give an indication of the
fixed control settings.
Equilibrium angles of sideslip in steady turning
with both modes of two-control operation are shown in
figure 3. It is to be noted that the angle of sideslip
is not greatly different in steady turning with either
type of control and in every case is positive.
Figure 3.— Angles of sideslip during steady turns at various angles of bank with differ
ent modes of two-control operation.
The only possibility of outward or negative sideslip
during the steady turn occurs when rolling and yawinp
moments are applied in combination. Such an occur¬
rence is illustrated in figure 4, which shows the effect
of secondary aileron yawing moments on the equilibrium
during 30° bank turns. At CT = 1.0 the sideslip becomes
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
83
negative, or outward, when the ratio NsfL$
negatively Nr/LT, i. e.:
_Cn Ix_Ns^Nr
K~cxlz L^Lr
exceeds
(31)
(See equation (25).)
Whether or not a given secondary aileron yawing
moment will reduce or increase the equilibrium side¬
slip angle during a steady turn depends on the spiral
stability of the airplane, for this characteristic deter¬
mines the sign of the equilibrium control setting.
Figure 4.— The effect of secondary yawing moments on sideslip during a 30° bank
steady turn; two-control operation with ailerons.
Thus, in the case of a spirally unstable machine the
aileron setting will be appropriate to recovery from
the bank and an adverse yawing moment will act in a
positive direction, aiding the turn. In any event,
spiral stability, if present, must be considered as a
small effect (with conventional airplanes) ; and the
control setting during steady turns is, if positive,
almost certain to be small so that secondary moments
will have little effect. (See tig. 4, CL — 0.35.)
TWO-CONTROL OPERATION IN UNSTEADY TURNS
The consideration of the equilibrium state is suffi¬
cient for the study of conditions during slowly executed
maneuvers of sufficient duration for the natural free
oscillations of the airplane to die out. In the case of
rapid maneuvers performed by more or loss quick
movements of the control the equilibrium conditions
are of secondary importance and the primary con¬
sideration is the oscillation and damping of the free
motion.
According to the previously outlined treatment, the
motions of the two-control airplane set up during un¬
steady turns will be studied by considering a constraint
impressed on the motion in the particular coordinate
in which the available control operates. Thus in one
case of rudder control a definite sequence of yawing
motions appropriate to the turn maneuver under con¬
sideration will be assumed. The free rolling motion
that the airplane takes up during the maneuver will
then be studied and compared with the rolling motion
that would be considered appropriate for the execu¬
tion of the maneuver.
The investigation of unsteady conditions during
various maneuvers required that the equations of mo¬
tion (equations (1) to (3)) be solved for different types
and variations of the impressed disturbances. The first
step in the procedure consisted in obtaining solutions
of the equations for “unit disturbances” substituted
into each coordinate of freedom.
The unit disturbance is defined by
1 (f) =0 when f<T
l(t) = l when 0
(32)
(see reference 3) and is taken to represent a disturbing
acceleration of unit magnitude applied instantly at
t= 0.
The solutions of the equations of motion for this
type of disturbance were found by methods described
in reference 4. The result thus obtained is analogous
Figure 5.— Yawing motion due to unit side disturbance; two-control airplane constrained in rolling (aileron operation; *=0).
84
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
to tlie so-called “indicia! admittance” of the electric-
circuit theory and was combined with Carson’s gener¬
alized expansion theorem (see reference 5) to obtain
the motion due to the varying forms of disturbance.
If Vi (t) is the motion calculated for a unit disturbance
l(t), and v(t) is the motion due to a varying disturb-
As the curves show, the actual yawing is delayed fc
an instant but in each case oscillates about the meai
value given by (35). The most favorable condition!
that at high speed {CL— 0.35) since the appropriat
yawing motion occurs with the least delay and the os
dilations are most quickly damped.
Figure 6.— Yawing motion due to unit yawing disturbance; two-control airplane constrained in rolling (aileron operation; k=0).
ance, say <p(t) (see equation (2)), then Corson’s theorem
may be written
®«.)=®i(<»)*>(0) + dt (33)
It was found convenient to evaluate this integral
graphically.
Figures 5 and 6 show the motions of the two-control
airplane constrained in rolling (aileron operation) due
to unit disturbances acting in each of the two remaining
As stated previously, the unit motions, or motion;
due to unit disturbances, were utilized in calculating
the effects of varying disturbances assumed during tun
maneuvers. Thus the curves given in figure 5 wen
used to find the motions due to a varying angle of ban!
by means of Carson’s integral (33). Actually, in con¬
straining the airplane to a definite bank angle as wa;
assumed, a varying aileron rolling moment has to bf
applied and, if this moment is accompanied by s
degrees of freedom. Figure 5 shows the yawing mo¬
tions resulting from a suddenly impressed sidewise
acceleration of 1 foot per second per second. The con¬
ditions here may be assumed to represent the effect of
an initial and constantly maintained angle of bank of
approximately
In order to maintain this bank angle without sideslip¬
ping, the airplane should immediately acquire a uni¬
form rate of yawing of approximately
secondary yawing moment, additional disturbances in
yawing will be introduced. The rolling motion will also
introduce a secondary disturbance in yawing equal to
ATPXp(t). Figure 6 shows the yawing motion produced
by a unit disturbance in yawing that was used in calcu¬
lating the effects of such impressed yawing disturbances.
This curve may be considered to represent the yawing
motion following the sudden application of a control
yawing moment. The final effect of this disturbance is
to cause the machine to assume a yawed attitude, turn¬
ing slowly under the influence of the side force vYv.
Figures 7 and 8 show the corresponding solutions of
the equations of motion (3) for the case of the airplane
constrained in yawing by a rudder control. Figure i
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
85
may be taken to represent the rolling motion following
an initial bank angle. Presumably the ideal condition
would be a rapid diminishing of this bank angle to
zero. The integrated areas under the curves shown
would then approach a definite value after a few oscilla¬
tions, which area should be equal to the initial bank
angle, namely approximately
(36)
Instead, the airplane continues to roll one way and
then the other, executing the pendulum-like oscillations
followed in practice. In other respects, it was thought
that any smooth curve representing the banking or
yawing of the machine up to a definite angle or rate
maintained steadily for a short time and followed by a
smooth recovery to straight flight would serve the pur¬
pose. Figure 9 shows the time history of the ideal
three-control turn that was assumed in the subsequent
investigation. In most cases the manuever was as¬
sumed to be completed in 6.28 seconds and this time is
taken to represent about the maximum rapidity with
which the maneuver could be performed at the lowest
speed using conventional-tj^pe controls. Figure 10
Iigure 8. Rolling motion due to unit rolling disturbance; two-control airplane constrained in yawing (rudder operation).
described in the discussion of the stability of this mo¬
tion. The damping of these oscillations is slight and is
most apparent at the lowest lift coefficient, Cz,=0.35.
Figure 8 is similar to figure 7 except that here the
rolling motion is due to a suddenly impressed angular
acceleration in rolling. These curves were used in
calculating the effect of varying rolling moments im¬
pressed indirectly by yawing motion LTXr(t). (See
equation (3).) Figure 8 is of interest in illustrating the
two more or less distinct modes of motion in free rolling
and sideslipping. It will be noted that the rolling
starts very rapidly (with an initial angular accelera¬
tion of one radian per second per second) but soon
takes up the slow swinging oscillation. As in the pre¬
vious case of rolling motion, the steady state finally
approached is a definite angle of bank.
The foregoing calculations are of interest in indicat¬
ing how the different types of two-control airplanes
may be expected to respond to attempted maneuvers.
The first step in the calculation of an actual complete
maneuver is to arrive at a specification for that part of
the motion which is assumed to be constrained. It
will be of interest to compare the motions executed by
the two-control airplane with the most perfect possible
coordination of the motions that might be obtained
with three-control operation. Obviously, it will be
necessary to specify a maneuver that is within the power
of the control to produce and it will be desirable to
conform the specification to a type of turn likely to be
shows the control-moment coefficients necessary to
constrain the rolling and yawing motions to the speci¬
fied maneuver with perfect three-control operation.
Under the conditions of two-control operation the turns
Figure 9.— Angle of bank and rates of rolling and yawing specified for 30° bank two-
control turn maneuvers.
will not be perfect owing to the sideslipping and it is
to be expected that this sideslipping will in some
degree modify the control settings.
86
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
In the calculations illustrated in figure 11 the banking
motion was assumed to be forced to follow the ideal
bank by means of a rolling control and the resultant
free yawing motions were computed. The reaction of
the machine was evidently favorable in this case.
This result could have been anticipated from the calcu-
Figure 10.— Control-moment coefficients necessary to produce specified manuever
with zero sideslip.
lations of stability, which showed that the free yawing
motion was of short period and strongly damped.
The curves of figure 11, although indicating the
advantage of rolling-moment control, also bring out an
imperfection in the coordination of the yawing motion.
The rolling motion itself tends to induce an unfavorable
Time , seconds
Figure 11. — Free yawing motion during 30° bank maneuvers performed with rolling
control.
yawing motion at the start of the maneuver due to the
adverse sign of ATP. This effect becomes more pro¬
nounced at the higher lift coefficients and, in the worst
case ((?£,= 1.8), produces an adverse change in the
heading of the machine of 2.0°. The total change in
heading produced by the maneuver at this speed is
approximately 50°.
From the foregoing considerations, it appeared that
a certain amount of favorable secondary aileron yawing
moment might be desirable to overcome the adverse
yaw caused by the rolling motion at the start of the
Time, seconds
Figure 12. — The effect of secondary yawing moments on yawing motions during
30° bank maneuver performed with rolling control; Cl =1.0. C„=± 0.210,
(k=± 0.15).
turn. The effects of secondary yawing moments of
both favorable and adverse sign applied in proportion
to the control rolling moment are illustrated in figures
12, 13, and 14.
Figure 13. — The effect of secondary yawing moments on sideslip during 30° bank
maneuver performed with rolling control; Cl= 1.0. Cn = ±0.21 Ci («=±0.15).
The curves shown were calculated by equation (2)
and take account of the increments of control displace¬
ment necessary to accommodate the rolling moments
introduced by the yawing and sideslipping oscillations.
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
87
The effect of these increments of control displacement
is to modify the stability of the yawing and sideslipping
motions, an adverse yawing moment reducing the
damping and lengthening the period. The results in¬
dicate especially the disadvantage of adverse yaw and
show that some improvement may be had from a
favorable yawing moment.
Figure H.— The effect of favorable secondary yawing moment on yawing motion
during 30° bank maneuver performed with rolling control; Cl= 1.8. C„=0.2lCi
(k=0.15).
In order to study more closely the possible beneficial
effects of a favorable aileron yawing moment, it is of
some interest to analyze further the control application
into several components. The component that results
in modification of the stability through the action of the
secondary yawing moment may be considered to be
directly favorable to improved coordination of the
Figure 15.— The effect of increased N, on yawing motion during 30° bank maneuver;
aileron operation (no secondary yawing moment); Cl =1.0.
yawing motion because it shortens the natural oscilla¬
tion period and increases the damping. With a given
proportion of favorable yawing moment, increasing the
dihedral angle should result in further improvement in
this respect since the apparent weathercock stability
(Nv— kLx) is increased in that way. Another compo¬
nent of the applied rolling control is directed to over¬
coming the damping of the rolling incident to the
maneuver. The secondary yawung disturbance thus
38548—38 - 7
introduced is of the same form as pNp and may be
calculated as
Np' = (Np— kLp) (37)
The condition for perfect coordination of banking
and yawing motion during the turn requires that the
acceleration in yawing be very nearly proportional to
the rate of rolling; namely,
ar^x* (38)
The component of rolling control directed toward
opposing the damping in rolling is applied in this way
Figure 16. — The effect of increased N , on sideslip during two-control 30° bank
maneuver; aileron operation (no secondary yawing moment) ; Cl = 1.0.
and it is seen that this component of the secondary
favorable yawing moment is properly directed toward
improved coordination of the yawing motion. The
component of control application necessary to acceler¬
ate the rolling motion does not, however, lead to a
desirable secondary yawing acceleration since this
acceleration is not proportioned to the rolling velocity.
Time, seconds
Figure 17.— Comparison of yawing motions during maneuvers of different time
extents; aileron operation (no secondary yawing moment); Cl =10.
This component results in the primary disadvantage
associated with favorable-yaw ailerons. Quick or
irregular movements of the control may lead to pro¬
nounced yawing oscillations if the secondary moment
is very great.
It appears that a decisive method of improving the
aileron-operated two-control airplane would be to
88
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
increase the weathercock-stability factor Nv. This
method would serve directly to reduce the sideslipping
to a minimum both in steady turning and in rapidly
executed turn maneuvers. Figure 15 shows the effect
of doubling Nv on the yawing motion during the maneu¬
ver performed at CL= 1.0. This modification of the
airplane shortened the natural period of the oscillation
and resulted in the yawing action taking place more
quickly. The effect on sideslip is shown in figure 16.
Although the maneuver ends with about 5° of outward
sideslip, this value will be quickly reduced to zero on
account of the natural stability of the motion. With
different timing of the maneuver it may, of course, be
brought to an end with no residual sideslip. The
following table shows the effect of arbitrarily increasing
Nv on the natural period of the yawing oscillations:
Ratio of
A, to that
of average
airplane
Period
Seconds
1
4. Hi
2
2. 92
4
2. 05
It is to be noted that an increase in vertical-fin area
will increase the derivative Nr as well as Nv and will
thus result in greater damping of the motion.
13
c;
o 7
Qj
<0
c
QJ
*.2
1
5 -/
c
6)
1 o
0
b
o
<t> ./
£
li
/c
leal yaw
curve
mg
Y/ / /
J/y
li
^///
i
i
P//
A
VA
/
Iff
i
V///.
7///
i/y
/A
m
V/A
//
0,
H
///A
7
■ / s /A
i/
m
y///
r/Y/AA
77A
///Ay
////a
///
m
n
'/y
/// / /
/////,
'////;
' /// /
n
p
W\
y///
V//A
/ / / / /
if
fl
ii
1
m
i
//]
Ol 2 3 4 5 6
Time, seconds
Figure 18— Yawing motion necessary to enforce assumed 30° bank maneuver with
rudder operation; <?l= 1.0.
A certain disadvantage associated with increased Nv
is the relatively greater tendency for spiral instability
and the consequent necessity for holding the control
against the steady turn. It may be expected, however,
that this undesirable tendency could be overcome by
properly proportioning the dihedral of the wings. The
greatest possible effect of increase of vertical-fin area
would be to cause the metacenter for yawing moments
xN (see discussion of stability) to approach coincidence
with the fin; it would then appear necessary to arrange
the metacenter for rolling moments ahead of this point
in order to accommodate any desired increase of vertical-
fin area and secure spiral stability.
Further improvement in the operation of the aileron-
controlled machine could be had by decreasing the
yawing derivative in rolling Np. Alteration of this
derivative apparently would require fundamental
changes in wing design, improvement being in the direc¬
tion of lower aspect ratio, which might, of course, con¬
flict with other requirements.
As pointed out, the maneuvers assumed in these cal¬
culations are considered to be more rapid than usual in
Figure 19.— Free angles of bank during turn maneuvers performed with rudde
compared with ideal bank curve; yawing constraints for 30° bank maneuver.
normal flight, since they represent the use of a large
proportion of the control power ordinarily available at
the lower speeds. With slower maneuvers the coordina¬
tion of the motions of the two-control airplane would
be expected to be much better, especially when the
duration of the maneuver becomes large relative to the
natural period of oscillation of the airplane. Figure 1/
shows the result of a calculation in which the duration
of the 6.28-second maneuver was doubled.
It is worth noting that the actual deflection of the
flight path of an airplane relative to the earth is accom¬
plished much more directly by banking than by steering
Regardless of the sideslipping and coordination of angu¬
lar motions, any decided acceleration of the path must
be brought about by inclination of the lift and is not
directly affected to any great extent by rotating the
airplane in yaw. Such deflection of the path would be
the principal objective in turning to avoid an obstacle,
Thus the airplane with rolling-moment control should
be capable of avoiding obstacles equally as quickly as a
conventional three-control airplane. As is the case
with three-control operation, the tendency of a two-
control airplane to accelerate downward when banked
must be counteracted by a movement of the elevator,
If the airplane is assumed to execute a sharp turn to
avoid an obstacle, the primary consideration will thus
be the ability to produce a specified bank. Under such
A STUDY OF THE TWO-CONTROL OPERATION OF AN AIRPLANE
89
conditions the pilot of the rudder-operated airplane
would be expected to make an effort at indirect control
of the bank without regard to the coordination of the
yawing motion. The question then arises as to what
yawing motion would have to be prescribed in the case
of the rudder-controlled machine to enforce the desired
motion in banking.
Figure 18 shows the yawing motion that results in a
bank curve similar to that given in figure 9. It appears
that, in order to attain the bank angle as shown, a
relatively powerful rudder control would have to be
applied about one-half second in advance of the usual
start of the turn. Further calculations showed that the
prescribed yawing motion could be attained throughout
if a rather large amount of rudder control were avail-
Figure 20.— Free rolling motion during turn maneuvers performed with rudder;
yawing constraints for 30° bank maneuver.
able. That such an attempt to follow a definite course
in banking would require a vigorous use of the rudder
is evident from the oscillation of the yawing curve.
In the case of two-control operation with a constraint
in yawing by means of the rudder, the yawing motions
shown in figure 9 were assumed and the resulting
free rolling motions were calculated. Figures 19 and
20 show the results of such calculations made at dif¬
ferent lift coefficients. The angles of bank and rates of
rolling attained are compared with those that would
be appropriate to the constrained yawing motion.
It is apparent from these and the preceding figures
that the two-control airplane operated with the rudder
cannot be expected to perform rapid maneuvers of the
type considered. The natural reaction of the rolling
motion is too slow and the damping is too slight to
enable even an approximate coordination of the mo¬
tions within the short time of duration of the maneuver.
Figure 21 shows the angles of sideslip attained with
the various modes of operation considered, summarizing
the results of the calculations.
The reasons for the inability of the rudder-controlled
airplane to execute rapid turns are: First, that the
secondary rolling reaction due to yawing motion is
insufficient to overcome the relatively great damping
of direct rolling motion; second, that for a rapid turn
the rate of rolling required on entry and recovery
greatly exceeds the maximum rate of yawing; and third,
that the free rolling and sideslipping oscillations set up
are not very well damped. The greatest possibility for
Time, seconds
Figure 21. — Angles of sideslip during two-control turn maneuvers with different
modes of operation; 30° bank turn maneuver.
improvement w’ould appear to be in increasing the
derivatives Lv and Yt. The first ( Lv ) would call for
increased dihedral angle and would serve to shorten
the natural period of the rolling and sideslipping motion,
while the second (F„) would call for increased area of
the side projection of the airplane and should improve
the damping of the oscillations. The following table
shows the effects of changing these derivatives on the
natural period and damping of the oscillations at
Cx,= 1.0.
Ratio of derivative to that of average
airplane
X,
Y .
W
1
2
1
2
Time to damp Vi, seconds-- .
Period, seconds _
12.4
15.3
36.6
9.9
03
7.65
36.6
9.9
6. 25
10.9
90
REPORT NO. 579 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
CONCLUSION
The lateral motion of a conventional airplane is more
stable when constrained in rolling than when con¬
strained in yawing. The stability of the free yawing
and sideslipping motion is greater than that of the
entirely free motion; the stability of the free rolling
and sideslipping is less than that of the entirely free
motion.
If a rolling-moment control is used to enforce an
arbitrary constraint in banking, the free yawing that
results will be approximately coordinated to the bank
if the airplane has the average degree of weathercock
stability (Nv). The yawing in this case is also ap¬
proximately adjusted to the speed of flight so that
with a given bank maneuver a more rapid rate of
yawing is attained at low speed than at high speed, as
is desirable. The deviation of the yawing from the
ideal is greater, however, at lower speeds and is also
greater in quick turns than in more slowly executed
ones. If the rolling control were designed to give a
moderate favorable yawing moment, the coordination
of the motions would be improved. Improvement may
also be effected by increasing the weathercock sta¬
bility. If, however, the aileron control gives the usual
proportion of secondary adverse yawing moment, the
coordination of the yawing with the banking will be
relatively very poor. The motions may then become
unstable and uncontrollable in an extreme case at high
lift coefficient. These latter statements are particularly
applicable to conventional-type ailerons, which are
considered as undesirable on this account for use at
low flight speed unless compensated by the rudder.
A rudder control may be used to enforce a constraint
either directly on the yawing motion or indirectly on
the rolling motion provided that the maneuver specified
is not too rapid nor the disturbances encountered too
severe. In the former case the free banking motion
occurs as a series of long oscillations that do not begin
to approximate the desired bank until some time after
the start of a maneuver or after the passing of a dis¬
turbance. During a rapid yawing maneuver the bank
that occurs is greater at low flight speed than at high,
indicating that the coordination of the centrifugal and
the gravitational accelerations is not adapted to the
desired variation with flight speed.
Although the coordination of the motions with
aileron control grows worse as the flight speed is re¬
duced, the coordination with rudder control improves
somewhat at the lower speeds. This effect would be
especially apparent if the rudder were applied in sucli
a way as to enforce indirectly a desired banking mo¬
tion. Such indirect control requires, however, that the
rudder be deflected in advance of the desired effect.
The yawing that arises when the bank is indirectly
controlled with the rudder is a very poor approxima¬
tion to the ideal yawing and calls for large and irregular
control movements.
The amount of sideslipping during steady turns is
not greatly different with either mode of operation. In
either case it appears desirable that the free motion of
the airplane show spiral stability so that control settings
opposing the turn will not be required.
In general, it is concluded that a reliable rolling-
moment control that does not give a secondary adverse
yawing moment would afford the most satisfactory
means for two-control operation. It appears that a
moderate amount of favorable secondary yaw would
be desirable although certain disadvantages appear if
the proportion is too great.
The disadvantage in two-control operation lies not
so much in the imperfection of control of the flight path
of the airplane relative to the earth as in the sideslipping
and sidewise accelerations that arise through the im¬
perfect coordination of the yawing and banking
motions. It appears possible that this tendency may
be .so reduced by the use of suitable control organs
and properly modified stability characteristics as to
be unobjectionable.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics.
Langley Field, Va., August 12, 1936.
REFERENCES
1. Routh, E. J.: Advanced Rigid Dynamics, vol. II. The
Macmillan Co. ,1905.
2. Weick, Fred E., and Jones, Robert T.: The Effect of Lateral
Controls in Producing Motion of an Airplane as Computed
from Wind-Tunnel Data. T. R. No. 570, N. A. C. A., 1936.
3. Bush, V.: Operational Circuit Analysis. John Wiley and
Sons, Inc., 1929, p. 41.
4. Jones, Robert T.: A Simplified Application of the Method of
Operators to the Calculation of Disturbed Motions of an
Airplane. T. R. No. 560, N. A. C. A., 1936.
5. Carson, J. R.: Electric Circuit Theory and Operational Cal¬
culus. McGraw-Hill Book Co., Inc., 1926.
REPORT No. 580
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
Bv Robert F. Selden and Robert C. Spencer
SUMMARY
A study has been made oj the influence of severed vari¬
ables on the pressure decrease accompanying injection of a
relatively cool liquid into a heated compressed gas. In¬
directly, this pressure decrease and the time rate of change
of it are indicative of the total heat transferred as well as
of the rate of heat transfer between the gas and the injected
liquid. Air, nitrogen, and carbon dioxide were used as
ambient gases; Diesel fuel and benzene were the injected,
liquids. The gas densities and gas-fuel ratios covered
approximately the range used in compression-ignition en¬
gines. The gas temperatures rangedfrom 150° C. to 350° C.
Several general conclusions may be drawn f rom the ex¬
perimental results: Vaporization begins immediately after
the start of injection; the initial rate of heat transfer is a
direct function of the initial temperature difference be¬
tween the gas and the fuel; and the heat transfer is less
efficient the greater the injected fuel quantity, even though
the total heat transferred is greater.
INTRODUCTION
It is generally recognized that the compression-igni¬
tion engine in its present state of development suffers
the disadvantage of inefficient utilization of its air
charge. Recognizing that the utilization of the air
must be partly dependent upon the fuel spray, Lee has
conducted a detailed photographic investigation of the
exterior characteristics of fuel sprays (reference 1). Ife
has also determined the spatial distribution of the fuel
within the spray (reference 2). These spray investiga¬
tions have been extended by tests with the N. A. C. A.
combustion apparatus and the results give an improved
insight into the gross physical and chemical processes
as they occur in the engine. (See references 3 and 4.)
The ignition lag in compression -ignition engines has
been shown to influence the character of the subsequent
explosion (references 5 and G). No entirely satisfactory
explanation of this fact has been given, but certain gen¬
eral conclusions can be drawn: In general, the fuel must
be heated after injection; the fuel and the air must be
mixed; and certain preliminary chemical reactions must
take place before the actual ignition can occur. The
observed lag is thus a composite of the intervals associ¬
ated with these processes. It follows that heating the
fuel prior to injection cannot reduce the ignition lag
indefinitely although some reduction may be accom¬
plished in this manner (reference 7). Rothrock and
Waldron have shown that appreciable vaporization
follows injection of the fuel into the combustion appara¬
tus (reference 8). The time required for this vapori¬
zation to begin was not established but, in view of
Wentzel’s theoretical analysis of the heating and vapor¬
ization of fuel droplets suspended in a heated gas
(reference 9), there is every reason to believe that appre¬
ciable vaporization occurs in a compression-ignition
engine during the ignition-lag period.
The present investigation was undertaken to isolate
the heat transfer accompanying the mixing of a fuel
spray and the ambient gas in a bomb and to study the
influence of several variables on this individual process.
The results of this investigation should give an insight
into the time required to effect some vaporization since
this process necessarily corresponds to a portion of the
total heat transfer. Experimentally, heat transfer is
not directly measurable in a system of this type; there¬
fore, resort has been had to an indirect approach, namely,
the measurement of the change in pressure accompany¬
ing the adiabatic exchange of heat between the gas and
fuel after injection of the fuel into a bomb. The pri¬
mary variables were the gas temperature, the gas density,
and the gas-fuel ratio. The effects of the nozzle design,
the fuel temperature, the kind of fuel, and the character
of the ambient gas were less extensively investigated.
Gas densities covering most of the range found in
engine practice .were used. For mechanical reasons
temperatures corresponding to those attained in com¬
pression-ignition engines at top center could not be used.
The maximum temperature employed was actually
somewhat less than that of the gas charge prevailing
at the start of injection (references 10 and 11) in com¬
pression-ignition engines.
ANALYSIS OF THE PROBLEM
The transfer of heat to a suspended droplet can take
place by two mechanisms: conduction and radiation.
Except insofar as their boundary conditions are altered,
the mass flow of gas, induced by the injection of the
liquid fuel, presumably is of little importance with re¬
spect to the individual droplets because of their low
relative velocity (reference 12). The situation may be
91
92
REPORT NO. 580 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
vastly different, however, for the spray considered as a
unit, particularly for injection into an engine having
induced air flow. Radiation to the surfaces of the
droplets takes place to some extent and, whereas the
actual magnitude of this exchange is uncertain, the
maximum rate for energy transferred in this manner
can be estimated for comparative purposes.
For conductive heat transfer there are two controlling
resistances: The first is within the droplet itself and
the second must he associated with the equivalent of a
film surrounding the droplet. The first can be analyt¬
ically treated but the second presents difficulties.
Because of the net transfer of molecules from the droplet
surface, the character of this film is not independent of
time, as is usually assumed in theoretical treatments.
(See references 9, 13, 14, and 15.) In fuel sprays the
vapor films about the liquid droplets probably inter¬
penetrate, thus necessitating some consideration of the
spray as a whole. Moreover, the fuel is not uniformly
distributed within the spray. In view of these diffi¬
culties no attempt will be made to establish any mathe¬
matical relations for the heat transfer through the film
encompassing the droplet.
Heat transfer within a droplet. — Ingersoll and Zobel
have published equations pertaining to the internal
heating of a rigid sphere suddenly inserted into a fluid
possessing a higher temperature (reference 16). These
equations may be modified to give, respectively, the
instantaneous center temperature tc and the average
temperature ta of the droplet:
tc— ( ts—ti )
t‘a == t i T“ (ts — tt )
/ —r2hH
-iwW
-SttW
\1
1-2 (e R1
-e Ri + e
R* _
■■)]
c / ~vi hH i 1 -9*2hn
where ts is the temperature of the shell, ° C.
tif the initial droplet temperature, ° C.
11, the radius of the shell, centimeters.
t, the immersion time, seconds.
A2, the thermal diffusivity of the liquid in the
droplet.
As applied to liquid droplets these relations do not
represent the effects of possible internal convection
currents. These currents, if present, would increase
the rate of temperature rise as determined by these
relations.
It follows from these relations that when A 2 is con¬
sidered constant, the increase in both the center and
average temperature above the initial droplet tempera¬
ture is a definite fraction of the difference tt; thus
tc~ti~oc ( ts—ti ) and ta—ti =j8 ( ts—ti ). The assumption
of a constant value of A2, independent of temperature in
the range employed, appears justified for the purpose of
qualitative comparisons in view of the uncertainty
involved in its estimation. An average value for the
range 49° C. to 350° C. can be estimated on the basis of
the average values of the thermal conductivity (0.00027
calorie per second per centimeter per degree C., refer¬
ence 17), the density (0.713 gram per cubic centimeter,
reference 18), and the specific heat (0.662 calorie per
gram per degree C., reference 19). These values result
in A,2= 0.000572 square centimeter per second.
Values of a and /3 are given in the following table
for several immersion intervals and droplet radii, the
largest radius corresponding to the initial average size
(reference 20). No actual values of droplet tempera¬
tures are given inasmuch as there is no adequate basis
on which to estimate their surface temperature. In¬
cidentally, the foregoing relations tacitly assume that
the surface temperature is instantaneously attained
and thereafter remains constant. This assumption does
not greatly invalidate the fact that the increase in the
temperature of the droplet, particularly the average
temperature as shown by the /3 values, attains a large
fraction of the possible increase in a remarkably short
time. Moreover, the smaller the radius the more
quickly this fraction approaches unity. As a result of
evaporation, the surface temperature does not attain
so high a value as it would if all the heat reaching the
drop served to heat it. Even so, such evaporation
presumably does not alter the establishment of thermal
equilibrium within the droplet and hence the a and (1
quantities still have significance.
.HEATING RATES FOR IMMERSED SPHERES
[fe ~ti =a{t,-t,); ta ~U =0 (t.-ti)}
\
\ Droplet fern __
\ radius\in-_.
\
\
\
\
\
\
Immersion \
time \
\
0.0015
.00059
0.0020
.00079
0.0025
.00098
a
0
a
0
a
0
Second
0.0001
0. 002
0. 464
0.000
0. 362
0.000
0. 296
.0003
. 154
. 706
.018
.573
.004
.479
.0005
.444
.826
. 128
. 690
.024
.587
.0007
. 658
.895
.296
.771
.092
.666
.0010
.838
.951
.520
.851
.344
.749
.0015
.874
. 962
.760
.927
.494
.842
.0020
.986
.996
.882
.964
.674
.900
Radiation from bomb wall. — Some insight into the
possible contribution of radiation from the bomb wall
to the total heat transfer follows from a consideration
of the maximum rate of radiation. If the very ques¬
tionable assumption is made that the droplets are
true black bodies suspended in a space filled with
black-body radiation, the net energy transferred in
calories per second is given by:
A//=1.37X10-4S
(reference 21) where
S is the surface area of the drop.
Tx, the bomb-wall temperature, degrees K.
T2, the droplet temperature, degrees K.
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
93
The extent to which the droplets are not black bodies
introduces a factor that reduces this rate. The exist¬
ence of black-body radiation within the bomb is actually
the case prior to injection, but thereafter the radiation
within the spray envelope undoubtedly corresponds
to a lower temperature than that of the bomb walls.
This fact again entails a diminution in the rate indicated
by the equation. The area S may be taken as equiva¬
lent to that of the number of droplets of average size
(reference 20) required for a spray of given weight.
For comparison with the observed rate of heat
transfer, expressed in this case in terms of rate of pres¬
sure drop, the calculated rate of radiant transfer must
be expressed in identical units. Although not indica¬
tive of the actual mechanism, this rate can be put in
terms of the units in which the experimental data are
expressed by considering all the radiant energy as
being derived from the ambient gas.
Basic considerations of experimental method. — The
observed decrease in pressure accompanied the decrease
in temperature of the ambient gas caused by the flow of
heat from it to the injected liquid. This process was
essentially adiabatic in view of the small rate of heat
transfer from the bomb wall. Cragoe’s empirical
relations (reference 17) for the specific and vaporization
heats of oils permit the calculation of the pressure
decrease that should accompany the complete vaporiza¬
tion of a given amount of fuel when all the heat is ab¬
stracted from the gas phase. When the total heat
absorbed by the fuel in vaporizing is equated to that
lost by the ambient gas, these relations lead to an
expression that can be solved by trial and error to give
the final equilibrium temperature:
NC„ti—4:9.5w
f~ NCV + 0 . 3 3 3 w + 0 . 000444 wf,
where N is the moles of ambient gas.
Cv, the molal specific heat of this gas, taken as
constant between tf and tu
ti} the initial gas temperature, °C.
w, the weight of injected fuel, grams.
It follows at once that the temperature drop (L — tf)
should remain constant for a given initial temperature
and gas-fuel ratio, i. e., essentially Njw. The cor¬
responding diminutions in the partial pressure of the
gas are calculable from the expression
,> „ P i(Tt— Tf)
1 f~ Tt
in which Pt is the initial pressure, atmospheres.
Pf, the final pressure, atmospheres.
Ti, the initial absolute gas temperature, de¬
grees K.
T f, the final equilibrium gas temperature,
degrees K.
This expression is strictly applicable only to the initial
stage of the heat-transfer process when little vapor
exists. Later in the process, however, these diminu¬
tions should be greater than the experimentally derived
maximum values to the extent of the partial pressures
of the vapor, these latter being directly proportional
to the initial pressure for a given initial temperature
and gas-fuel ratio. Thus the calculated actual drop to
be expected under these stipulated conditions is in
accordance with
(Pt- Pi) =P\^T‘Tp~P\
where C is a correction factor necessitated by the pres¬
ence of the fuel vapor. This factor is equal to the
partial pressure of the vapor of the injected liquid di¬
vided by the initial gas pressure. The partial pressure
was obtained from the perfect gas law and the known
bomb volume, gas temperature, fuel weight for the par¬
ticular gas-fuel ratio, and an estimated average molec¬
ular weight of 200 (reference 22). It follows from this
expression that the pressure drop should be directly
proportional to the initial pressure if the fuel derived
all its heat from the gas phase under the assumed condi¬
tions of constant initial temperature and air-fuel ratio.
Some conception of the rate of heat transfer can also
be obtained from the experimental results, particularly
for the early part of the process in which the number of
moles of gas is essentially invariant. It follows from the
perfect gas law that the rate of pressure change is
related to the rate of temperature change by
dP NR dT
dt V dt
wherein R is the gas constant.
V, the volume of the bomb.
Also, the rate of change in the energy content of the
gas phase must equal the rate of heat transfer, thus:
dt WV
(IT
dt
If minor variations in Cv and Ware neglected, it follows
that the rate of heat transfer is proportional to the
rate of pressure decrease. For the practical purpose of
showing the trends in the present data it is sufficient to
use these rates interchangeably as though they were
synonymous.
The expression
dP NR
dt V
dT
dt
can
also be used to com¬
pare the relative rates of temperature drop in different
gases when the corresponding rates of pressure change
are known for a given initial gas temperature, density,
and gas-fuel ratio. The initial pressure under such
conditions is very nearly proportional to N, hence the
ratio of the initial rate of pressure drop to the initial
pressure is proportional to the initial rate of tempera¬
ture drop irrespective of the nature of the gas.
94
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
APPARATUS AND METHOD
The experimental method employed in this investi¬
gation consisted in photographically recording with a
suitable indicator the decrease in pressure following the
injection of a definite quantity of liquid into a spherical
bomb containing a gas at a known temperature and
pressure. With the exception of a few minor modifica¬
tions this apparatus was essentially as described in
reference 23. The present arrangement is shown dia-
grammatically in figure 1. The essential parts were a
bomb, a constant-temperature bath, a fuel-injection sys¬
tem, and an optical-type differential-pressure indicator.
The stainless-steel bomb has a volume of GOO cubic centi-
of 0.050 inch (fig. 2). The fuel weights were varied bt
changing the injection pressures; the latter variet
from about 194 to 600 atmospheres (2,850 to 9,OOi
pounds per square inch) for each nozzle. The requisite
injection pressure for a given fuel quantity was deter,
mined just prior to a series of tests at each temperature.
The injection period ranged between 0.002 and 0.00*
second, depending upon the injection pressure used
The high-pressure indicator employed in earlier work-
references 6, 11, and 23) was altered to record small
pressure differences by substituting a thin corrugated
phosphor-bronze diaphragm for the heavy steel dia¬
phragm and by providing a gas connection between the
sealed chamber above the diaphragm and the bomb
A, air gage.
B, bimetallic strip.
C, bomb.
D, cam.
E , check valve.
F, clamping rings.
G, clutch.
H, condenser, 8 microfarad.
I , contact points.
J , cooling coil.
K, exhaust.
L, film drum.
M , from compressed-gas bottle.
N , from high-pressure pump.
O , fuel-circulating pressure gage.
P, fuel high-pressure gage.
Q , fuel reservoir.
R, gear pump.
S, heating coil.
T, high-pressure reservoir.
U, holder for bomb.
V, indicator diaphragm.
W, injection tube.
X, injection valve.
Y, lamp.
Z, lens.
A', motor.
B', oil bath.
C\ orifice, 0.020 inch.
D', phase-changing gears.
E', pivoted mirror.
F', poppet valve.
G', relay.
H
resistance lamps,
spark coil,
spark gap.
quick-acting valves,
spark-timing switch,
stirrer.
N ', synchronous motor.
O', thermometer.
P', voltage 220 a. c.
Q', voltage 230 d. c.
J
K
L
M
Figure 1.— Diagrammatic sketch of the apparatus.
meters and is provided with openings for the injection
valve, the gas inlet and exhaust fittings, and the indicator.
The liquids used in the constant-temperature bath
were S. A. E. 30 lubricating oil for the low tempera¬
tures and an approximately 1:1 mixture of sodium
and potassium nitrates for the high temperatures.
The bath temperature was kept within ± 2° C. of the
desired value by an automatic control.
The injection system delivered a single fuel charge
of the desired weight upon the release of a trip mech¬
anism. The injection valve was so constructed that
fuel could be continuously circulated through it,
thereby maintaining a constant fuel temperature of
49° ±1.5°C. Three nozzles were used, all having
equivalent orifice areas: A 13-orifice, a 2-impinging-
jets, and a single-orifice nozzle with an orifice diameter
proper. The same initial pressure was applied to botli
sides of the diaphragm but, just before injection, a
valve inserted in this connection was closed. This
procedure permitted the subsequent pressure difference
to actuate the indicator and thus to generate a trace oi
the pressure-difference variation with time on the film
This valve was opened again immediately after injection
in order to minimize the interval within which the dia¬
phragm remained deflected. A spark, recorded as a
vertical line on certain records, marked the start ol
injection. This spark and injection start were syn¬
chronized by observing the spray with a neon-tube
stroboscope actuated by the switching device on the
injection system that ordinarily controlled the spark.
The film drum was driven by a synchronous motor to
provide the time scale.
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
95
Air,"" nitrogen, and carbon dioxide were used as
ambient gases; nitrogen was substituted for air in the
Section A OB'
D
D'
(a) The 13-orifice nozzle; plane DD' is identical with BB', and plane CC' is
identical with AA'.
(b) The 2-impinging-jets nozzle.
orifice
(c) The single-orifice nozzle.
Figure 2. — Diagrammatic sketches of the three nozzles.
tests at the higher temperatures because air permitted
auto-ignition of the fuel oil at 230° C. with certain gas-
fuel ratios. A few tests were made with carbon dioxide
38348—38 - 8
because its physical characteristics were considerably
different from the other two gases. The gas densities
correspond to 5, 10, 15, and in some tests 20 atmos¬
pheres absolute at 100° C. All gases were considered
to be ideal when computing the pressures corresponding
to the several densities and temperatures. The initial
gas temperatures ranged from 150° to 350° C.
Different liquids were injected: An automotive
Diesel fuel (Auto Diesel) was investigated most
extensively because of its practical importance; ben¬
zene, because its critical temperature was within the
available temperature range; and water, because of its
large heat of vaporization. The water tests were not
very extensive and, as they failed to show any interest¬
ing dissimilarities, these data have been omitted. The
700
Knn\ - ! - J - J - 1 — — -f- - - - 1 -
° uO so 40 60 80 100
Percentage distilled
Figure 3. — The A. S. T. M. distillation curve for Auto Diesel fuel.
Diesel fuel had a viscosity of 70 and 52 Saybolt seconds
Universal at 38° and 99° C. (100° and 210° F.), respec¬
tively, and a density of 0.831 gram per cubic centimeter
at 15° C. Its A. S. T.M. distillation curve is given in
figure 3.
RESULTS
The data derived from the experimental records
corresponding to the injection of Diesel fuel are pre¬
sented in table I. Typical records for an intermediate
fuel quantity (0.284 gram) and gas densities of 4.73
and 14.19 grams per liter are reproduced in figure 4.
The effect of the nozzle design on the heat transfer to
the spray, all other controllable variables being con¬
stant, is illustrated by representative records in figure 5.
Results obtained when Diesel fuel was repeatedly
injected into a single, individual gas charge are pre¬
sented in table II. Figure G comprises the corre¬
sponding records, taken with a gas temperature of 250°
C. It is to be noted that these records do not corre¬
spond to consecutive injections.
96
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The results obtained witli benzene are presented in
table III and figure 7. These tests were limited to the
smaller weights because of the greater pressure changes
per unit weight of liquid.
An inspection of the experimental records reveals
two time intervals more or less clearly defined on all the
start of injection corresponds, with one exception, to
the vertical line appearing on some of the records and
is coincident with the A points; i. e., the decrease it
the gas pressure began immediately after the first pan
of the fuel charge entered the bomb. The one excep-
tion (record 295, fig. 5) was due to improper synchro-
(a) Gas density, 4.73 grams per liter; gas-fuel ratio, 10.
Figure 4.— Variation of pressure drop with gas temperature. Diesel fuel; fuel weight, 0.284 gram.
pressure-time curves. Three characteristic points are
designated on all the records reproduced: A, the point
at which the pressure drop begins; B, the end of the
initial pressure drop (or which the rate was essentially
constant; and C, the minimum pressure point. The
nization of the injection start and the timing spark.
The A-B interval and the pressure drop associated with
it are indicative of processes occurring immediately
after the injection starts. This interval is therefore
of primary interest with respect to compression-ignition
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
97
engines. The whole A-C interval, on the contrary, is
of no immediate interest in this respect and corre¬
sponds to the period within which heat is being abstracted
from the gas phase at a rate greater than the rate of
transfer from the bomb wall. The A-C interval is
partial pressure of the vaporized fuel. Records repre¬
senting this condition were not obtained as the rela¬
tively low rate of heat transfer from the bomb wall
would have necessitated an extended deflection period
for the diaphragm.
(b) Gas density, 14.19 grams per-liter; gas-fuel ratio, 30.
Figure 4.— Continued. Variation of pressure drop with gas temperature, Diesel fuel; fuel weight, 0.0284 gram.
influenced so little by most of the available variables
that no theoretical basis for its approximate constancy
is at present evident. Eventually, upon reestablishing
thermal equilibrium, the pressure should increase
beyond its initial value to an extent represented by the
Spray photographs shown in figure 8 illustrate the
manner in which sprays from the 13-orifice and the
2-impinging-jets nozzles penetrate air at room tem¬
perature and a density of 14.19 grams per liter for an
intermediate injection pressure.
98
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
PRECISION OF RESULTS
The reproducibility of the experimental results
depended upon the nonvariation of the fuel quantity
and the indicator calibration. The maximum devia¬
tions in the observed data for apparently identical
conditions amounted to roughly ±5 percent of the
average values. The variation in fuel weights, for
apparently identical injection pressures, was approxi¬
mately the same for all weights and amounted to about
±3.5 percent of the actual weight for the lower injec¬
tion pressures or to ±1 percent for the higher.
weight, prevented the use of the larger fuel weights,
The objectionable feature of the shift arose from the
fact that a given deflection before and after a particular
test did not correspond to equivalent pressures. A
possible error of perhaps ±5 percent may arise in this
way; at 350° C. the error is undoubtedly greater.
When the data from the records were evaluated, some
personal error was introduced, particularly for the
A-B portion of the curve wherein the interval is more or
less arbitrary and the distances on the record are often
too small to be accurately measured. The magnitude
of this uncertainty is shown in figure 9, for which the
Figure 5. — Effect of nozzle design on pressure drop. Diesel fuel; fuel weight, 0.284 gram; gas-fuel ratio, 30; gas density, 14.19 grams per liter; gas temperature, 250° C.
At temperatures of 250° C. and above, the indicator
showed a decided tendency to change its zero point as
a result of creeping of the diaphragm, particularly
during calibration when the deflection period was
relatively great. The extent of this shift increased
with the amount of deflection, the time of deflection,
and the temperature. The deflection interval was
diminished as much as possible during calibrations by
a quick application and release of the gas pressure.
The zero point immediately after deflection was taken
as the proper basis for calibration in spite of its tend¬
ency in many cases to drift back toward its original
position. At 350° C. this restoration was less evident
and the shift assumed serious proportions. This fact,
together with the increased deflection per unit fuel
data were taken by two observers from the same records.
The individual deviations are rather great, but the mean
curves seem to fit either set of data equally well. At
150° C. the records were so flat in the neighborhood of
the minimum point that C was taken as the center of
the flat portion of the curve. For the larger deflections
the trace near the minimum point contained a wave of
relatively low frequency. An average of the ampli¬
tudes of the first cycle was applied as a negative cor¬
rection to compensate for this wave.
One other point of incidental interest is the change
in fuel temperature as a result of the injection process.
The passage of the fuel through the nozzle would ordi¬
narily result in a small decrease in temperature on the
basis of the Joule-Thonison effect (reference 24), assum-
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
99
ing the coefficient to be positive as for certain other
hydrocarbons (reference 25). Qualitative experience
indicates, however, that the net effect is a temperature
increase due to friction in the orifice and the conversion
of the kinetic energy of the spray into heat. The
and vaporization. Lee has shown (reference 20) that
the degree of subdivision attainable with a hydraulic
in jection system under operating conditions approaches
a practical limit. For the practical range of gas densi¬
ties and injection pressures, however, it is impossible
Figure 6.— Influence of fuel-vapor concentration, prior to injection, upon pressure drop. Diesel fuel; fuel weight per injection, 0.568 gram; gas density, 10.35 grams
per liter; gas temperature, 250° C.
change is believed to be too small to be of any interest
in the interpretation of the present results and will
therefore be ignored.
DISCUSSION
On the basis of diffusion and heat-transfer concepts
the size of a droplet must influence its rate of heating
to vary the distribution of droplet sizes without at the
same time varying the rate of spray penetration. This
concomitant variation prevents the isolation of any
effect that can be associated solely with the distribution
of droplet sizes. In the subsequent discussion it is
well to bear in mind that the same condition should be
true of certain other quantities that may represent an
aggregation of variables.
100
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 7, — Effect of gas temperature on pressure drop. Benzene as fuel; fuel weight. 0.284 gram; gas-fuel ratio, 10; gas density, 4.73 grams per liter.
.004
Figure 8.— Spray penetration. Gas density, 14. 19 grams per liter; injection pressure, 5,800 pounds per square inch.
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
101
THE A-B INTERVAL
The A-B intervals correspond to the early part of the
spray development for which the rate of heat transfer
is essentially constant for a particular record. It is
possible that this constancy is in some way associated
with the approximately constant initial rate of spray-
tip penetration (references 1 and 26). The magnitude
of this interval is comparable with the ignition lag in
compression-ignition engines. For this reason any con¬
clusions based upon this interval are also applicable to
such engines, provided that proper allowances are
made for differences in chamber size and air tempera¬
ture. The photographs shown in figure 8, together
with more extensive penetration data (reference 1),
show that this interval is essentially equivalent to the
time (0.002 to 0.003 second) required by the sprays to
influenced by the temperature gradient between the
gas and the fuel at two gas densities and several fuel
weights is illustrated in figure 9. These initial slopes
become more negative, i. e., the initial rate of heat
transfer increases, as either the temperature difference
or the fuel weight increases. Increasing the gas density
decreases the numerical magnitude of the slope for a
given fuel quantity but does not greatly alter the tem¬
perature dependence of the initial rate of pressure drop
of the pressure-time curve: corresponding lines in figure
9 have roughly the same slope.
The increased density evidently decreases the effec¬
tive transfer area in the early part of the spray as might
be expected from the slower rate of spray development
shown by the photographs reproduced in reference 1.
The decrease cannot be attributed to a lower rate of
Initial temperature difference between gas and fuel, °C.
traverse a distance of 4 inches, the approximate diam¬
eter of the bomb.
This association of the moment of impingement with
point B is supported by the fact that the interval de¬
creases as the gas density decreases, i. e., as the pene¬
tration increases. (See table I, column 7.) On the
contrary, the interval is not appreciably shorter for the
single-orifice nozzle in spite of the greater penetration
to be expected with it. The period is about the same
for carbon dioxide as for nitrogen in contradistinction
to the longer A-C interval with carbon dioxide. In¬
creasing the fuel quantity increases the injection period
by a maximum factor of 3, yet the interval remains
essentially the same. The interval also proved to be
independent of the fuel used.
Initial rate of heat transfer. -The magnitude of the
initial rate of pressure drop, as shown by the particular
pressure-time curve, is representative of the total rate of
heat exchange between the gas and the fuel for the early
part of the spray . The manner in which this initial rate is
heat transfer per unit area because the coefficient of
heat conductivity should be nearly independent of
density and the coefficient of heat transfer might be
expected to increase with gas density (reference 27).
Carbon dioxide gave rise to a greater rate of temperature
drop than did nitrogen, even though its rate of pressure
drop was smaller. This fact may be demonstrated by
dividing the values of the initial slope in column 9 of
tables I and III by their respective initial pressures, as
outlined earlier in this paper. As the specific heats of
nitrogen and carbon dioxide do not differ greatly on a
weight basis, carbon dioxide must have given a greater
initial rate of heat transfer. Since carbon dioxide has
a lower coefficient of heat conductivity, it must give a
greater effective heat-transfer area. The slopes for
benzene (table 111) are slightly greater than for Diesel
fuel (table I) owing perhaps to a combination of the
differences in the properties (molecular weight, specific
heat, heat of vaporization, etc.) of the two fuels.
102
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
For the lowest density the impinging- jets nozzle gave
a heat-transfer rate similar to the 13-orifice nozzle but
at the highest density its rate was substantially less.
The single-orifice nozzle gave a smaller rate at all den¬
sities. The maximum cylinder pressures obtained with
similar nozzles and the N. A. C. A. combustion apparatus
show the same trends, indicating that better initial
mixing of fuel and air, together with the resulting
improvement in heat transfer, occurs with the high-
dispersion nozzles (reference 3). No information rele¬
vant to the effect of vapor concentration on the ignition
lag can be obtained from such an engine study, presum¬
ably because all nozzles giving at least moderate fuel
dispersion permit the optimum air-vapor mixture
somewhere within the spray and thus give approxi¬
mately the same ignition lag.
The contribution of radiation to the total heat-trans¬
fer rate can be shown to be negligible on the basis of
the treatment given in an earlier section. If record
418 is considered to be typical of the others, the rate of
pressure drop equivalent to the maximum rate of radia¬
tion that could occur is only 1 percent of the observed
rate. It appears that radiation contributes little
toward heating the fuel injected into an engine except
for the possibility of unvaporized fuel becoming sur¬
rounded by a cloud of radiating combustion products.
Even in this case, the conductive heat exchange can
be shown to predominate if its rate per degree tempera¬
ture difference remained constant and independent of
the gas temperature to the extent indicated by the
data in column 10 of table I.
Effect of temperature on initial heat transfer. —
Straight lines seem to agree with the data plotted in
figure 9 within the limits of the uncertainty involved
and, moreover, such lines are in agreement with a rate
of heat transfer directly proportional to the temperature
difference. The fact that the lines are straight indicates
that the gas temperature has little influence on spray
development within the range employed (reference 28),
measured in this case by the effective area available
for heat transfer. This area appears to be constant
for a given density and fuel weight; otherwise a com¬
pensating change in the heat-transfer coefficient must
be assumed. There is no indication that the slopes of
the lines of figure 9, and hence the corresponding
heat-transfer coefficients, will assume different values
at the higher temperatures attained in an engine.
The extrapolation, however, is too great to be of more
than qualitative interest. The mass flow of gas in¬
herent in an engine (reference 4) would lead to greater
effective transfer areas and thus increase the apparent
rate of pressure decrease indicated in this figure.
The ratios of the initial slope values given in column
9 of tables I and III to the respective products of fuel
weight and initial fuel-gas temperature difference give
a fundamental basis for comparing the relative efficacy
of the heat transfer in all cases for a given ambient
gas. It follows from such ratios that the rate of heat
transfer varies directly with the initial temperature
difference, as stated earlier in connection with figure 9,
Increasing the weight of Diesel fuel leads to considerable
decrease in these values but with benzene the tendency
is not so evident. This difference indicates that the
effective heat-transfer area is more nearly proportional
to the fuel weight for benzene than for Diesel fuel,
Again, as with the initial slopes, these ratios are some¬
what greater for benzene, but it is not known Avhether
this situation arises from a greater heat requirement
or from better spatial distribution of the spray. The
latter seems most probable in view of the effect of
fuel viscosity on the distribution of fuel within the
spray (references 2 and 29).
Fuel vaporization.— The records reproduced in figure
6 show that some evaporation of the fuel occurs during
the A-B interval. If all the heat transferred served
merely to heat the liquid fuel, it is evident that the
initial rate of heat transfer should not decrease as it
does in these records. As more and more fuel is
injected into the same gas charge, thermal equilibrium
being reestablished before each injection, such a condi¬
tion is approximated as the partial pressure of the vapor
and the saturation pressure of the liquid approach one
another. Certainly the relatively small molecular
concentrations of vapor that produce the diminutions in
initial heat-transfer rate evident even after a single
injection can only be effective in the observed manner
by retarding the evaporation of the fuel. These
records show that the heat transferred to the vapor or
to the fuel in effecting vaporization represents an
appreciable part of the total heat transferred to an
ordinary spray during the A-B interval. Kothrock and
Waldron (reference 8) have presented conclusive evi¬
dence that considerable vaporization does occur in a
high-speed engine but the rate, of course, is indeter¬
minate as in the present case. The speed of the engine
proved to be influential, presumably for two reasons:
differences in mechanical mixing of the spray with the
air and certain changes in the thermal boundary
conditions of the spray. Photographs in reference 30
of sprays injected into cold and heated air show a
distinct decrease in the spray penetration with the hot
air. It is quite probable that vaporization of the fuel
within the spray envelope contributed to this decrease
in addition to the changes in fuel temperature and air
viscosity, which were cited in explanation of this
phenomenon.
THE A-C INTERVAL
Effectiveness of heat transfer. — Even though the
B-C portion of the A-C interval has no particular
connection with engine operation, it does present some
information of interest on the effectiveness of the heat
transfer. This effectiveness is shown most readily by
comparing with the actual pressure drop the calculated
pressure drop that should take place if all the fuel had
vaporized. The nearer the experimental value ap¬
proaches the calculated value the greater the effective-
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
103
ness of the transfer. Calculated and observed pressure
changes are plotted against the initial nitrogen (or air)
pressure in figure 10 for several temperatures and a
gas-fuel ratio of 20.
The disagreement between the calculated and ob¬
served pressure drops is very striking and is much too
great to be associated with heat transferred from the
bomb wall to the gas phase during the A-C interval,
as evidenced by the slow rate of pressure rise after
point C. A probable explanation is that a good fraction
of the fuel struck the wall, deriving most of its heat
therefrom. This assumption is supported by earlier
observations that a definite pattern of the sprays could
be seen on the bomb wall after certain explosion tests
(reference 23) and particularly by the photographs in
figure 8. At lower gas densities or with the single-
orifice nozzle, the penetration should be greater (refer¬
ence J) and the time required to traverse the bomb
somewhat shorter. In any case the sprays struck the
bomb wall long before minimum pressure was attained.
In view of the discrepancy between the calculated
and observed pressure changes it is rather surprising
that the experimental pressure drops are directly pro¬
portional to the initial pressure. There is no particular
reason for believing that the vapor left the wall in
temperature equilibrium with it; i. e., that this vapor
could abstract little or no heat from the gas phase,
unless perhaps the mass motion of the gas was too slow
to effect the removal of the vapor from the immediate
neighborhood of the wall in the interval examined.
The ratio of observed to calculated pressure drop is
indicative of the fraction of the total heat contributed
by the gas phase. It follows from figure 10 that above
250° C. the fraction of the total heat contributed by the
walls became relatively constant at all temperatures
for a given density and a gas-fuel ratio of 20, indicating
that a constant fraction of the fuel charge struck the
wall at temperatures above 250° C., the gas density
being almost noninflu ential.
The total pressure drop subsequent to injection
increases with initial temperature, fuel quantity, and
to some extent with initial density, although in the
higher range this latter change is not very evident.
There is also a slight decrease in this drop (table I,
section 7) with a moderate increase in fuel temperature,
showing that in this case less total heat is transferred
to the portion of the fuel charge that normally absorbs
heat from the gas phase. With carbon dioxide as the
ambient gas, the drop is less than that for nitrogen,
but a consideration of the relative initial pressures
shows that the corresponding temperature drops are of
the same magnitude. This similarity might be ex¬
pected because the spray development is about the
same for a given density irrespective of the nature of
the gas (reference 28) and, on a weight basis, the specific
heat of carbon dioxide is not greatly different from that
of nitrogen in this temperature range. For a given
fuel weight benzene gives a greater drop than does the
Diesel fuel, presumably owing to the greater heat
required for vaporization. This presumption assumes
that the same fraction of the fuel (benzene or Diesel fuel)
fails to strike the wall under identical circumstances.
The benzene tests also indicate that the surface tem¬
perature of the drops is well below the ambient-gas
temperature; although the gas temperatures employed
were near to or above the critical temperature of
benzene, the fact that the A-C interval was about the
same for benzene as for Diesel fuel indicates a droplet
temperature much below the critical point.
Time to attain minimum pressure. — Small variations
of the A-C interval are evident but, because of possible
errors, these variations may not be real. In any case
the variations cannot be associated with any primary
variable. The interval is greatest for carbon dioxide,
intermediate for air, and least for nitrogen; it increases
with the fuel quantity for the lower but not for the
Figure 10.— Comparison of calculated and observed pressure drops at various
temperatures.
higher weights; and there appears to be a slight in¬
crease with gas density. As the total pressure drop
increases with an increase in the fuel weight and to
some extent with an increase in gas density, it is con¬
ceivable that the latter trends arise from an “over¬
shooting” of the true decrease in pressure because of
the increased amplitude of the wave evident after
point C. The records for benzene, however, fail to
show such trends.
In view of the wide variation of the fraction of the
fuel that strikes the bomb wall with varying fuel
weights and given gas density, the minimum point
cannot be logically associated with the moment of com¬
plete evaporation of the fuel on the wall. This con¬
tention is further substantiated by the failure of
benzene to give a shorter interval; its greater volatility
should enable it to evaporate more rapidly from the
bomb surface. It has previously been shown that non¬
uniformity of the gas-vapor mixture exists for at least
0.0G second after injection (reference 23). An attempt
was made to mix the charge with a 4-blade fan driven
at 7,000 r. p. m. but, as the A-C interval corresponded
to only two revolutions of the fan, it is not surprising
104
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
that the interval was unaltered. Since the rates of
heat transfer from the wall and to the fuel are equal at
C, it would seem that the interval should depend upon
the nonuniformity of the mixture, which in turn should
be dependent upon the injected fuel weight and the gas
density. Actually, the interval is practically independ¬
ent of both variables.
CONCLUSIONS
1. The injection of liquid fuel into a heated and com¬
pressed gas has furnished data on the initial rate of
heat exchange between the ambient gas and the fuel.
The actual rates of vaporization were indeterminate,
but it is shown that vaporization began immediately
after injection started. The same situation must also
be true for engines.
2. For given experimental conditions, the initial rate
of heat transfer was essentially constant during the
time required for the spray to traverse the bomb.
This initial rate was found to be proportional to the
initial temperature difference between the fuel and the gas.
The total heat transferred in engines must be greater
owing to the greater initial temperature difference.
3. The initial heat-transfer period was approximately
constant (0.0020 ±0.0005 second) for the 13-orifice, 2-
impinging-jets, and single-orifice nozzles tested and
also for benzene and Diesel fuel, which have quite
different volatilities and viscosities.
4. At the temperatures investigated the transfer of
heat by radiation was negligible as compared with that
transferred by conduction. This situation must also
exist in an engine until the start of flame combustion.
5. The efficacy with which heat transfer took place
decreased considerably with increasing fuel quantity
at all densities and temperatures investigated.
6. Under all conditions a good fraction of the total
heat absorbed after the spray had traversed the bomb
must have occurred at the bomb wall.
Langley Memorial Aeronautical Laboratory,
National xVdvisory Committee for Aeronautics,
Langley Field, Va., August 25, 1936.
REFERENCES
1. Lee, Dana W.: A Comparison of Fuel Sprays from Several
Types of Injection Nozzles. T. R. No. 520, N. A. C. A., 1935.
2. Lee, Dana W.: Measurements of Fuel Distribution within
Sprays for Fuel-Injection Engines. T. R. No. 565,
N. A. C. A., 1936.
3. Rothrock, A. M., and Waldron, C. D.: Effect of Nozzle
Design on Fuel Spray and Flame Formation in a High-
Speed Compression-Ignition Engine. T. R. No. 561,
N. A. C. A., 1936.
4. Rothrock, A. M., and Waldron, C. D.: Fuel Spray and
Flame Formation in a Compression-Ignition Engine Em¬
ploying Air Flow. T. R. No. 588, N. A. C. A., 1937.
5. Boerlage, G. D., and van Dyck, W. J. D.: Causes of De¬
tonation in Petrol and Diesel Engines. R. A. S. Jour.,
Dec. 1934, pp. 953-986.
6. Rothrock, A. M., and Waldron, C. D.: Some Effects o[
Injection Advance Angle, Engine-Jacket Temperature,
and Speed on Combustion in a Compression-Ignition
Engine. T. R. No. 525, N. A. C. A., 1935.
7. Gerrish, Flarold C., and Ayer, Bruce E.: Influence of Fuel-Oil
Temperature on the Combustion in a Prechamber Com¬
pression-Ignition Engine. T. N. No. 565, N. A. C. A., 1936
8. Rothrock, A. M., and Waldron, C. I).: Fuel Vaporization
and Its Effect on Combustion in a High-Speed Compres¬
sion-Ignition Engine. T. R. No. 435, N. A. C. A., 1932.
9. Wentzel, W.: Ignition Process in Diesel Engines. T. M,
No. 797, N. A. C. A., 1936.
10. Ellenwood, F. O., Evans, F. C., and Chwang, C. T.: Effi¬
ciencies of Otto and Diesel Engines. A. S. M. E. Trans.
OG P-50-6, Jan. -April 1928, pp. 1-22.
11. Rothrock, A. M., and Cohn, Mildred: Some Factors Affect¬
ing Combustion in an Internal-Combustion Engine.
T. R. No. 512, N. A. C. A., 1934.
12. Rothrock, A. M., and Spencer, R. C.: Effect of Moderate
Air Flow on the Distribution of Fuel Sprays after Injec¬
tion Cut-Off. T. R. No. 483, N. A. C. A., 1934.
13. Nusselt, Wilhelm: Warmeiibergang, Diffusion und Verdun-
stung. Z. f. a. M. M., vol. 10, 1930, pp. 105-121.
14. Fuchs, N.: Uber die Verdampfungsgeschwindigkcit kleiner
Tropfchen in einer Gasatmosphare. Phys. Zeit. Sowjet-
union, vol. 6.3, 1934, pp. 224-243.
15. Sherwood, T. K., and Gilliland, E. R.: Diffusion of Vapors
through Gas Films. Indus. Eng. Chem., vol. 26, 1934,
pp. 1093-1096.
16. Ingersoll, L. R., and Zobel, O. J.: An Introduction to the
Mathematical Theory of Heat Conduction. Ginn and
Co. 1913, p. 133.
17. Cragoe, C. S.: Thermal Properties of Petroleum Products.
Misc. Publication No. 97, Bur. Standards, 1929.
18. National Bureau of Standards: National Standard Petroleum
Oil Tables. Circular No. 154, Bur. Standards, 1924,
pp. 95-1 13.
19. Gaucher, L. P.: Specific Heat of Liquid Pure Hydrocarbons
and Petroleum Fractions. Indus. Eng. Chem., vol. 27,
1935, pp. 57 64.
20. Lee, Dana W.: The Effect of Nozzle Design and Operating
Conditions on the Atomization and Distribution of Fuel
Sprays. T. R. No. 425, N. A. C. A., 1932.
21. Walker, William H., Lewis, Warren K., and McAdams,
William IL: Principles of Chemical Engineering. McGraw-
Hill Book Co., Inc., 1927, p. 162.
22. Watson, K. M., and Nelson, E. F.: Improved Methods for
Approximating Critical and Thermal Properties of
Petroleum Fractions. Indus. Eng. Chem., vol. 25, 1933,
pp. 880-887.
23. Cohn, Mildred, and Spencer, Robert C.: Combustion in a
Bomb with a Fuel-Injection System. T. R. No. 544,
N. A. C. A., 1935.
24. Lewis, Gilbert Newton, and Randall, Merle: Thermo¬
dynamics and the Free Energy of Chemical Substances.
McGraw-Hill Book Co., Inc., 1923, p. 68.
25. National Research Council: International Critical Tables
vol. V. McGraw-Hill Book Co., Inc., 1929, p. 146.
26. Schweitzer, P. H.: The Penetration of Oil Sprays in Dense Air,
Tech. Bull. No. 20, Penn. State Coll., 1934, pp. 108-124.
27. McAdams, William H.: Heat Transmission. McGraw-Hill
Book Co., Inc., 1933, pp. 20, 96, 216, and 246.
28. Joachim, W. F., and Beardsley, Edward, G.: The Effects of Fuel
and Cylinder Gas Densities on the Characteristics of Fuel
Sprays for Oil Engines. T. R. No. 281, N. A. C. A., 1927
29. Lee, Dana W., and Spencer, Robert C.: Photomicrographs
Studies of Fuel Sprays. T. R. No. 454, N. A. C. A., 1933
30. Gelalles, A. G.: Some Effects of Air and Fuel Oil Tempera¬
tures on Spray Penetration and Dispersion. T. N
No. 338, N. A. C. A., 1930.
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
105
TABLE I
PRESSURE CHANGE ASSOCIATED WITH HEAT TRANSFER TO DIESEL FUEL
1
2
3
4
5
6
7
8
9
10
Initial gas pressure
Gas density
Initial slope per
Gas-
Fuel
Pressure
Interval
Interval
Initial slope
gram per ° C.
Record
Atmos¬
pheres.
absolute
Pounds per
square inch
(gage)
fuel
weight
drop
A to B
A to C
(atmospheres
di (Terence
number
Grams per
liter
Pounds per
ratio
(gram)
(atmosphere)
(second)
(second)
per second)
/ atmospheres \
cubic foot
\second gram °C.J
1. AIR AT 150° C
(302° F ); FUEL TEMPF, RATURE, 49° C.; 13-ORIFICE NOZZLE
17 !
5.67 1
69
4.73 |
0. 296
20
0. 142
0. 10
0. 0013
0.023
-38
-2.7
34
15
. 189
. 12
.0015
.023
-40
-2. 1
35, 19
35 20
10
. 284
. 15
.0015
. 023
-53
-1.8
5
. 568
. 26
.0020
. 023
-65
-1. 1
37
11. 34
152
9.46
.592
40
. 142
. 12
.0017
.023
-29
-2.0
38
30
. 189
. 16
.0020
.023
-40
—2. 1
39
20
.284
.20
.0020
. 023
-50
-1.7
40
15
.378
.25
. 0020
.023
-60
-1.6
23,41
44
10
.568
.36
. 0020
. 023
-65
— 1. 1
17.01
235
14. 19
.888
60
. 142
. 12
.0015
.023
-33
-2.3
45
4f>
45
. 189
. 16
. 0020
.025
-30
-1. 6
30
.'284
.22
. 0020
.025
-40
-1. 4
26
20
. 426
.30
.0020
.025
-55
-1.3
27
15
.568
.39
. 0020
.027
-55
-1. 0
50
22.68
319
18.93
1. 184
40
.284
.23
. 0020
.030
-40
— 1.4
49
20
.568
.38
. 0020
.027
—50
— . 9
2. AIR AT 200°
C. (392° F.)
; FUEL TEMPERATURE, 49'
C.; 13-ORIFICE NOZZLE
73
6.34
79
4.73
0. 296
20
0. 142
0. 15
0.0015
0.023
-47
-2. 2
56
15
. 189
. 18
. 1X115
. 023
-68
-2.4
75
10
.284
.25
.0020
. 023
—75
— 1.7
70
5
.568
.46
.0015
. 023
-100
— 1. 2
12.68
172
9. 46
. 592
40
. 142
. 18
. 1X120
.027
-35
— 1. 6
78
81,79
80
82
20
.284
.32
. 0020
. 027
— 70
— 1. 6
15
.378
.41
. 0025
.027
-72
-1.3
10
.568
.61
. 0025
.027
—88
— 1. 0
19. 02
265
14. 19
.888
60
. 142
. 18
. IK 120
. 029
-25
— 1. 2
-1. 1
83
84
85
86
30
284
.34
. 1X125
. 029
—48
20
.426
.48
. 0025
.029
— GO
— .9:5
15
. 568
.61
.0025
. 030
-72
— . 84
25. 36
358
18. 93
1. 184
80
. 142
. 16
. 0020
. 029
-20
— . 93
-1.2
89
88
40
. 284
.31
. 0020
. 030
—50
20
.568
.57
.0020
.030
—65
— . 76
3. NITROGEN AT
200° C. (392° F.); FUEL TEI
dPERATURl
E, 49° C.; 13
-ORIFICE
NOZZLE
202
222
223
205
225
207
227
209
211
230
213
214
215
234
235
236
6. 56
82
4.73
0. 296
20
15
0. 142
. 189
0.14
. 17
0. 0015
.0020
0. 023
.023
-50
-52
-2.3
-1.8
-1.9
-1.0
-2.5
-1.9
10
. 28 4
.26
.0018
.023
—83
5
. 568
.48
. 0025
. 023
—88
13. 12
178
9. 46
.592
40
20
. 142
.284
. 20
.33
.0015
. 0020
.023
.023
—53
-80
15
.378
.45
. 0020
. 023
—100
-no
-1.8
-1.3
-1.9
-1.7
10
. 568
.65
.0020
. 0‘23
19. 68
275
14. 19
.888
60
30
. 142
.284
.21
.37
. 0020
. 0022
. 024
. 024
.023
.025
1 II 1 M 1 1
cc p,J g J r J ±
20
. 426
.51
. 0025
— 1.4
-1.0
15
. 568
.67
. 0025
26.24
371
18. 93
1. 184
80
40
. 142
.284
. 18
.37
. 0020
. 0020
. 023
.024
—1.4
-1. 4
-1. 1
27
. 426
.51
. 0025
. 023
.026
20
.568
.63
. 0025
— . 93
_ — — _ _
4. NITROGEN AT 250° C. (482c
F.); FUEL TEMPERATURE, 49° C.; 13-ORIFICE NOZZLE
177
178
191
192
193, 181
182. 194
183, 195
184
196
197, 186
198, 187
188
7.25
92
4. 73
0. 296
20
15
0. 142
. 189
0. 22
.26
0.0015
.0018
0. 023
.023
-65
-83
-115
-150
-55
-96
-2.3
-2. 2
10
.284
.37
.0020
. 02.1
.023
.024
.023
.024
— 2. 0
-1.3
-1.9
-1.7
-1.6
5
.568
.69
. 0020
14. 50
199
9. 46
.592
40
20
. 142
. 284
.27
.48
.0018
.0025
15
.378
.65
. 0025
— 124
10
. 568
. 0025
— 1 4 0
-53
-100
-1.9
-1.8
-1. 2
-1.1
21. 75
305
14. 19
.888
60
30
. 142
. 284
.30
.52
. 0015
.0020
.025
.024
.025
20
. 426
.75
. 0025
— 100
15
. 568
. 0025
— 120
5. NITROGEN AT 250° C. (482°
F.); FUEL TEMPERATURE,
82° C.: 13-ORIFICE NOZZLE
255
239
257
241,258
242
260, 243
261, 244
262, 245
246
247, 264
265
266
7. 25
92
4. 73
0. 296
20
15
0. 142
. 189
0. 20
.23
0. 0020
. 0020
0. 023
.023
. 023
. 023
.023
.023
.024
. 025
. 025
. 025
-60
-70
-2.5
-2. 2
10
.284
.36
. 0020
. 0020
5
. 568
. 65
14. 50
199
9. 46
.592
40
20
. 142
. 284
. 27
.47
. 001 (
.0022
— 65
-100
-2. 1
-1.8
-1.3
15
.378
.60
. 0025
. 0025
.0020
. 0022
. 0025
— 112
10
.568
.83
— 124
21. 75
305
14. 19
.888
60
30
. 142
.284
. 27
.50
— oO
-91
-1.9
-1.5
20
.426
.66
. 025
15
.568
.88
. 0025
. 025
— 104
106
REPORT NO. 580 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I— Continued
PRESSURE CHANGE ASSOCIATED WITH HEAT TRANSFER TO DIESEL FUEL
1
2
3
4
5
6
7
8
9
10
Record
number
Initial gas pressure
Gas density
Gas-
fuel
ratio
Fuel
weight
(gram)
Pressure
drop
(atmosphere)
Interval
A to B
(second)
Interval
A to C
(second)
Initial slope
(atmospheres
per second)
Initial slope per
gram per 0 C.
difference
f atmospheres \
Atmos¬
pheres
absolute
Pounds per
square inch
(gage)
Grams per
liter
Pounds per
cubic foot
Vsecond gram ° C. /
6. NITROGEN AT 300° C. (573° I
FUEL TEMPERATURE, 49° C.: 13-ORIFICE NOZZLE
394
7. 94
102
4. 73
0. 296
20
0. 142
0. 24
0. 0020
0. 024
— 75
-2. 1
398
15
. 189
. 27
. 0020
. 023
—95
-2.0
390
10
. 284
.42
. 0020
. 023
-130
-1.8
399
5
.568
.86
. 0020
. 024
-180
— 1. 3
4C4
15. 88
219
9. 46
.592
40
. 142
.29
.0017
.025
-82
-2.3
401
20
. 284
. 56
. 0020
. 025
-135
— 1. 9
402
15
.378
. 74
. 0025
.025
-140
— 1. 5
403
10
. 568
. 0025
-160
-1. 1
405
23. 82
335
14. 19
.888
60
. 142
.32
.0015
. 026
-60
— 1.7
406
30
. 284
. 61
. 0020
. 026
— 110
— 1.6
408
22. 5
.378
. 78
. 0025
.026
— 112
— 1. 2
407
20
.426
.0025
-132
- .93
7. NITROGEN AT 350° C. (662°
F.) ; FUEL TEMPERATURE, 49° C.; 13-ORIFICE NOZZLE
418
8.63
112
4. 73
0. 296
20
0. 142
0. 27
0.0017
0. 023
-100
-2.3
415
15
. 189
. 35
. 0017
. 025
— 123
-2. 2
416
10
. 284
. 52
.0020
. 024
— 156
— 1.8
417
5
. 568
.92
.0025
. 025
-190
-1. 1
420
17. 26
239
9. 46
.592
40
. 142
.38
.0018
.025
-94
-2. 2
437
30
. 189
. 47
. 0025
.025
-96
— 1.7
438
20
. 284
. 0025
. 025
-132
— 1. 5
439
25. 89
366
14. 19
.888
60
. 142
.40
. 0020
. 026
-70
— 1. ♦>
440
45
. 189
. 50
. 0020
. 026
-95
— 1. 7
441
30
. 284
.71
. 0025
.025
-124
-1.5
8. NITROGEN AT 250°
C. (482° F.); FUEL TEMPERATURE, 49° C.; IMPINGING-JETS NOZZLE
270
7. 25
92
4. 73
0. 296
20
0. 142
0. 25
0. 0020
0.023
-60
-2. 1
271
15
. 189
. 29
. 0020
.023
-80
-2. 1
272
10
. 284
. 37
. 0020
.022
— 110
— 1.9
273
5
. 568
.62
. 0020
.023
— 155
-1. 4
274
14. 50
199
9. 46
.592
40
. 142
.28
. 0025
.024
-48
-1.7
275
20
. 284
. 45
. 0025
.025
-8(1
-1. 4
276
15
. 378
. 57
. 0025
.024
— 100
- 1. 3
277
10
. 568
. 74
.0025
.025
-116
-1.0
278
21. 75
305
14. 19
.888
60
. 142
. 29
. 0022
.024
-41
-1.4
279
30
.284
.-44
. 0025
. 026
-64
-1. 1
280
20
. 426
.63
. 0025
. 027
-92
-1. 1
281
15
. 568
. 76
. 0025
.027
— 100
-.88
9.
NITROGEN AT 250° C. (482° F.);
FUEL
TEMPERATURE, 49°
CL; SINGI
K-O K 1 FIT E NOZZLE
286
7. 25
92
4. 73
0. 296
20
0. 142
0. 10
0. 0015
0. 023
-33
-1.2
287
15
. 189
. 15
.0025
.022
-44
-1. 2
288
10
.284
.22
.0020
.023
-70
-1. 2
289
5
. 568
. 43
. 0020
. 020
-110
— .97
290
14. 50
199
9. 46
.592
40
. 142
. 16
. 0020
.023
-40
-1.4
291
20
. 284
. 29
. 0020
. 023
-65
-1. 1
292
15
. 378
. 40
. 0020
. 022
-95
-1. 2
293
10
. 568
.53
. 0025
.022
-104
-. 91
294
21. 75
305
14. 19
.888
60
. 142
.20
. 0020
.024
-45
-1.6
295
30
. 284
.33
. 0020
.023
-65
-1. 1
296
20
. 426
. 51
. 0025
.025
-88
— 1.0
297
15
. 568
. 0025
-96
-. 84
10. CARBON DIOXIDE AT 200° C. (392° F.); FUEL TEMPRATURE, 49° C
; 13-ORIFICE NOZZLE
131
4. 18
47
4. 73
0.296
20
0. 142
0. 09
0. 0012
0. 030
-42
-2.0
91
15
. 189
. 11
. 0015
. 035
-47
-1.6
114
10
.284
1. 6
.0015
. 030
-1.6
115
5
.568
3.0
. 0015
. 030
-80
-.93
95
8. 36
108
9. 46
.592
40
. 142
. 11
.0015
.035
-33
-1.5
117
20
. 284
.22
, 0020
. 030
-55
-1.3
97
15
.378
.27
. 0020
. 030
-60
-1.0
119
10
. 568
.41
.0020
.032
-70
-.82
100
12. 54
170
14. 19
.888
60
. 142
. 12
.0015
.030
-27
-1.3
121
30
. 284
.24
. 0020
.035
-50
-1.2
122
20
.426
.34
. 0020
. 035
-70
-1. 1
123
15
. 568
.44
.0020
.035
-70
-.82
125
16. 72
231
18. 93
1. 184
80
. 142
. 12
.0015
.037
-27
-1.3
126
40
.284
.25
.0020
.037
-40
-.93
127
27
.426
.33
. 0020
.037
-55
-.85
128
20
.568
.44
.0020
.038
-55
-.64
11
CARBON
DIOXIDE
AT 250° C.
(482° F.); FUEL TEMPERATURE, 49° C.; 13-ORIFICE NOZZLE
158
4.62
53
4. 73
0. 296
20
0. 142
0. 12
0.0015
0. 030
— 50
-1.7
159
15
. 189
. 16
.0020
.030
—55
— 1. 4
160
10
. 284
92
. 0015
.030
-100
-1.8
161
5
. 568
. 44
. 0020
.030
-100
-.88
162
9. 24
121
9. 46
. 692
40
. 142
. 18
.0015
.030
—53
-1.9
163
20
. 284
. 33
. 0020
.031
-90
-1.6
164
15
. 378
. 44
. 0020
.031
-100
-1.3
165
10
. 568
. 65
.0020
. 030
-121)
-1.0
166
13. 86
189
14. 19
.888
60
. 142
.21
. 0016
.032
-50
-1. 7
167
30
. 284
.37
. 0020
.031
-90
-1.6
168
20
.426
. 52
.0020
.031
-100
-1.2
169
15
. 568
. 68
. 0025
. 033
-100
-.88
170
18. 48
257
18. 93
1. 184
80
. 142
.21
. 0015
.033
-40
-1.4
171
40
. 284
.39
. 0020
. 033
-75
-1.3
172
27
.426
.54
. 0020
.033
-100
-1.2
173
20
.568
.69
.0020
.035
-100
-.88
HEAT TRANSFER TO FUEL SPRAYS INJECTED INTO HEATED GASES
TABLE II
EFFECT OF FUEL VAPOR ON PRESSURE CHANGE FOR DIESEL FUEL
10
1
2
3
4
5
6
7
8
9
Record
Initial ga.
Atmospheres
absolute
(approx.)
pressure
Pounds per
square iuch
(gage)
Fuel quan¬
tity injected
(gram)
Injec¬
tion
Fuel in
bomb before
injecting
(grams)
Pressure
drop A to C
(atmosphere)
Interval A to
B (second)
Interval A to
C (second)
Initial slope
(atmospheres
per second)
NITROGEN AT 250
C. (482° F.)
FUEL
TEMPERATURE, 49° C
; 13-ORIFICE NOZZLE
380
15. 88
219
0. 568
1
0.000
0. 94
0. 0025
0. 025
-156
381
.568
2
.568
. 70
.0020
. 025
— 140
382
. 568
3
1. 14
.57
.0025
.025
- 104
383
.568
4
1. 70
. 57
. 0020
.025
— 105
384
.568
5
2.27
.51
.0020
. 025
-105
385
to
to
.568
8
3. 98
. 42
.0025
.025
-80
386
. 568
11
5. 68
.39
. 0020
. 025
-90
387
. 568
17
9.09
.37
. 0020
. 025
-90
388
.568
23
12.5
.33
. 0020
.023
-90
389
16. 57
229
.568
34
18.7
.31
.0020
.023
-80
NITROGEN AT 350c
C. (662° F.);
FUEL
TEMPERATURE, 49° C.
13-ORIFICE NOZZLE
446
17.26
239
0. 284
1
0. 000
0. 63
0. 0025
0. 023
-148
447
. 284
5
1. 14
.46
. 0022
.024
—95
448
. 284
10
2.56
.29
.0025
. 025
-56
449
18. 08
260
. 284
15
3. 98
.22
.0020
.024
-55
TABLE III
PRESSURE CHANGE ASSOCIATED WITH HEAT TRANSFER TO BENZENE
1
2
3
4
5
6
7
8
9
10
Record
number
Initial gas pressure
Gas density
Gas-
fuel
ratio
Fuel
weight
(gram)
Pressure drop
(atmosphere)
Interval A
to B
(second)
Interval A
to C
(second)
Initial slope
(atmospheres
per second)
Initial slope
tier gram per ° C.
difference
( atmospheres \
\seeond-gram 0 C ./
Atmospheres
absolute
Pounds per
square inch
(gage)
Grams per
liter
Pounds per
cubic foot
1. NITROGEN AT 250° C. (482° F.);
FUEL TEMPERATURE, 49°
C.; 13-ORIFICE NOZZLE
315
7. 25
92
4.73
0. 296
20
0. 142
0. 30
0. 0020
0. 025
-85
-3.0
316
15
. 189
.35
. 0020
.024
—too
-2. 6
317. 323
10
. 284
.54
. 0025
. 023
-124
-2.2
318
14. 50
199
9. 46
.592
40
. 142
.33
. 0025
.025
-64
-2. 2
319
30
. 189
. 40
. 0020
. 025
-95
-2. 5
320
20
.284
.62
.0025
.024
-124
-2. 2
2. NITROGEN AT 300° C. (572° F.)
FUEL
TEMPE
RATURE, 49
C-; 13-ORIFICE NOZZLE
301
7. 94
102
4. 73
0. 296
20
0. 142
0. 36
0. 0020
0. 023
-85
-2.4
302
15
. 189
.42
. 0020
. 025
-11(1
-2.3
303
10
. 284
.64
.0025
.024
-144
-2.0
305
15. 88
219
9. 46
.592
40
. 142
.39
.0020
. 025
-90
-2.5
306
30
. 189
.48
. 0025
. 024
-92
-1.9
307
20
.284
.76
.0025
.024
-140
-2. 0
3. NITROGEN AT 350° C. (662° F.); FUEL TEMPERATURE, 49° C.; 13-ORIFICE NOZZLE
331
8.63
112
4.73
0. 296
20
0. 142
0. 37
0. 0020
0. 024
-105
-2.5
332
15
. 189
.45
. 0025
. 024
-112
—2. 0
333
10
.284
.69
. 0025
.023
-172
-2. 0
334
17. 26
239
9.46
.592
40
. 142
.43
.0025
.024
-92
-2. 2
335
30
. 189
. 56
. 0025
. 023
-112
—2. 0
336
20
.284
.85
. 0025
.024
-172
-2.0
REPORT No. 581
MEASUREMENTS OF INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
AND THEIR RELATION TO THE CRITICAL REYNOLDS NUMBER OF SPHERES
By Hugh L Dryden, G. B. Schubauer, W. C. Mock, Jr., and H. K. Skramstao
SUMMARY
The investigation oj wind-tunnel turbulence , conducted
at the National Bureau oj Standards with the cooperation
and financial assistance oj the National Advisory Com¬
mittee jor Aeronautics, has been extended to include a
new variable, namely, the scale oj the turbulence. This
new variable has been studied together with the intensity
ol the turbulence, and the effect oj both on the critical
Reynolds Number ol spheres has been investigated.
By the use oj a modification of the usual hot-wire
apparatus incorporating two hot wires suitably connected
and mounted so that the cross-stream distance between
them may be varied, it has been found possible to determine
the correlation between the speed fluctuations existing at
the two wires. If ux and u2 are the velocity fluctuations
in the direction of the mean speed at the first and second
wires, respectively, a correlation coefficient R(y), equal
to i~==U]~ may be found as a function of the separation
\ux2ffu22
y. A length characterizing the scale oj the turbulence
may then be defined by the relation —
L=fR(y)dy
o
The intensity oj the turbulence as given
by
■y/u2
U'
where
U is ihe average speed oj the stream, and the quantity L
were determined by measurements in an air stream made
turbulent to various degrees by screens oj various mesh.
The value oj L near the screen was found to be about the
same as the wire size oj the screen, but increased with
distance downstream from the screen. The quantity L
may be regarded as a rough measure of the size of the
eddies shed by the wires of the screen. The intensity was
found to decrease with distance in accordance with the
law oj decay derived by G. I. Taylor.
Hot-wire measurements oj turbulence are in error
where the quantity L is oj the same order as the length
of the wire used. In the present work corrections jor the
lack oj correlation over the entire length oj the wires have
been made in the measured values oj L and
■y/u2
um
With both L and known jor the stream with the
several screens , the critical Reynolds Numbers oj spheres
were investigated. It was found, that the critical Reynolds
I )
Number depended on j-
where D is the diameter oj the
sphere, as well as on
IT’
and that a junctional relation
between the critical Reynolds
Number
and
-\/ u2/ D\A
~u\l)
suggested by G. I. Taylor, was satisfied to within the
experimental uncertainty. It is shown that the effect oj
the size oj the sphere that has been observed by other in¬
vestigators is but a particular manifestation oj the fore¬
going more general relation.
INTRODUCTION
The turbulence of the air stream is generally recog¬
nized as a variable of considerable importance in many
aerodynamic phenomena, especially those observed in
wind tunnels. The drag of an airship model may vary
by a factor of 2, the drag of a sphere by a factor ol 4,
and the maximum lift of an airfoil by a factor of 1.3
in air streams of different turbulence. The determina¬
tion of turbulence is now a routine matter in many
wind tunnels, the most common method being that of
determining the value of the Reynolds Number of a
sphere for which the drag coefficient is 0.3, the so-
called critical Reynolds Number.
The critical Reynolds Number of a sphere is a meas¬
ure of the aerodynamic effect of turbulence on a par¬
ticular body and not a direct measurement of the tur¬
bulence. A direct measurement of the intensity ol the
turbulence can be made by means of a hot-wire ane¬
mometer suitably compensated for the lag of the wire
(reference 1). The intensity of the turbulence is
defined as the ratio of the root-mean -square speed
fluctuation at a point to the mean speed. The experi¬
ments described in reference 1, (fig. 7), show a good
correlation between the intensity of the turbulence
and the critical Reynolds Numbers of spheres. In
subsequent work at the National Bureau of Standards
(reference 2) in which various honeycombs were used
in the same wind tunnel and the entrance cone was
modified, the correlation was not nearly so good.
The existence of a fair correlation was confirmed by
Millikan and Klein at the California Institute of Tech¬
nology (reference 3). These investigators noted that
109
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
110
the critical Reynolds Number of the sphere depended
to some extent on the diameter of the sphere, decreas¬
ing as the diameter increased.
Since the critical Reynolds Number occurs at lower
speeds for larger diameters, it might be supposed that
the variation of the critical Reynolds Number with
diameter really indicated a variation of the intensity
of the turbulence with speed. The direct measurements
of the intensity by the hot-wire anemometer show,
however, that this explanation cannot be correct.
We are thus led to the idea that the scale of the turbu¬
lent pattern must be considered. In fact, as early as
1923, Bacon and Reid, in reference 4, predicted an
effect of the scale or “grain” of the turbulence and stated
that the “effect of scale of turbulence is to control the
degree with which true dynamic similarity may be
maintained throughout a series of tests with spheres
of different size.” A study of this subject was begun
at the National Bureau of Standards in the fall of 1933.
In order to investigate experimentally the effect of
scale of the turbulence as well as its intensity, measure¬
ments of the critical Reynolds Number of spheres were
made in a stream rendered turbulent by screens of
various mesh. The investigation was conducted in the
4^-foot wind tunnel, the screens being placed one at a
time completely across the upstream working section
of the tunnel. In all, five nearly similar square-mesh
screens were used, ranging in size from a 5-inch mesh
made of round rods 1 inch in diameter to a %-inch mesh
with a wire diameter of 0.05 inch. The purpose of the
several screens was to vary the scale of the turbulence,
it being supposed that the scale would be proportional
to the mesh of the screen. It was decided subsequently
to measure some dimension characteristic of the fluctu¬
ations themselves, and the dimension chosen was that
derived from measurements of the correlation between
velocity fluctuations at points at varying distances
apart transverse to the stream.
Values of the intensity of the turbulence measured by
the hot-wire method at different distances downstream
from the several screens showed that the turbulence
decayed rapidly at first and then more slowly with
increasing distance from the screens. Hence in the
sphere measurements the intensity of the turbulence
produced by any one screen could be varied by varying
the distance between the sphere and the screen.
As may be seen from the foregoing discussion, the
complete program included several problems, which
are treated in the five separate parts of the report as
outlined below:
I. The measurement of correlation between velocity
fluctuations with modified hot-wire equipment, and the
derivation of a length to define the scale of the turbu¬
lence, by G. B. Schubauer, W. C. Mock, Jr., and H. K.
Skramstad.
II. Measurements of the intensity and rate of decay
of turbulence employing the usual type of hot-wire
equipment, by G. B. Schubauer, W. C. Mock, Jr., and
II. K. Skramstad.
III. The determination of the critical Reymolds Num¬
ber of spheres under conditions where both the intensity
and the scale of the turbulence are known, by Hugh L,
Dry den, G. B. Schubauer, and W. C. Mock, Jr.
IV. The mathematical theory pertaining to the cor¬
rection of the measurements, both of scale and intensity,
for lack of complete correlation of the fluctuations over
the entire length of the wires, by II. K. Skramstad.
V. Certain subsidiary matters relating to the varia¬
tion of the correlation coefficient with the frequency
characteristics of the measuring apparatus and with
azimuth, by Hugh L. Dryden, G. B. Schubauer, and
W. C. Mock, Jr.
Throughout the later stages of the work, the staff
has been fortunate in being able to discuss by corre¬
spondence various aspects of the problem with G. I.
Taylor, of Cambridge, England. The discussion of the
experimental results is given in terms of his statistical
theory of turbulence outlined in reference 5.
I— THE SCALE OF TURBULENCE AS DERIVED FROM
MEASUREMENTS OF CORRELATION BETWEEN YE-
LOCITY FLUCTUATIONS
When air flows past guide vanes or straighteners,
such as those commonly used in wind tunnels either
separately or in the form of a honeycomb, a considerable
amount of eddy motion is set up and is carried along
with the stream making the flow turbulent. Guide
vanes are necessary to prevent large and erratic speed
fluctuations, which would exist in the absence of the
vanes, as well as to guide the air around turns. It may
be assumed as a rough approximation that the eddy
size and hence the scale of the turbulence is controlled
by some dimension characteristic of the size or the
arrangement of the guide vanes. For the case where
the guide vanes are arranged in the form of a honey¬
comb, G. I. Taylor (reference 5) has assumed that the
scale of the turbulence is proportional to the size of the
cells of the honeycomb.
Figure 1 shows a sketch of the 4-}2-foot tunnel used in
the present work, in which a honeycomb (B) of 4-inch
cells was located at the extreme entrance end and was
followed by a contraction in diameter from 1 0 feet at
the honeycomb to 4-% feet at the working section. Owing
to the rather rapid decay of eddy motion, the turbulence
always decreases in intensity with distance from its
source. In the working section of the present tunnel
the intensity of the turbulence was 0.85 percent.1 The
law of eddy decay and the factors governing the scale
of the turbulence will be taken up in detail in later
sections.
In order to vary the twm quantities, intensity and
scale, the five screens listed in table I w'ere placed indi-
1 This is the value corrected for the effect of the length of the wire used in the mea$’
urement. The uncorrected value as observed with a wire 8.4 millimeters long was
0.7 percent.
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
111
vidually across the upstream working section of the
tunnel at the position indicated in figure 1. Figure 2
shows photographs of a small portion of each of the
screens, illustrating their relative size and type of
construction. It is quite evident that the stream will be
rendered turbulent by the eddies shed from a given
screen and that the initial size of the eddies, and hence
the scale of the turbulence near its point of origin, will
be determined by some dimension of the screen. An
effort was made to obtain screens of uniform mesh and
wire size and to have the five screens as nearly similar
to one another as possible. It will be seen by the varia¬
tions in dimensions shown in table I and by the difference
in type of construction shown in figure 2 that neither
condition was exactly fulfilled. Since the deviations
from the nominal size found by comparing columns 1
and 2 in table I are not outside the average deviations
Figure 1.— Diagram of the wind tunnel showing position of screens and length of
wooden cells— 4 in. square, 12 in. long, Mo in. wall. C
of the individual meshes from the mean, the nominal
mesh size was used as the length characteristic of the
screen.
It will appear later that the scale of the turbulence
near a screen corresponds more nearly to the wire size
than to the mesh size. This fact should not be con¬
strued to indicate that the wire size determines the scale
since the correspondence depends on the way in which
the scale is defined. Since the screens may be regarded
as geometrically similar, it is immaterial whether the
size of the screen is specified by the wire size or the
mesh size.
Immediately downstream from the screens the wakes
of the individual wires or rods caused the air speed and
the turbulence to vary with position across stream.
However at distances greater than 15 mesh lengths the
regular pattern of the screen was found to have disap¬
peared, leaving the average speed approximately uni¬
form and the turbulence nearly uniformly distributed.
The uniformity of the stream will be discussed at greater
length in connection with the sphere measurements in
part III.
HOT-WIRE EQUIPMENT USED IN TURBULENCE MEASUREMENTS
A brief description of the essential features of the hot
wire and its application to studies of turbulence will
suffice here, since full accounts dealing with such equip¬
ment may he found in the literature, notably in refer¬
ences 1, 6, and 7. Fundamentally the apparatus con¬
sists of a particular type of hot-wire anemometer with
an electrically heated wire of such small diameter that
the speed fluctuations of the stream in which the wire
is placed will cause changes in the wire temperature.
The fluctuating voltage drop across the wire, accom¬
panying temperature and resistance changes, would
serve as an indication of the speed fluctuations were
it not for the failure of the wire to follow the faster
working section. A and D: paper tubes— 1 in. diameter, 4 in. long, M2 in. wall. B:
: metal tubes — 3 inch diameter, 12 in. long, 0.025 in. wall.
fluctuations because of the lag introduced by its thermal
capacity. It is however, possible to compensate for
this characteristic of the wire by means of an electric
network containing an inductance and resistance having
the opposite effect. The voltage output of the wire is
usually amplified before compensation is introduced,
and then the compensated voltage is given additional
amplification to enable it to be measured. The indi¬
cator used in the present work was a thermal type milli-
ammeter connected to the output of the amplifier. This
instrument indicated the mean square of the alternating
current output of the amplifier and, with the amplifier
calibrated against a known input voltage, the meter
reading could be used to calculate the mean square of
the compensated voltage fluctuation. In addition, the
direct voltage drop across the wire was measured by a
potentiometer. All the information necessary for cal¬
culating the root-mean-square of the speed fluctuation
was thus made available. Details of such calculations
are given in reference 1. The factors on which com-
112
REPORT NO. 581 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
pensation depends and the formula for computing the
compensation are given in reference 6.
The amplifier used in the present work was not the
one described in reference 7, a new amplifier of a similar
type having since been built to make possible the use of
an alternating current power supply. The frequency
If the turbulence is isotropic, as it will later be shown
to be at a sufficient distance from the source of the
disturbance, the fluctuations have equal velocity com.
ponents in all directions. It is usual, however, to
interpret the measured velocity fluctuations as beim
made up wholly of the component u in the direction of
3^ inch mesh
1 inch mesh
2 inch
mesh
5 inch mesh
Figure 2.— The screens used to produce turbulence showing relative size and type of construction.
characteristics of both the old and the new amplifiers,
when combined with the compensating circuit were such
as to give satisfactory compensation to all frequencies
from a few cycles per second to about 1,000 cycles per
second. The platinum wire used in the present work
was 0.016 millimeter in diameter ; the length was usually
5 millimeters, although some older results are given for
which the wire length was 8.4 millimeters.
the mean speed and to neglect entirely the normal
component v. The justification for doing so lies in the
fact that the v component when superposed on the mean
speed has a very much smaller effect on the cooling of
the wire than a u component of the same magnitude.
The in tensity of the turbulence is therefore expressed in
l=% _
terms of jj-> where -yju2 is the root-mean-square of the
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
113
u component of the fluctuations and U is the average
speed. The term “percentage turbulence” is commonly
used to denote 100
V^2
"TT*
application of hot-wire equipment to correlation
MEASUREMENTS
The determination of the scale of the turbulence in¬
volved a procedure closely related to that just described
since the length characterizing the scale could best be
derived from the distance transverse to the stream over
which correlation existed between velocity fluctuations.
It was therefore desired to obtain the correlation be¬
tween the velocity fluctuations at two points separated
by known distances across the stream and to express
this correlation in terms of the conventional correlation
coefficient
p^ UiU2__
V Ui1 2-\l u2
where ux and u2 are the velocity fluctuations at the
points 1 and 2, respectively. The bars signifiy average
values. In general, R will be a function R(y) of the
separation of the two points, where y is the distance
between the points transverse to the stream. It was
decided to adopt as a measure of the scale of the turbu¬
lence a length L defined as
L= R(y)dy
A length so defined is in accordance with the convention
adopted by G. I. Taylor in reference 5.
The experimental problem therefore resolved itself
into the determination of the correlation between
velocity fluctuations by means of two hot wares. By
way of illustrating the method, let us assume two identi¬
cal wires heated to the same average temperature and
placed parallel to one another at a given distance apart.
If ex and e2 are the instantaneous values of the fluctuat¬
ing voltage over the twro wires separately, the drop
across the two, when they are connected so that their
voltages oppose one another, is (ex — e2). When the
resultant voltage is fed into an amplifier, the indications
given by a thermal type milliammeter in the output of
the amplifier will be proportional to (ex — e2)2, where the
bar signifies that the meter indicates the average. If
compensation is introduced to correct for the attenua¬
tion of the higher frequency fluctuations by the wire,
then ex and e2 become proportional to ux and u2, the
velocity fluctuations at the twro wares,2 and the resultant
meter reading will be proportional to (ux — u2)2.
By the same reasoning it may be seen that a meter
reading proportional to ( ux+u2 )2 is obtained if the
wires are connected so that their voltages add. Figure
3 is a diagram of the electric circuit which shows, in
To
amplifier
6 V poten tiome ter 6 V
Figure 3. — Diagram of the circuit used in the measurement of correlation between
velocity fluctuations.
addition to the heating circuits, two sets of potential
leads running from the wires to the switch AB by means
of which the potentials from the wires may be either
added or opposed. If Ma is the meter reading obtained
when the voltages are added and Mb is the reading
when opposed, then
Ma=K(ux-\- u2)2=K(ux2+u22+2u1u2) (1)
Mb= K(ux—u2)2=K ( ux 2 + u2 — 2uxu2) (2)
where K is simply the constant of proportionality.
Forming Ma—Mb and Ma-\-Mb and dividing
Ma—Mb 2 uxu2 /ox
Ma-\-Mb U2-\~U22
If the turbulence is uniformly distributed across the
stream so that the average square of the fluctuations is
the same at wares 1 and 2, then ux=u22=u2} and equa¬
tion (3) becomes
Ma—Mb_uxu2
Ma-\-Mb u2
1 The voltage fluctuations are proportional to the velocity fluctuations only when
the latter are small. This condition was closely fulfilled for the conditions of the
present experiments.
(4)
114
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Under such conditions it is evident that
uxu2 uxu2
u~ V^i2V^22
which is the conventional correlation coefficient. Since,
however, it is only possible to measure the average of
the fluctuations along wires, the lengths of which in
the present case were 5 millimeters, ux and u2 cannot
he interpreted as fluctuations at points. Hence the
observed correlation coefficient will be denoted by R'
as distinguished from R , the coefficient of correlation
between the fluctuations at two points.
A little consideration will show that the correlation
must depend on the separation of the two wires. For
example, if the wires are brought close together so
that a disturbance striking the one must strike the other
also, ux becomes equal to u2 and R' equal to unity. On
the other hand, when the wires are very far apart, the
instantaneous ux will bear no relation to the instanta¬
neous u2, and uxu2 and hence R' will equal zero. Values
of R' between these two limits may be obtained by
taking readings for various separations of the two
wires.
An alternative procedure found more convenient
than the foregoing one, but less exact if the turbulence
is not uniform or conditions are not steady, is to take
only meter reading Mb corresponding to various
separations of the wires. Denoting by Mbm the meter
reading obtained when the wires are so far apart that
no correlation exists, we have by equation (2)
M b 00 = K{u2 -f- u2)
Forming the quotient
Mb _ux-\-u22—2uxu2_ 2uxu2
Mbm u2-\-u2 u2-\-u2
and, as before, when u2=u22=u2
, _ u-[U2
* \ / 00 ^9 **
ML b vr
Obviously Ma could have been used alone in a similar
manner but, since Ma does not approach zero for a
correlation of unity as does Mb, this method was less
sensitive and was never used.
In the wiring diagram of figure 3 the potentiometer
and amplifier circuits are omitted since these are
standard pieces of equipment. It will be observed
that two separate heating circuits are used, the separa¬
tion of the two circuits being convenient to allow the
potential drops across the wires to be either added or
opposed. After the current in one of the circuits was
set equal to the desired value of 0.2 ampere, as de¬
termined by the potentiometer and standard resistance
/q, the current in the other heating circuit was set to
the same value by making the drop across the 1 ohm
standard resistance in this circuit equal to that across
the 1 ohm standard resistance in the other circuit
The potentiometer was also used to measure the
voltage drop across each wire. From the voltage drop
the current, and the temperature coefficient of resist¬
ance, the temperature of the wire could be computed, a
quantity required to compute the compensation
resistance.
Figure 4. — The traversing apparatus used to vary the distance between hot wire
in the measurement of correlation between velocity fluctuations.
By means of the traversing apparatus shown u
figure 4, the distance between the wires could be varied
and R' measured as a function of the distance. The
side view of the apparatus clearly shows the two sets of
prongs each 1 foot in length from the support to the
needle tips to which the wires were attached. The
! outer set A is fixed rigidly to the vertical supporting
member while the inner set B, to permit rotation, $
fixed to a vertical shaft running down through the
supporting member to the outside of the tunnel. Th>
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
movable prongs are slightly shorter than the fixed
prongs to allow the movable wire to swing past the
fixed wire and thereby permit settings on either side.
This clearance was usually no more than a few tenths of
a millimeter. Distances were indicated on a linear
scale below the tunnel by means of a pointer attached
to the vertical shaft carrying the movable prongs.
The height of the apparatus was such as to place the
wires in the center of the tunnel when in use. The
wires were of platinum 0.016 millimeter in diameter
and about 5 millimeters long, care being taken to make
the lengths of the two as nearly equal as possible.
Soft solder was found to be very convenient and quite
satisfactory for attaching the wires to the prongs.
The displacement of the movable wire by the swing¬
ing motion just described lias the disadvantage that the
wire moves in an arc of a circle rather than in a straight
line and so suffers a downstream displacement as well
as a lateral one. This defect increases in importance
with the magnitude of the spacing; but, since neglecting
the downstream displacement could not introduce an
error greater than 2 percent in the measured scale of
the turbulence for the greatest spacings encountered,
no attempt was made to take it into account.
VARIATION OF CORRELATION WITH DISTANCE
With the apparatus placed at various distances back
of the screens listed in table I, traverses were made by
taking meter readings for various settings of the
movable wire relative to and on either side of the fixed
wire. The results obtained are illustrated in figure 5
by the plotted points and the solid curves. The posi¬
tive and negative branches are the result of taking
observations with the movable wire set first to one side
and then to the other side of the fixed wire. Among
the features to be noted are: first, the order of magni¬
tude of the distance over which correlation exists and,
second, the increase in this distance with increasing
screen size.
The absence of points at the top of the curves indicates
that it was never possible to observe the perfect corre¬
lation that must exist in the imaginary case of two
coalescing wires. One reason for this difficulty is
apparent when it is realized that the wires cannot be
brought together without mutual interference. A hen
the movable wire began to enter the wake of the fixed
wire, a sharp reduction of correlation was observed.
These data are not shown in the figure. Another cause
of incomplete correlation near zero is the initial displace¬
ment necessary to allow the wires to pass one another.
The effect of this displacement will be taken up in
greater detail in part Y. Another possible cause is a
poor matching of the wires; but, as shown by the follow¬
ing example, this feature is not so important as might
be supposed. If we reconsider equations (1), (2), and
115
(4) with the response produced by ux differing from
that produced by u2 by a factor k, we obtain:
M a = K(uxk+u2y = K (kW + V + 2 ku^j
Mb = K (ujc —u2)2=K {k2u2 T u2 — 2 kuxu2)
Ma—Mb 2 k uxu2
Ma-\-Mb k2Jr 1 u2
where u2=u2—u2. If we suppose k to equal 0.8, then
T2-f-T==^da = 0.976. In other words, if the two wires
r+l 1-64
differed in length by 20 percent, the final result would be
reduced by only 2.4 percent.
As was pointed out earlier, R' is not the correlation
between the velocity fluctuations at two points in the
stream, but is rather the correlation between the fluctua¬
tions over two wires — in this case, over wires 5 milli¬
meters in length. Figure 5 shows that the correlation
drops considerably in a distance of 5 millimeters; hence
speed fluctuations at points, say at the center of each
wire, must be different from those that are found for the
average over the whole wire. Qualitatively at least it
may be seen that the difference between the observed
correlation and that existing between points will depend
on the length of the wires and the rapidity with which
correlation falls off with distance. In part IY, methods
are developed for correcting all hot-wire results, whether
of correlation or percentage turbulence, for this lack of
complete correlation over the entire length of the wire
or wires used. The R curves shown by the broken line
in figure 5 were obtained by applying this correction to
the R' curves. The R curves therefore represent the
variation of correlation with distance between points
and are consequently independent of wire length.
To compute R curves from the many observed R'
curves, would have proved quite laborious; hence the
procedure adopted was to obtain by graphical integra¬
tion of the R' curves the observed scale of the turbulence
L' , defined as
L’ = R' (y)dy
and then to correct these by dividing by the factor K2,
given in part IV, and so obtain the true scale of the
turbulence L, defined as
L= ( mR(y)dy
Jo
CHARACTERISTIC LENGTH OR SCALE OF TURBULENCE
In table II are given the values of L' and L expressed
as fractions of the mesh size J\f of the screen that
U
produced the turbulence. A comparison between
and ~r will show the
M
magnitude of the wire-length cor-
116
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
correction is applied. Observations taken 40 mesh lengths from screens. Wind speed 40 ft. /sec.
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
117
section. In order to put the results for the several
screens on a comparable basis, distances downstream
from the screens, as well as Lf and L, have been ex¬
pressed in terms of the mesh of the screens; that is, in
terms of
x
M'
where x is distance downstream measured
from the screen. It will be apparent that the scale of
L
L
t
>
''O
-
-1-
A '1
o
□
o
.
o P--
■6
cl - -
A
. ^
x l
Vi
y 1
o
JV— —
o
■" o
9
&
M
U H ii li II —
—A
£
tyo
:>
X *
- u
7 - O
"
-+
0 40 80 120 160 200 240
x/M
Figure 6.— Observed scale of turbulence at several distances from the screens.
f 00
L'= I R' (y) dy, M=mesh of screen.
Jo
the turbulence produced by a given screen is not a
constant quantity but increases with distance from the
screen. With the exception of the dependence of the
scale on the size of the screen and distance from the
screen, L appeared to be unaffected by varying condi¬
tions of the stream. For example, no effect of air
Figure 7. — Scale of turbulence corrected for wire length at several distances from
the screens. L= j R ( y ) dy, At = mesh of screen.
Jo
speed great enough to appear above the experimental
variations could be found even though tests were made
repeatedly to find an effect; nor did any variation
with air temperature appear, even for such variation
as from 12° C. to 30° C. Nearly all of the measure¬
ments given in the table were made at an air speed of
40 feet per second.
The important facts about L' and L are more clearly
L’ L
shown in figures 6 and 7 where and respectively
X
are plotted against , It may be noted first that the
increase with distance is quite marked, and second
L'
that the values of y> show much more of a svstematic
M
change from screen to screen than do values of In
fact, values of ^7 seem to be grouping close to a single
curve. Systematic differences still exist, however,
between the results for the several screens in figure 7
and show that the turbulent patterns are not exactly
similar. This condition may be due to lack of similarity
in the screens or to the residual turbulence produced
by the honeycomb in the entrance of the tunnel. Table
I and figure 2 show that the screens are similar in re¬
gard to major dimensions but different in details of
construction. In view of these causes of departure
from a single relation, separate curves were put through
each set of points.
In figure 6, straight lines were arbitrarily drawn
through the points without much consideration as to
the appropriate type of curve. The curves of figure 7
were, however, drawn only after considerable study,
since it was necessary to know the type of curve
L x
representing the relation or relations between y^ and ^
for future applications. Using the method of least
squares, relations of the form
and
were fitted to the data for each screen separately and to
the data for all screens taken together. When the
second-degree equation was tried, the coefficient c,
came out positive for some screens and negative for
others, a condition which led to the conclusion that
the data could be represented more consistently by
the simpler linear relation. Least-square straight
lines have therefore been drawn through the points of
figure 7. The equations of the separate lines, as well
as of a single line fitted to all the data are listed in table
III
Both figures 6 and 7 show a scatter among the points
which indicates either a change in the turbulent pat¬
tern from time to time or considerable experimental
uncertainty. In the worst cases the maximum spread
among repeated determinations of
L
M
for the same
screen and the same position reached 30 percent, and
in such cases the average deviation from the mean was
as great as 10 percent. It will be seen from the curves
118
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
that the scatter was less than this for many of the
determinations. Extensive study was given to possi¬
ble causes of these variations, after which it was con¬
cluded that the main cause lay in the uncertainty in¬
volved in determining the point where the correlation
reached zero; that is, where the curves of figure 5
touch the y axis. This uncertainty could be traced to
the variations in the meter readings caused by the
longer period fluctuations. These variations tended to
make the meter difficult to read, especially when the
wires were far apart, and to mask the initial changes
in the average meter reading accompanying the onset
of correlation as the wires were brought together.
The linear law of increase in L should not be regarded
as a universal one applying to turbulence regardless of
source. Neither should it be regarded as strictly true
for the turbulence produced by screens, since there can
be little doubt that some residual turbulence from the
honeycomb was present in all cases. The important
fact here is that under a particular set of conditions the
scale of the turbulence for an air stream is given by
figure 7 ; and keeping these conditions the same, the
figure may be used to indicate the scale in connection
with the investigation of other properties and effects of
turbulence, such as those given in subsequent parts of
the report.
TAYLOR’S THEORY OF CORRELATION
In reference 8, G. I. Taylor gives the relation
t>_ i y 2 /frA2 . yi /aw
2lu2\dyJ ' 4 lu2\dy2J
(-i)n
y
In
(2 n) \u2 \ dyn
dnu
(5)
which was deduced from cpiite general considerations.
The assumptions involved are, first, the physical one
that u2 does not vary with y and, second, a mathema¬
tical one that it is possible to differentiate an averaged
quantity. Both assumptions appear to be legitimate.
From this relation it follows that R must be an even
function of y. In reference 5, Taylor has extended his
deductions as follows:
In the neighborhood of y— 0, it is evident that a
good approximation of the equation (5) is afforded by
R= 1-
y2 /duY
2\u2\dy)
(6)
where the terms of yi and higher powers have been
neglected. Equation (6) should then closely represent
the region of the curve of R plotted against y near
/ y \ ~
y— 0. Solving equation (6) for \J^j) ’ we
=2»2
(7)
It is interesting to examine the curves of figure 5
in the light of the foregoing theory. The restriction
imposed by equation (5) that R be an even function of
y requires that the curves leave the axis y = 0 with zero
slope. This condition was never found in the observed
R ' curves, possibly because it was impossible to examine
the top of the curves in detail due to their extreme
narrowness. A slight rounding is apparent at the apex
in all of the R' curves, but this has disappeared with
the application of the wire-length correction and is not
at all in evudence in the R curves. As seen from figure
21 in part IV, where the difference between tne R' and
R curves is small, the R curve may be closely repre¬
sented by
R=eZ ®
for which the initial slope is -y- In view of the
uncertainties near R= 1, however, it is quite possible
that a sharp change in the slope begins near the origin
of y to allow the initial slope of zero as required by
equation (5) instead of — given by equation (8).
_ y_
If R in equation (7) is replaced by e i, it may be seen
b}T expansion of the exponential and passing to the
du
by
is obviously impossible since, as will be seen by equa¬
tion (13), the rate of dissipation of energy in the
turbulent motions must then be infinite. It must be
concluded therefore that equation (8), although a good
approximation on the average, is not correct near R= 1.
II— MEASUREMENTS OF INTENSITY AND RATE OF
DECAY OF TURBULENCE
limit y= 0 that ^
Y
) becomes infinite. This condition
MEASUREMENTS OF THE INTENSITY BY THE HOT-WIRE METHOD
Using the hot-wire method described in part I,
measurements were made of the intensity of the turbu¬
lence at various positions back of the screens listed in
table I. The single hot wire used in this work was
electrically welded to steel needles which formed the
tips of a set of fixed supporting prongs.3 These prongs
mounted on a holder, which held the wire near the
center of the tunnel and about 18 inches ahead of the
supports, took the place of the apparatus shown in
figure 4. The rest of the apparatus — omitting, of
course, that part required by a second wire — was the
same as that used in the correlation measurements.
The wire was of platinum 0.016 millimeter in diameter
and was about 5 millimeters long for the more recent
set of measurements.
In earlier work, before the importance of the wire-
length correction was recognized, a wrire of about 1
3 Electrically welding the wire to the prongs is generally found to be superior to
soft soldering in the measurement of percentage turbulence because of the necessity
of maintaining the calibration of the wire over long periods of time. This require¬
ment was not so stringent in the correlation work since there the properties of the
wire and its junctions needed to remain constant only during the time of a traverse.
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
119
centimeter length was usually used to gain greater sen¬
sitivity than was afforded by a shorter wire. The most
recent of such measurements taken with a wire length
of 8.4 millimeters, which at the same time apply to the
turbulence produced by the screens listed in table I,
are given in references 9 and 10. For purposes of com¬
parison, these results are given here in table IV and in
figures 8 and 9, along with the more recent results ob-
x/M
Figure 8.— Intensity of turbulence obtained with wires of dilTerent length at several
distances from the screens. Old data — wire length 8.4 mm. New data— wire
length 4.7 mm. (Wire-length correction not applied.) M=mesh of screens.
tained with a wire of length 4.7 millimeters. Both sets
of results are plotted with x[M as abscissa in figure 8,
without being corrected for the effect of wire length, and
in figure 9 with the wire-length correction applied. The
uncorrected values are denoted by the subscript w.
It may be noted in figure 8 that the results obtained
with the 8.4-millimeter wire show a systematic increase
for increasing mesh size for all screens except the 3 %-
and 5-inch mesh. The results for the 4.7-millimeter
.06
.05
.04
.03
1 .02
0/
0 40 80 120 /SO 200 240 280 320 360 400
x/M
Figure 9. — Intensity of turbulence corrected for wire length at several distances
from the screens. Old data— wire length 8.4 mm. New data— wire length 4.7 mm.
A7=rnesh of screens.
wire show much less of this tendency and no attempt
has been made to draw separate curves through the
points. They fall distinctly above the value for the 1-,
}•>-, and ff-inch screens obtained with the longer wire
but are in fair agreement with the long wire results for
the 3%- and 5-inch mesh screens.
Before the results with the shorter wire were available,
the occurrence of the separate curves for the several
38548—38 - 9
1
O/d
doto d
Vew
of a
-f-c* — Z"i
_ 1
M
= %
- /a"
- / '
=
V
A
D>
A
□
o
\
T.
-5*
nermc
7 difft
ision
+
o
xNA
'
u J
% -
screens was believed to be due in part at least to an
effect of wire length in relation to the scale of the tur¬
bulence; but there still remained the possibility of a lack
of similarity in the turbulent flow pattern, caused per¬
haps by some departure from geometrical similarity in
the screens themselves. When the results for the shorter
wires were obtained, it became certain that the effect
of wire length was largely responsible for the systematic
differences. By that time the reason for such an effect
was understood and the method of correction given in
part IV was available. Figure 9 shows the result of
applying the corrections. The systematic differences
have been greatly reduced and the values for the long
and short wires have been brought into agreement.
The magnitude of the correction applied to the indi¬
vidual values may be judged from table IV, where both
the corrected and uncorrected values are given.
The hot-wire measurements at any given point were
always made at a number of wind speeds ranging usually
from 20 to 70 feet per second. Throughout this range
was found to be independent of the speed.
MEASUREMENTS OF THE INTENSITY BY THE THERMAL DIFFUSION
METHOD
Figure 9 also shows good agreement between the cor¬
rected values of the turbulence obtained by the hot¬
wire method and those obtained by the method of
thermal diffusion. The latter is an independent method
of measuring the intensity of the turbulence, the tech¬
nique of which is described in reference 9. The measure¬
ments from which the values given in figure 9 were
calculated are also given in this reference for the screens
listed in table I. The points for the several screens are
not given separate designation since no systematic
differences from screen to screen appeared.
Briefly the method of thermal diffusion consists of
determining the width of the heated wake at a fixed
distance back of a rather long but fine heated wire in
the air stream by traversing the wake with a small ther¬
mocouple. In the measurements of reference 9 the
width of the wake at half the temperature rise at the
center of the wake, obtained from the curve of tempera¬
ture distribution across the wake, was used as a measure
of the width. The apparatus was so arranged that the
angle subtended at the heating wire for different posi¬
tions of the thermocouple was obtained; hence the
results are given in terms of the angle subtended by the
width of the wake at half maximum temperature.
After the angle had been corrected for the spreading
of the wake caused by the thermal conductivity of the
air, it was found that the remaining angle, denoted by
ctturb, was directly proportional to the turbulence in
the stream and independent of the scale. For the
conditions obtaining in the experiment it is possible to
apply the theory of diffusion by continuous movements
given by Taylor in reference 8 to calculate the intensity
120
REPORT NO. 581 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
of the turbulence from atuTb directly.4 The equations
leading to the calculation are given in reference 5 in a
form directly applicable to the results of reference 9.
These original references should be consulted for details;
it suffices to state here that the relation connecting aturb
and the intensity of the turbulence is
ctturb (degrees) = 134.9^
where -yjv2 is the root-mean-square of the cross-stream
component of the fluctuation velocity and U is the
average speed of the stream.
It will be observed that
-yju2
Tr
is obtained by the hot¬
wire method, whereas XL- is obtained from thermal
U
diffusion. The fact that
/=f
XL agrees well with
U u
V v2 •
A-JL m
figure 9 indicates that the turbulence must be closely
isotropic; that is, that the cross-stream fluctuations
are on the average the same as those along the stream.
The agreement of the values obtained by these two
independent methods also furnishes good evidence that
the method of correcting the hot-wire results for wire
length is reliable.
No effect of wind speed on the value of a,UTb coidd be
found throughout the range of speeds investigated,
which ranged from 8 to 55 feet per second. The ther¬
mal diffusion method then offers additional evidence
that the intensity of the turbulence does not vary with
wind speed.
THEORY OF DECAY OF TURBULENCE
The usual concept of turbulence is that small fluid
masses moving with velocities relative to one another
give rise to the observed velocity fluctuations whose
root-mean-square value is used as a measure of the
intensity of the turbulence. The average distance over
which the fluctuations may be regarded as completely
correlated will serve as a measure of the average linear
dimension of the fluid masses. The average velocity of
the masses with respect to the mean velocity may then
be identified 5 with yju2, the intensity as given by the
hot-wire anemometer; and the average linear dimension
may be identified with L, the scale as obtained from
the area under the correlation curves.
4 This calculation is rigorous only when the fluctuation velocity of a particle at the
heating wire and that of the same particle after the interval of time required for the
particle to reach the thermocouple are perfectly correlated. The distance of 2 inches
between the heating wire and the thermocouple, which existed when atu rt was meas¬
ured, was small enough and the time interval consequently short enough to prevent
any detectable departure from perfect correlation for all the screens. In fact, no de¬
parture from perfect correlation could be detected even at (! inches. Unfortunately
reference 8 was not discovered before the publication of reference 9, and as a result this
important calculation was not included.
1 Actually, Vw2 is the root-mean-square of the x component of the velocity fluctua¬
tions. In the equations to follow, the total velocity of the fluid masses should be used;
but since u2=v2=w'* 1, the total velocity will differ from the x component only by a
numerical factor. This factor will be absorbed along with other factors of propor¬
tionality in the constants C\, Ci, C%, etc.
In order to obtain the law of decay of turbuleui
motions, it is necessary to know the equation of motion
of the fluid masses. In the choice of this equation we
are guided by the fact that the solution must yield
results in accordance with experiment, which are that
the rate of decay is a function of ^ and that ~r k
M U
independent of the average speed U.
Let us assume that the force resisting the motion oi
the fluid mass is proportional to the product of density
by cross-sectional area by the square of its speed relative
to the mean flow. If m is the mass of fluid moving with
velocity -\u2, C\ is the resistance coefficient, and t is the
time, the equation of motion is
m^f+C,PLV= 0 (9)
Setting m proportional to pU
d^‘
L
hr
dt
4- Coll2 =0
Integrating
(V
U2) o
k=~C2i
u2
'l dd
0 L
where {yju2)0 is the value of ylu2 at t= 0. Taking the
origin of the turbulence at the screen and x as the dis-
tance downstream from the screen, we may set t=j-\
where U is the average speed of the stream. When this
substitution is made the law of decay becomes
U U __ _ p Cx dx
(yju2)0 yju2 J° L
(10)
This equation satisfies the requirement that
(V“2)o
4
w
u
independent of U if
U
is independent of U. fi’e
may infer that this last condition is true from the
observation that the resistance of any given screen
varies approximately as the square of the wind speed
and hence that the flow in the immediate vicinity of the
screen remains similar at different speeds.
It may be shown that no other resistance law in which
the resistance is expressed as a function of the velocity
yju2 .
will lead to a law of decay giving independent of l
Taylor derives the law of decay expressed by equa¬
tion (10) in a somewhat different way. He assumes
(reference 5) from the phenomena of turbulent flow in
pipes that the average rate of dissipation of energy pu
unit volume is given by the expression
(If
w_c,P(V«2);
L
The dissipative stresses within the medium, which
act in opposition to the motion of elementary turbulent
currents in the manner expressed by equation (9,
arise from the action of viscosity in regions where
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
121
velocity gradients exist. In terms of the velocity
gradients and the viscosity the rate of dissipation may
be expressed by
where n is the coefficient of viscosity and u, v, and w
are the fluctuation velocities in the x, y, and 2 directions,
respectively. For isotropic turbulence Taylor, in
reference 5, has reduced equation (12) to the form
W=7.5n
(13)
Two expressions therefore exist for the mean rate of
dissipation of turbulent energy: Equation (11) in terms
of the fluctuation velocities and the scale, and equation
(13) in terms of the velocity gradients due to the fluctua¬
tions. As has been pointed out in part I, deter¬
mines the shape of the top of the correlation curves
near the value of R— 1, and in principle at least, the
dissipation could be determined from equation (13)
with the aid of the correlation curves. As has been
seen, the correlation curves under the conditions of
the present experiments are too narrow at the top to
permit the accurate determination of the dissipation
in this way.
The turbulent energy content per unit volume of the
fluid is ^ p(u2-\-v2-\-w 2) or since u2=v2=w2, is %pu2. The
rate of change of this energy, or the rate of dissipation
is therefore
W~—~ Tjd(u2)
2P dt 2 pir dx
(14)
where l is the average speed of the stream and x is
distance along the stream. Equating the two expres¬
sions for W given in equations (11) and (14) and sim¬
plifying, we get
Ud^u2) ~ dx
(V^)2 T
which is equivalent to equation (10).
Equation (15) may be put in the form
(15)
Ud{M-rd
(V*)’ ‘
(16)
in which ^ may be replaced by a-f b ^> given in part I.
Substituting and integrating, we get
u_ u _c5
-y/u2 (-y/ u2) 0 6
or changing to log10
J7 _
V^2 (V U2) 0
a
b
logio
(17)
where (Vw2)o is the value of Vw2at-v^=0. The same
result would have been obtained from equation (10)
L x
had the relation between ^ and ^ been substituted
there.
U
in figure 10 —= has been plotted against T log,n
■yju2 ^ h
(1 T “ w^cre a and b have been given the separate
values for the several screens from table Ill. The plot
has been made using only the data for the 4.7-milli¬
meter wire, which is believed to be less subject to error
in the wire-length correction than the data for the
longer wire. The points are seen to lie along straight
lines as well as may be expected from the experimental
precision. The separate curves for each screen are due
to some extent to the systematic differences from screen
to screen in figure 9, not clearly shown by that type of
plot, but are to a greater extent due to the separate
curves used to represent the relation between d, and
±\1 l\j
in figure 7 ; that is, to the different values of a and b.
The evidence afforded by figure 10 that equation (17) is
of the proper form to represent the decay is to show
further that the three experimental facts:
1. independent of U
-ylu2
2. A decay of p- given by figure 9
122
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
L
3. An increase of ^ given by figure
are all consistent with one another. Having given any
two of these conditions, the third must follow.
By least square fitting of the straight lines in figure
U
10 to the data, the constants y-,— c- and CQ of equation
W«7»
(17) have been evaluated and tabulated in table V.
The value of
seen
to vary considerably from
screen to screen, which may be partly due to differences
in the geometrical shapes of the screens but more prob¬
ably to errors involved in the curve fitting. On the
III— THE CRITICAL REYNOLDS NUMBER OF SPHERES
The use of a sphere as an indicator of turbulence in
wind tunnels was originally proposed by Prandtl (ref-
erence 11). If one measures the drag force F on a
sphere of diameter D in an air stream of speed U, the
air being of density p, and viscosity p, and plots the
^ F
drag coefficient CD~ - ; - against the Reynolds
7r T~) 2 I TT2
4° 2pU
Number UD—> it will be found that at lowr Reynolds
M
Numbers CD is approximately constant and equal to
about 0.5. At Reynolds Numbers within a range of
values dependent on the turbulence of the air stream CD
160
120
80
40
O
Figure 11. — Theoretical decay eur%-es.
other hand, the coefficient C6, which is closely analogous
to a resistance coefficient of the fluid masses, is nearly
constant.
To return to a more simple type of representation, we
may consider figure 11, where -y= has been plotted
-yjuz
X
against for the several screens, along with the theo¬
retical curves given by equation (17) with the constants
listed in table V. The new data with the shorter wire
from which the constants were evaluated must, of course,
fit the curves. The old data obtained with the longer
wire and the thermal diffusion data are added to show
that they too are not inconsistent with the theory.
decreases rapidly to values in the neighborhood of 0.1.
Prandtl suggested that “observation of such resistance f
curves for spheres gives a means of comparing the air
streams of different laboratories, with respect to their
lesser or greater turbulence.” The decrease occurs at
higher Reynolds Numbers in streams of lower turbu¬
lence.
When a technique had been developed for measuring
the intensity of the speed fluctuations by means of the
hot-wire anemometer and associated equipment, one
of the authors with A. M. Kuethe attempted with some
success to calibrate the sphere as a device for measuring
the intensity of the turbulence (reference 1). To make
the sphere results quantitatively definite, we proposed
| to define the critical Reynolds Number of a sphere as
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
123
the value of the Reynolds Number at which the drag
coefficient of the sphere is 0.3. 6 This proposal has been
rather generally adopted.
As more data were accumulated in wind tunnels with
different honeycomb arrangements (references 2 and 3),
the calibration of the sphere in terms of the intensity
of the turbulence became more and more unsatisfactory.
Millikan and Klein noted that the critical Reynolds
Number depended on the diameter of the sphere. It
became apparent that a more comprehensive study was
needed.
Such a study has been carried out with the coopera¬
tion of the National Advisory Committee for Aero¬
nautics. The general plan and the guiding principles
have already been stated in the Introduction to this
paper. The preceding sections give the methods by
which the turbulence was varied, that is, by the use of
a series of geometrically similar screens of square mesh.
Measurements could be made at various distances from
the screens. Data as to the intensity and scale of the
turbulence at various distances are given in the preced¬
ing sections. The present section describes the
metrically opposite the spindle. In the hemisphere
containing the spindle at an azimuth angle of 157%°
from the impact hole, one or more holes are drilled to
make connection to the annular space between the
tubular spindle and the inner concentric tube. Suita¬
ble connecting nipples are provided at the end of the
tail spindle.
The differential pressure between the impact hole
and the wake can be measured bv mounting the pres¬
sure-sphere rigidly with the tail spindle parallel to the
direction of flow and connecting the nipples to the two
sides of a manometer. The downstream holes were not
located on the spindle or at the junction of sphere and
spindle because we wished to avoid any necessity for
controlling the exact geometrical form of the tail
spindle.
The results are expressed in terms of a pressure
coefficient obtained by dividing the differential pressure
given by the pressure-sphere by the velocity pressure.
For small Reynolds Numbers the pressure coefficient is
approximately 1.4 and for high Reynolds Numbers
about 0.9, the rapid decrease from one value to the
measurements of the critical Reynolds Number of
spheres and its variation with the intensity and scale
of the turbulence.
THE PRESSURE SPHERE
The measurement of the resistance of a sphere in
wind tunnels of varying size is somewhat inconvenient.
The accurate determination of the forces on the sup¬
ports is time-consuming, and the fact that the balances
in normal use are of greatly varying sensitivity in large
and small wind tunnels necessitates the construction
of a special balance of suitable sensitivity. To simplify
the procedure we began in November 1933 the use of a
“pressure-sphere” (references 12 and 13). The pres¬
sure-sphere is shown diagrammatically in figure 12.
It consists of a smooth sphere 7 mounted on a tubular
tail spindle Within the tubular spindle is an inner
concentric tube that connects to an impact hole dia-
6 We did not know at the time that Prandtl had suggested the use of the value 0.36.
7 We have generally used standard bowling balls, diameter 5 inches or 8.55 inches.
The departure of these balls from a spherical form is very small.
other occurring at a Reynolds Number dependent on
the turbulence of the air stream.
Mr. Robert C. Platt, of the Committee’s staff at
Langley Field, kindly undertook the comparison of the
pressure-sphere results with force measurements for
spheres of several sizes. He reported that a value of
the pressure coefficient of 1.22 was approximately
equivalent to a drag coefficient of 0.3. Hence it was
decided to define the critical Reynolds Number of the
pressure sphere as the Reynolds Number at which the
pressure coefficient is 1.22. It is recognized that the
equivalence is not an exact one. The detailed results
obtained by Mr. Platt are described in reference 14.
A great advantage of the pressure sphere is the ease
with which measurements may be made in flight or on a
traveling carriage. Mr. Platt describes measurements
of both types, which yield a value of the critical Reyn¬
olds Number in turbulence-free air of 385,000.
The pressure-sphere method was independently
developed by S. Hoerner (reference 15) at the Deutsche
124
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Versuchsanstalt fur Luftfahrt, with some difference in
detail. The rear holes were located in the tail spindle
at its junction with the sphere. Pressures are referred
to the static pressure of the air stream and hence the
DVL pressure coefficients are equal to 1 minus our pres¬
sure coefficients. Hoerner used as critical Reynolds
Number that for which the pressure at the rear holes
was equal to the static pressure, corresponding to a
pressure coefficient of 1.00 on our convention. Hence
his values of critical Reynolds Number are somewhat
higher than ours.
Hoerner also studied the relation between drag
coefficient and pressure coefficient. His results on a
single sphere in relatively smooth flow indicate that a
pressure coefficient of 1.18 on our convention corres-
sponds to a drag coefficient of 0.3, in fair agreement
with the value of 1.22 obtained from the more extended
measurements of Platt. It must be emphasized, how¬
ever, that the relations between the values of the
critical Reynolds Number as determined by drag
measurements and by pressure measurements with
different locations of the pressure openings are only
approximate, and sufficient work has not been done to
determine the influence of turbulence, sphere diameter,
and exact location of the rear holes.
MEASUREMENTS WITH SPHERES
Some preliminary studies were made of the repro¬
ducibility of the results obtained with several supposedly
identical pressure spheres. Three commercial 5-inch
bowling balls were used to determine the critical
Reynolds Number corresponding to the turbulence in
the 3-foot wind tunnel of the National Bureau of
Standards. The values obtained were 273,000, 276,000,
and 272,000, which agree very well.
The extended series of measurements in the 4}2-foot
tunnel behind the several screens were made with two
spheres, one 5 inches and the other 8.55 inches in
diameter. The working distances could not exceed
about 15 feet because of the iimited length of the working
section. In order to avoid large variations in mean
speed, the closest distance had to be 15-mesh lengths or
greater. Since the spheres are of finite size, extending
over a distance of many mesh lengths for the smaller
screens, the closest distance was further limited to
avoid large changes of turbulence over the sphere. In
no case was the closest distance less than 1 foot. The
actual working distances, selected somewhat arbitrarily,
were 1, 3, and 6 feet for the }{- and Jo-inch screens; 3, 6,
and 9 feet for the 1-inch screen; 4, 7, and 10 feet for the
3^ -inch screen; 6 feet 5 inches and 11 feet 2 inches for
the 5-inch screen.
The data obtained for the l-incli screen are plotted in
figure 13 for the 5-inch sphere and in figure 14 for the
8.55-incli sphere. The values of the critical Reynolds
Number corresponding to the several distances were
read from these and similar curves, the critical Reynolds
Number being defined as previously explained as the
Reynolds Number for which the pressure coefficient
is 1.22. The results are given in table VI.
It will be noted that the curves of figures 13 and U
show abrupt changes of slope at pressure coefficients ol
1.1 to 1.15. After some investigation it was discovered
that the use of four symmetrically located rear holes
instead of a single hole gave curves without breaks, and
hence that the breaks were probably due to local asym¬
metry in the flow about the sphere. Figure 15 shows
curves obtained under the same conditions as the
curves in figure 14 except that a sphere with four rear
holes was used. The values of the critical Reynolds
Numbers are unchanged arid the breaks are absent.
In order to obtain some idea of the effect of the smal
departures from a uniform speed distribution, traverses
were made with the sphere behind the 5-inch screen
that showed the greatest departures. At a distanced
6.4 feet from the screen, the critical Reynolds Number
was 107,000 and 109,000 in two runs at the center;
107,000, 2 inches below the center; 108,000, 4 inches
below the center; and 109,000, 2 inches above the
center. At a distance of 11.2 feet, values of 145,000
and 148,000 were obtained at two positions.
Table VI gives a summary of the pertinent data on
. -ylu2
the critical Revnolds Number. The values of V are
J U
taken from the least-square lines of figure 10, and the
values of L from the least-square lines of figure 1.
Figures 16 and 17 show the relation between critical
-r 'xl V?
Reynolds Number and -^j-for the several screens as ob¬
tained with the 5 and 8.55 inch spheres, respectively.
The points obtained at a distance of 1 foot (encircled in
plotting) are not in good agreement with the other ob¬
servations and the curves have not been extended
through them. Evidently 1 foot is too close a working
distance for spheres of this size. The observations
show a systematic variation from screen to screen and
a systematic variation with the diameter of the sphere
The larger the screen mesh, the greater the intensity re¬
quired to give a specified critical Reynolds Number.
The larger the diameter, the smaller the intensity
required.
G. I. Taylor suggested in correspondence that the
critical Reynolds Number should be a function of the
quantity
where L is the scale of the turbu¬
lence. The data plotted in terms of this quantity are
shown in figure 18. Except for the measurements
made at a distance of 1 foot, the observations for both
spheres and all screens lie remarkably well on a single
curve, certainly within the observational errors.
The details of the reasoning that led Taylor to this
suggestion have been published in reference 16. It may
be stated in general terms that the foregoing combina¬
tion of intensity and scale of turbulence occurs in the
expression for the root-mean-square pressure gradient
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
125
.8 1.2 1.6 20 2.4 2.8 3.2 3.6
Rx/O'5
Figure 13. — Pressure coefficients for 5-inch sphere behind 1-inch screen.
Figi re 14. — Pressure coefficients for 8.55-inch sphere behind 1-inch screen.
Figure 15.— Pressure coefficients for 8.55-inch sphere with four rear holes behind
1-inch screen.
Figure 16.— Critical Reynolds Number for 5-inch sphere behind all screens.
Figure 17.— Critical Reynolds Number for 8.55-inch sphere behind all screens.
1/5
126
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
in the turbulent flow, and that the effect of turbulence
is assumed to be that of the pressure gradient on tran¬
sition.
The wind-tunnel equipment available at the National
Bureau of Standards unfortunately does not permit the
extension of the curve in figure 18 to a critical Reynolds
Number exceeding 270,000. In most of the more re¬
cently constructed wind tunnels, values exceeding this
value are found. In the large tunnels, the large scale
of the turbulence contributes to the high value but, in
addition, the intensity is of the order of 0.7 percent or
less. The accurate measurement of these small fluctu¬
ations is an experimental problem of very considerable
difficulty.
DETERMINATION OF AVERAGE VELOCITY PRESSURE
In the production of artificial turbulence in wind
tunnels for the purpose of studying the aerodynamic
effects of turbulence, it is desired to vary the magni¬
tude of the rapid fluctuations without introducing de¬
partures from a uniform distribution in space. Ower
and Warden (reference 17) concluded that wire or cord
networks were unsuitable because of the introduction
of variations in the mean speed produced by the
“shadows” of the wires. This general conclusion is
somewhat tempered in their detailed discussion by the
recognition that the uniformity will depend on the dis¬
tance from the network at which observations are made
and that the uniformity may be satisfactory at dis¬
tances of the order of 144 wire diameters or 24 mesh
lengths. In view of this criticism of networks as
sources of turbulence it seems desirable to review the
studies that were made behind the screens used in the
present series of measurements to determine the degree
of uniformity of the mean speed and the average value
of the velocity pressure for computing the pressure
coefficients of the spheres.
A preliminary series of traverses was made for the
purpose of determining the distance at which the pat¬
tern of the screen disappeared. For the IF, and
1 -inch-mesh screens, a simple impact tube with outside
diameter of )8 inch and inside diameter of }{6 inch was
used, the static side of the manometer being connected
to the wall plate used as a source of reference pressure
in the operation of the tunnel. For the larger screens,
a standard pitot-static tube was used. Observations
were taken at about 24 points along a line parallel to
the horizontal wires of the screen and in a horizontal
plane passing midway between two wires of the screen.
The spacing was inch, inch, / inch, % inch, and 1
inch for the IF, Vr, 1-, 3 /-, and 5-inch-mesh screens,
respectively. Traverses were made at several distances
from about 4 to 20 mesh lengths from the screen. For
distances less than 12-mesh lengths, the pressure varied
regularly with maxima and minima corresponding to
the spacing of the wires of the screen. The curves
resemble those shown in reference 17 and are therefore
not reproduced in this paper. At distances greater
than 12-mesh lengths, there was no regular pattern.
In order to give some idea of the magnitude of the
variation, the maximum and mean deviations of the
single observations from their arithmetic mean have
been computed and are tabulated in table VII. Both
quantities are very large close to the screen but rapidly
decrease. For distances greater than 12-mesh lengths
the gain in uniformity is comparatively small. Hence
it was concluded that observations should not in am
case be made at distances closer than 12-mesh lengths
and, as a precautionary measure, the closest distance
used was actually 15-mesh lengths. From table IV.
it is seen that the maximum value of
■yju2
~u
is accordingly
limited to about 0.05.
At the distances for which sphere data had been or
were to be obtained, a more extended traverse was
made with a standard pitot-static tube. Observations
were taken at 12 equidistant points along circles of
radii 2, 5, 8, 12, and 18 inches from the tunnel axis, in
some cases for three speeds. The maximum and mean
deviations of the single observations from their arith¬
metic mean are also tabulated in table VII for these
traverses.
It will be observed that the mean deviations approach
different values for the different screens as the distance
from the screen is increased: 2.2 percent for the 5-inch
screen, about 2.0 percent for the 314-inch screen, about
0.5 percent for the 1-inch screen, about 1.0 percent for
the 14-inch screen, and about 1.0 percent for the 14-inch
screen. It is probable that these differences reflect
corresponding differences in the geometrical accuracy of
the spacing of the wires of the screen. The uniformity
obtained with the 1-, and }4-inch screens is com¬
parable with that obtained in the free stream, the mean
deviation of the pressure from the average being 1.0
percent or less, corresponding to 0.5 percent or less in
the speed.
The measurements described in this paper extended
over a considerable period of time and it was not prac¬
ticable to install a screen and complete all measure¬
ments before removing the screen, because of the
necessity of making other tests. The procedure in
most of the sphere tests was to determine the ratio of
the velocity pressure at the axis of the tunnel to the
reference wall plate pressure as a function of the speed:
then at one value of the reference pressure to determine
the speeds at six points on a circle of 2-inch radius. A
faired curve through the points observed in the first
run was adjusted as indicated by the ratio of the mean
of the six values on the 2-inch circle and the value at
the center to the value at the center. For all screens
except the 314-inch screen, the value adopted did not
differ from that given in table VI by as much as the
mean deviation given in that table. For one installa-
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
127
tion of the 3%-inch screen, the difference somewhat
exceeded the mean deviation.
From a study of the results given later, an error of
1 percent in the determination of the mean velocity
pressure produces an average change of 4,500 ±500 in
the value of the critical Reynolds Number. It is
believed that the error in the values used did not in
any case exceed the mean deviation given in table VII
and was probably less than half that value, which rep¬
resents the mean deviation over an area much larger
than the sphere. The effect of the small departures
from a constant speed (as contrasted with an error in
the average speed) on the value of the critical Reynolds
Number is not known but is probably small for de¬
partures of 1 percent or less, as indicated by sphere
traverses behind the 5-inch screen previously described.
DISCUSSION
The relationship exhibited in figure 18 shows that a
given small percentage change in the intensity of the
turbulence produces approximately the same effect as
a change of five times as much in the scale of the tur¬
bulence. Since the diameter of the sphere enters into
the ordinate, the critical Reynolds Number depends on
the diameter, but here also it requires a percentage
change in diameter approximately five times as great
as in the intensity of the turbulence to produce the
same effect.
It is of some interest to inquire whether the ratio
of the values of the critical Reynolds Number for two
air streams depends on the diameter of the sphere used.
The ratio will be independent of diameter if and only
if the curve of figure 18 is of the form
=CR
n
crtt
It may be seen by plotting on logarithmic paper that
the observations do not fit such a curve except over
short distances. Hence if the diameter of the sphere
is varied through a sufficiently wide range, the ratio
of two values as well as the absolute values of the
critical Reynolds Number of the sphere for two air
streams will depend on the diameter.
The use of spheres of different diameters in the same
air stream does not give a separation of the effects of
scale and intensity, since each observation when^ re¬
duced gives only the value of (jp^5. If 3^- is
independently measured, it is theoretically possible to
determine L but the precision is very poor because of
the small slope of the curve of figure 18 and the presence
of the fifth root.
In the presentation of the experimental data and the
discussion up to this point, we have regarded the sphere
as a turbulence-measuring device that was to be cali¬
brated in terms of the intensity and scale of the turbu¬
lence. It is also possible to consider the sphere as a
typical object of aerodynamic study and the data as the
38548 — 38 - 10
aerodynamic characteristics of the sphere as a function
of turbulence. These data may then give some clue
as to the effect of turbulence on other bodies in which
the phenomenon of separation is involved.
The first conclusion that mav be drawn by inference
is that some linear dimension corresponding to the di¬
ameter of the sphere enters into the turbulence variable.
In the case of an airfoil, the ratio of the chord of the
airfoil to the scale of the turbulence would be of im¬
portance. If, for example, we consider tests on two
similar airfoils of different size in the same air stream
and at the same Reynolds Number, the maximum lift
coefficient may be expected to differ because of the
influence of the scale of the turbulence. This result
would be analogous to the different drag or pressure
coefficients observed at the same Reynolds Number
for spheres of different sizes in the same air stream.
Because of the fifth root, and the limits on the possible
size variation in a given wind tunnel, the effect will be
small and perhaps escape detection. But if a sufficient
range of variation is made, the effect will be found.
A second inference is that the effect of turbulence on
some other body will not necessarily be the same as that
on the sphere. The shape of the curve of figure 18 is
undoubtedly related to the pressure distribution char¬
acteristics of the sphere and the resulting boundary
layer thickness. The pressure distribution over an
airfoil will be quantitatively different and the relation
between turbulence and the Reynolds Number for
transition will be different. Hence if the sphere curves
for two air streams are considered to differ only by a
shift along the Reynolds Number axis, that is, by a
turbulence factor formed from the ratio of the two
Reynolds Numbers, and if by analogy curves of maxi¬
mum lift coefficient in these same two air streams are
considered to differ only by a similar turbulence factor,
the factors cannot be considered the same for spheres
and airfoils or even for two different airfoils. Here
again the effects may be small and not readily detected.
The concept of turbulence factor as previously defined
has been found very useful. Because of the small effect
of compared with
L U
the factor has so far proved
to be a sufficiently good approximation in engineering
practice although, as we have shown here, it is only an
approximation.
IV— THE EFFECT OF WIRE LENGTH IN MEASURE¬
MENTS OF INTENSITY AND SCALE OF TURBULENCE
BY THE HOT-WIRE METHOD
In the measurements of intensity and scale of turbu¬
lence described in parts I and II, hot wires approxi¬
mately 5 millimeters long were used, the length being
sufficiently great so that air velocity fluctuations on
one part of the wire are not completely correlated with
those on another part. As will be shown, this lack of
correlation causes the root-mean-square voltage fluc¬
tuation across the wire to be reduced by an amount
128
REPORT NO 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
that depends upon the rate of falling off of correlation
along the wire. This reduction in root-mean-square
voltage fluctuation must be taken into account in all
measurements of fluctuating velocities by hot-wire
anemometers, including its effect on measurements of
the intensity of the turbulence and its effect on meas¬
urements of the scale of turbulence.
THE EFFECT OF WIRE LENGTH ON INTENSITY MEASUREMENTS
Suppose a hot wire of length l carrying a constant
current to be placed in a turbulent air stream per¬
pendicular to the direction of flow', as in the experi¬
mental arrangement for measurements of intensity of
turbulence. If the fluctuating potential drop across
the wire is fed into an amplifier compensated for the
thermal lag of the wire, the output voltage, denoted by
e , will be directly proportional to the fluctuations of air
speed on the hot wire.8
For the case of complete correlation of velocity
fluctuations at all points of the wire, the fluctuating
output voltage will be given by
ei—Kul
where u is the fluctuating air velocity, l the length of
the wire, and K a constant of proportionality, depending
X
U 1
ur
l
Us
Un
y
Figure 19. — Schematic diagram illustrating nonuniform conditions along the wire
as used for measurement of intensity of turbulence.
on the dimensions of the hot wire, its resistivity and
temperature coefficient of resistivity, the current
through the wire, the mean speed of the air flow, and
the amplification.
The output meter on the amplifier (a thermal type
milliammeter) gives indications proportional to the
mean square of the output voltage, given by
7?=K2l2u2 (18)
pletely correlated. Let us assume the wire to be
divided into n equal segments, each of length A z, and
let the velocity fluctuation of the air passing over airy
segment be denoted by Ui. (See fig. 19.) For this
case the output voltage from the amplifier will be given
bv
n
e = Ky^;UjAz
i= 1
and its mean squared value by
e2=K2Az2(Z,u1)2 (19)
=K2Az2[u2-\-u22-\-u32Jru42-\- .... -\-un2
+ 2uiU2 + 2u2u3 + 2u3ui + .... +2^n_iU„
-\-2u1u3-\-2u2ui-\- .... -\-2un_2un
+ 2 u4u4-\- .... +2 un_3un
+ 2 UiUn]
Tbe correlation coefficient R between jmy~two velocity
fluctuations, ur and us, is defined as
Jl= urus
'yju^yju2
Since the mean square of the velocity fluctuations along
the wire is constant
u2=u2=u 2
ir, UTUs
u2
Let us assume that the correlation between the
velocity fluctuations at any two segments is a function
only of the distance between the segments; that is
UTUS t-> / f 1 A \
^=f = R({r—s}Az)
u 2
where, as in previous parts of the paper, H followed by
a quantity in parentheses means the value of R at a
distance equal to that quantity. Thus:
UlU2=U2U3— .... =Un_xUn=R(Az) U2
UiU3=u2Ui= .... =un.2un=R(2Az)u2
Now consider the ease where the velocity fluctua¬
tions at various points along the wire are not com-
s This result is true if the velocity fluctuations are small compared with the mean
velocity of flow. (See reference 6.)
UiU4 — u2ub= .... =un_3un=R(3Az)u2
U\Un —R({n—\}Az)u1
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
129
Equation (19) thus becomes:
e2=K2Az2u^n+2(n-l)R(Az) +2(n-2)R(2Az) -\-2(n-3)R(3Az) + .... +2R({n- 1 }As)J
= K2u2^nAz2 + 2n As j/? (Az) Az-\-R (2Az)Az~\-R (3 Az) Az + .... 4-i?({»— 1 }A;?)A<
-2^AzR(Az)Az-\-2AzR(2Az)Az+3AzR(SAz)Az+ _ + (n- \)AzR{{n- 1 } Az)AzU
Now let the number of segments n increase indefi¬
nitely, and the length of each segment As approach
zero, in such a way that the product vAz is always equal
to the length of the wire l. Passing to the limit, we have
^=EV[2/|; R(z)dz-2f‘ zR(z)dz]
=2 K2u2f* ( l—z)R(z)dz (20)
Comparing this expression with equation (18), the
effect of the incomplete correlation of velocity fluctua¬
tions at different points on the wire is to reduce the mean
square fluctuation voltage and thus the meter reading
in the ratio Kx\ given by
A",!= ?=2j; ( l-z)R(z)dz (21)
In the calculations of intensity of turbulence de¬
scribed in part II, the square root of the output meter
reading enters as a multiplying factor. Thus, to obtain
the true value for the intensity of turbulence, the calcu¬
lated values must be multiplied by the factor Kx, given
by equation (21). In order to obtain numerical values
for Ki, R(z) must be known as a function of 2.
THE EFFECT OF WIRE LENGTH ON SCALE MEASUREMENTS
Let us now consider the effect of incomplete correla¬
tion of velocity fluctuations at different points of the
wire on measurements of the correlation of velocity
fluctuations, as described in part I. Suppose two wires
A and B, each of length l and carrying a constant
current, be placed in a turbulent air stream, parallel to
one another, a distance apart y, and in a plane perpen¬
dicular to the direction of flow. (See fig. 20.)
Let us assume each wire to he divided into n seg¬
ments, each of length Az, and let the velocity fluctua¬
tion on any segment of A be denoted by uu and of B by
Vt. As in the previous discussion, the fluctuating output
voltage across each wire will be given by:
n
eA =KY.UiAz
i= 1
n
eB=KY4viAz
=i
The correlation between the voltage fluctuations eA
and cb will obviously be a function of y. Let us then
define a correlation coefficient R'(y), representing the
correlation between the voltage fluctuations of wires
A and B, placed a distance y apart. Thus, by defini¬
tion, R' (y) is given by
R'(y)
€a(B
Making use of the foregoing equations and of the
fact that the mean square of the velocity fluctuations is
the same at the two wires, we have:
R' (: y ) =
K2Az2{Au,)(^vi)_
‘(Aw,-)2
(22)
r - y - H
Figure 20. -Schematic diagram illustrating nonuniform conditions along two wires
as used for measurement of scale of turbulence.
R' (y) may be obtained experimentally as described in
part I. Now
(2Uj) (2vt) Az2=Az2[u1v1-j-n^v2-hu3v3-j- ....
+ U\V2- f-^2»3+ • • • . -\-Un-£n
+uivl-\-uzV2+ .... +WA-1
+ tt|P3+ • • • • +Un-&n
+ «8»1 + .... +V»-2
+ UlVn
+ Unv i]
Now let us assume that the correlation of the velocity
fluctuations at any segment of A with that at any
130
REPORT NO. 581 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
segment ol B is a function only of the distance between the segments. That is,
Thus
'UTVS
-^=R{^{r-s)2Az2+if)
Uivl=u2v2=uzv3= .... ~unvn=R(y)u2
UxV2 = U2Vz = UzVi— .... =un_lvn
=u2vx=uzv2=uiv 3= .... =unvn-i=R( v (Az)2+y2)u2
UlVi = U2Vi = U3Vs= .... —U„ _ 2t*n
=uavl=uiv2=usv3— .... = w A - 2= Jt(\ (2W+y2W
UiVn=uni\=R ( v (« — 1)-A22T?/)w2
(VII(5^)A22=Vi-t»7f(y) + 2(«-l)B(%Ui)^2) + 2(H-2)/?(VC2T^V) + 2(n-3)K(V(3iip+F)
. . . .+2i?(-v (n-D^+a/2)]
nAz2R(y)-{-2nAz\R(-yi’Az2->ry2)Az-\-R(-\ (2Az)2-{-y2)Az-\-R(^ (3Az)2-\-y2)Az-\- ....
— u‘
K(\ (n-iyAz2+y2)A^-2\AzR(s(Az)2+y2)Az + 2A2fi(V(2Ag)2+y2) Az+3AzR{ v (3Az)2+?/)A2+
. . . . — 1)A zR { \ (u — 1 ) ~Az2~\~y~) Az
,1
J
Now let the number of segments of each wire n in¬
crease indefinitely and the length of each segment As
approach zero in such a way that the product nAz is
always equal to the length of each wire, I. Passing to
the limit, we have:
(AUi) (AVi)Az-
— 2 U*
(l~z)R(^*+y2)dz
From equations (19) and (20)
T^pA22=2p f (l—z)R(z)dz
Jo
Thus equation (22) becomes
\\l-z)R^¥T7)dz
tv
( l-z)R(z)dz
Jo
(23)
The scale of the turbulence L has been defined as the
integral
L = f R(y)dy (24)
Let us denote by L' the following integral:
L' =
L ' may be determined experimentally as described in
Part I, and L may be found by dividing U by a factor
K2, defined as
-JL (25)
~L
If R(y) is a known function of y, the integrations
expressed in equations (23) and (24) may be per¬
formed, and numerical values of K2 computed.
CALCULATION OF FACTORS FOR APPLICATION TO EXPERIMENTAL
RESULTS
It may be seen from equation (23) that the shorter
the wires used and the more slowly R(z) varies with z,
the more nearly will the right-hand member of this
equation approach U(y). Thus curves of R'(y) ob¬
tained under conditions where L is much larger than I,
resulting either from large scale of the turbulence or the
use of short wires, should indicate the character of the
function R(y).
In figure 21 are shown observed values of R'(y)
representing the average of eight traverses at 200
inches behind the 5-inch-mesh screen where the fore¬
going conditions are most nearly fulfilled. These
points are seen to lie closely to the curve, which is an
exponential curve represented by the equation
R'(y)=e
where L' is the uncorrected scale of the turbulence,
Since the correction is small, let us assume that Rim)
is given by
*(!/)=«"r (26)
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
131
and determine what form will be taken by R'(y) and
what values will be obtained for K{ and K2.
20
40 60
y, mm
Figure 21.— Observed correlation coefficient as a function of y. Points, average of 8
V
traverses at 200 inches behind 5-inch screen; curve, plot of R'=e L'
Equation (23) becomes
-v'zHt2
R'(y)> =i
1
(l—z)e l yz
(27)
The factor Ku given by equation (21) becomes
l
AY
(28)
and K2, given by equation (25) becomes
R’ (y)dy (29)
It is convenient to write these equations in non-
dimensional form, changing to the new variables
y
i
r~V *~VC~L
In this notation equation (28) becomes
1 c
Ki =
Jafo i+o)
V Jo
Equation (27) becomes
(30)
R'(r)
C\ . -cVrs+>'s ,
(1— s)e ds
.Jo _
ri -cs
(1 — s)e ds
Jo
n , -c v’r2+s! ,
: 2 AY 1(1— s)e ds
(31)
/ 2 f (i l—s)e Ldz
n • (r) = 2 K,2 )o ( 1 ■ - «)[/«» +/' (0) P +/" (0)|| ■ +f (0) |v + + - }■
Equation (31) is not directly integrable but may be
evaluated for large values of r by expansion in a power
series in s 2 and integrating term by term.
Let
f(s2)=e-c^^
Expanding / in powers of s2, equation (31) becomes
•Ids
=/+2[/(0) -t-tf(o) + T/" (0) +Zg.r (0)
Evaluating the terms in this series
/( 0)=e-(T
/'(0) = --| 7
c( 1 -1 -cr)e
....1
, — CT
f"( 0) =
4 r3
c(3+3cr+ c2r2) e
r d'J - - 8rt
Equation (31) then becomes
L'(r) — K2e
2 y,-CT
, _ c _ , c(l+cr)
12 r 120 r3
/. , , c2r2\
cl l+cr+-g- )
~ 448 r5^
+
(32)
132
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The first four terms of this series will give values of
R' (r) with sufficient accuracy for r/> 1. For smaller
values of r, a series containing positive powers of r must
be obtained.
Rewriting equation (31)
R' (r)— 2 Ki2
_Jo Jo
The second integral can be evaluated directly
j s e~c^Ti+s*(L$=^e~ cr (1 -f-cr) — g-cVc-t-i(i_^c^. r2+l) J
The first integral may be evaluated by expanding the
integrand in a series of powers of c \V2+$2.
f ' e-V3+5(fo= f Ti -c(rJ+s2)‘'2+^(C+s!)
|(r!+«!)3,2+ _ Ids
observed correlation too large at large values of r by a
factor K\ (see equation 32), and to change the shape of
the curve for small values of r.
In figure 23 are shown some experimental curves of
R'(y) as a function of y/M for different ratios of the
length of the hot wire to the scale of the turbulence,
that may be compared to the curves of figure 22. The
similarity of these two sets of curves can be noted.
Let us now consider the effect of incomplete correla¬
tion of velocity fluctuations along the hot wires on the
value of L' obtained by integration of the experimental
R'(y) curves. Writing equation (29) in terms of r
instead of y
c3
3!'
Let 7„(r) = J (r2+s3)n/2ds. We then have
Figure 22.— Theoretical values of R and of R' as a function of cr or y /. for various
values of c.
7f'(r)=27ir'[^T (1+Cv^+T)_Vl(I+H>
+70(r)-c7,(r) +|)/2(r) -|/s(r)
+f,7((r)+ ■ • • J
(33)
In(r) may be computed from the following recurrence
formula:
r , N >2+l)"/2 , n r T A
4(0 n+1 +n+[4-2(0
where I0{r) = 1
r/N (r2 + 1)1/2 , r2 . t_,l
U(r)=~ — ^-+2 sm i r
In figure 22 is shown a curve of 7?(c=0) and of R' as
a function of cr(=y/L) for various values of c. It is
seen that the effect of the incomplete correlation of
velocitv fluctuations along the wires is to make the
K2=lLj"R'(r)dr
(34)
f.Oi
.8
.6
R'
.4-
.2
w
V\\
\w
\ \
M - V4 " -
= /■<
" = 5“
- A
- +
\i
\ \
Q
V
\
N
' F /
\ r
V
S. " - ^
A
0
.2
.4
.6 .8
y/M
1.0
1.2
I A
Figure 23.— Experimental values of R’(y) for various values of y/M for comparison
with figure 22.
This integral may be evaluated by graphical integra¬
tion of R' ( r ) calculated from equation (32) and (33),
or as follows: Substituting (31) in (34)
K2=2Ki2c J °° -s)e~c^^dsdr
Transforming this surface integral into polar coordi¬
nates, by the transformations
r—p cos 9 s = p sin 9 dsdr=pdpdd
7*jt/2 peace
K. — 2KJc J (1 — p sin 9)e~Cppdpd9
Jo Jo
Integrating with respect to p:
e ccsce . 2 sin de ccsce 2 sin#",,.
2'— + — ? - ?-|<w
R 7t/2/; — CC8C0 / o \
1
k9=
lc-2+cJ(c)
(35)
e~~c — 1 T* c
The integral J (c) cannot be evaluated directly but may
be expanded in an asymptotic series, which will give
J (c) for sufficiently large values of c. For small values
of c, however, it is most easily evaluated by Simpson’s
rule.
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
133
Table VIII gives values of Kx and K2 as a function
of c H) computed from equations (30) and (35).
Curve A of figure 24 shows K2 plotted as a function of
7 7
Curve B shows K2 as a function of an<l is ob-
L
tained from curve A by dividing the abscissa of a given
point on A by the ordinate of that point and then
plotting that ordinate above the new abscissa obtained.
Curve B is used for the correction of the experimental
data on correlation of velocity fluctuations. The
procedure is as follows: The area under the experi¬
mental curves of R' as a function of y is obtained, from
which is found L' . The ratio of l, the length of the
hot wires, to L' is calculated and from curve B, figure
24, the factor K2 is found. L' is then divided by K2 to
obtain L.
Figure 24. — The factor as a function of l/L and IjL’ .
The numerical values obtained for the correction
factors Kx and K2 depend, of course, on the assumption
that R may be represented by equation (26), and thus
can be expected to be accurate only in so far as equation
(26) represents the true variation of correlation with
distance. It is seen from figure 21 that there is a
tendency for R or R' to fall off initially more rapidly
with distance than the exponential relation until the
correlation falls to about 0.3, and then less rapidly,
finally falling to zero instead of approaching zero
asymptotically.
The correction factors thus computed can be con¬
sidered only as approximations, and more accurate
determination of the variation of the correlation co¬
efficient R with distance, especially for small distances,
is needed in order to improve materially their accuracy.
V— VARIATION OF CORRELATION COEFFICIENT WITH
FREQUENCY CHARACTERISTICS OF THE MEASURING
APPARATUS AND WITH AZIMUTH
In the development of the experimental technique
for measuring the scale of the turbulence, certain
unexpected phenomena were encountered. These phe¬
nomena were studied to only a limited extent, usually
only with regard to their bearing on the measurement
of the scale of the turbulence as previously defined.
The incidental and incomplete studies of these phe¬
nomena give additional information as to the charac¬
teristics of turbulent flow and since we cannot at
present pursue these studies further, the information
obtained is placed on record for the benefit of others
who may wish to do so.
EFFECT OF COMPENSATION FOR LAG OF WIRE
In our first measurements of the correlation coeffi¬
cient, no compensation was made for the lag of the
wire. We erroneously assumed that, if the two wires
were identical in every respect including lag, there
would be no effect of the lag on the value of the corre¬
lation coefficient. Fortunately, the actual experiment
was tried and it was discovered that the introduction
of compensation had a very large effect. Two typical
comparisons are shown in figure 25. When no com¬
pensation was used, the observed correlation coefficient
fell off much more slowly with the separation of the
wires. As a result, the observed scale Lf was much
greater. For example, for the 1-inch screen at a dis-
L'
tance of 40 mesh lengths, the observed jj without
compensation was 0.602 as compared with 0.308 ob¬
tained with proper compensation, an error of nearly
100 percent. Similarly for the 3%-incli screen at a dis-
L'
tance of 41 mesh lengths, the observed jj without
compensation was 0.464 as compared with 0.2 36 ob¬
tained with proper compensation. The difference in
a number of comparisons at different distances wTas
always greater than 50 percent.
Since the presence or absence of compensation corre¬
sponds simply to different frequency characteristics of
the measuring apparatus, it was inferred that the results
indicated a variation of the correlation coefficient with
frequency, the disturbances of lower frequency being
correlated over greater distances than the disturbances
of higher frequency.
CROSS-STREAM CORRELATION FOR VARIOUS FREQUENCY BANDS
Measurements were made with a set of electric
filters to study the correlation for various frequency
bands. The compensating circuit was used, so that
the results represent, as closely as can be obtained, the
variation of the correlation with frequency. The
available filters w^ere high- and low-pass filters designed
for connection as band-pass filters. The nominal
frequency bands were 0-250, 250-500, 500-1500, 1500-
3000, and 3000-°° cycles per second. Ideal filters would
(five a uniform transmission within the band and no
transmission outside the band. The actual character¬
istics are shown in figure 26. Although extremely good
for acoustic measurements, the filters are far from ideal
for the present purpose.
134
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 25.— Correlation curves showing effect of compensation. Curves for 1-inch mesh observed at 40 mesh lengths aft. Curves for 314
inch mesh observed at 41-mesh lengths aft.
C
s
is
0
£
Frequency , c.p.s.
Figure 26.— Frequency characteristics of filters.
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
135
Measurements of correlation were made at a distance
of 40 mesh lengths behind the 1-inch screen at speeds of
20 and 40 feet per second for the bands 0-250, 250-500,
500-1500. The intensity in the two higher bands was
so small that satisfactory measurements could not be
made. The results are shown in figure 27. The large
effect of frecpiency is obvious. In the 500-1500 band
negative correlations are observed, indicating that for
frequencies in this band an increase in speed at one
wire tends to be associated with a decrease in speed at
the other. No attempt was made to correct these
observations for the finite length of the wires. Some
idea of the magnitude of the effect can be obtained
from figure 5. The application of the corrections would
not change the general picture.
0 5/0/5 20 25 30 35 40
y , mm
Figure 27. — Correlation curves corresponding to several frequency bands. 1-inch
screen, 40 mesh lengths aft.
A rough analysis of the distribution of the intensity
of the turbulence with frequency was made by means of
the filters for a distance of 26 mesh diameters from the
1-inch screen. The results are shown in table IN. The
analysis is rough because of the variation of the attenu¬
ation of the filters with frequency. Allowance has been
made for the differences in average attenuation. The
change in the distribution with the change in mean
speed is consistent with the assumption that the fluctua¬
tions at a point are the result of a pattern of eddy motion
in space that is carried along with the mean speed of
the stream and changes but little as the mean flow
travels a distance of a few centimeters. One may
consider the eddy system from the point of view of a
stationary observer, in which case it may be described
by giving the statistical distribution of intensity with
frequency. Or one may consider the system from the
point of view of an observer moving with the stream,
in which case the system may be described by giving
the statistical distribution of intensity with wave
length. A wave length X in the second picture corre¬
sponds to a frequency / in the first equal to U/\, where
U is the mean speed. If the statistical distribution of
intensity with wave length in space is independent of
mean speed, the distribution of intensity with frequency
when the pattern is observed at a fixed point is shifted
toward higher frequencies as the mean speed is in¬
creased. The filter bands are so wide that no complete
analysis can be made. It is seen, however, in figure 27,
that for a given frequency band the correlation falls off
more rapidly with distance at 20 feet per second than
at 40 feet per second. The same frequency band cor¬
responds to shorter wave lengths at 20 feet per second
than at 40 feet per second. For example, the 250-500
filter used in a stream of mean speed 20 feet per second
(610 centimeters per second) selects wave lengths of
1.22 to 2.44 centimeters, whereas in a stream of 40 feet
per second (1,220 centimeters per second), the same
filter selects wave lengths from 2.44 to 4.88 centimeters.
When no filter and no compensation are used, the
apparatus weights the various frequencies according
to the law - ,2y2> where / is the frequency and A is
a lag constant of the wire. For this condition the cor¬
relation falls off less rapidly than for the 0-250 filter.
Experiment shows that, if the apparatus does not
weight all frequencies uniformly, the observed correla¬
tion curve varies with the mean speed; but, if the fre¬
quency compensation is correct, the observed correla¬
tion curve is independent of the mean speed. This
experimental result is again consistent with the hypoth¬
esis that a fixed eddy pattern independent of mean
speed is transported past the measuring apparatus at
the mean speed. The frequency pattern then varies
with the speed. If the apparatus responds uniformly
to all frequencies, there will be no effect of mean speed ;
but, if there is frequency distortion, apparent varia¬
tions with mean speed will be introduced.
ALONG-STREAM CORRELATION
In order to avoid troublesome constant errors in the
measurement of the distance between the two wires of
the correlation apparatus, it was decided to allow one
wire to travel behind the other with a clearance of a
few tenths of a millimeter, so that measurements could
be taken on both sides, the zero position being located
by the wake disturbance of the upstream wire. This
procedure introduces an error whose magnitude was
estimated by studying the correlation along the stream
direction. Figure 28 gives a comparison between the
correlation coefficients transverse and parallel to the
stream at 25 K inches behind the 1-inch screen at 40 feet
per second. The correlation falls off more slowly along
the stream. From these data it may be estimated that
the peaks of the correlation curves are somewhat re¬
duced, the maximum being reduced by about 5 percent
1 36
REPORT NO. 581 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
when the clearance is 0.3 millimeter and the scale of
the turbulence is as small as 5 millimeters. The effect
on the determination of the scale of the turbulence is
entirely negligible, but this factor adds to the effects
of finite wire length and the noise level of the amplifier
to make impossible the studies of the curvature near
the peak of the curve, which are desired in connection
with Taylor’s theory.
The effect of frequency characteristics of the measur¬
ing apparatus was also studied for the along-stream
correlation. The results at 25 % inches behind the 1-inch
screen are plotted in figure 29. These curves are very
suggestive. We have already stated that the filters
select a given band of wave lengths, the 250-500 filter
selecting a mean wave length of 1.83 centimeters at
20 feet per second and 3.66 centimeters at 40 feet per
second. These values agree remarkably well with the
‘‘wave lengths” exhibited by the correlation curves
along stream. The high negative correlations indicate
a high degree of “coherence”, the fluctuation at the
Figure 28. — Comparison of transverse and longitudinal correlation. 1 -inch-mesh
screen, 25-14 mesh lengths aft. Wind speed 40 ft. /sec.
upstream wire being repeated a short time later at the
downstream wire. It appears probable that if it were
possible to make the measurements with a very narrow
frequency band, the correlation wnuld vary several
times between + 1 and — 1 as the along-stream separa¬
tion were increased.
Taylor predicted a relation between the transverse
and longitudinal correlation in isotropic turbulence,
namely, that the correlation coefficient R varied with
the azimuth 9 according to the law
1— R=(l— Rt) (sin2 cos2 9)
where Rt is the transverse correlation coefficient.9
The longitudinal correlation RL is then given by the
relation
2(1 — i?z,) = (l — Rr)
The results of figure 28 do not confirm this relation,
since the ratio of 1 —Rr' to 1 — RR at y=2 mm is more
nearly 1.4. For smaller or larger values of y, the ratio
is less. It does not appear that the correction for finite
wire length as computed in part IV would alter this
result by more than 10 percent.
In order to study the matter further, the little rotat¬
ing holder suggested by Taylor (reference 5) was con¬
structed and attention confined to measurements of the
ratio. Some results taken with and without the filters
Figure 29.— Correlation curves observed along stream corresponding to several
frequency bands. 1-inch mesh screen, 2514 inches aft.
Figure 30.— Variation of correlation with azimuth as two wires 5 mm long spaced
9 mm apart are rotated from a position along stream (zero angle) to a position across
stream (90° angle) .
with wires 2 millimeters apart at 25 inches behind
the 1-inch screen are shown in table X. The ratio
varies markedly with frequency and for a given filter
with mean speed, as would he expected from figure 29.
The value with no filter was about 1.4.
A few measurements with a 9-millimeter spacing of
the wires at 38 mesh lengths behind the 3%-inch screen
9 In reference 5, the sin and cos of this equation are interchanged.
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
137
are shown in figure 30. The curves represent the rela¬
tion 1 — 7?' = 0.150 (sin- 0-(- — cos2 d) for the uncompen¬
sated run and 1— #' = 0.365 (sin2 ^+^^8 COs2 0^ortlie
compensated run. Here again for the uncompensated
run 1 — R' changes by a factor greater than the theo¬
retical factor 2 between (9=0 and 0=90° and for the
compensated run, less than 2.
This departure from Taylor’s theory might be con¬
sidered an evidence of departure from isotropy but the
evidence previously presented as to agreement of values
from hot-wire measurements and from measurements
of thermal diffusion indicates that such is not the case.
Another possibility is that some systematic experi¬
mental error has been overlooked or that the theory of
correction for wire length is not based on valid assump¬
tions. The few measurements recorded in this section
show that the correlation curves vary with the frequency
of the fluctuations considered. Hence the effect of
finite wire length is different in different frequency
bands, producing a frequency weighting in the appara¬
tus that has been shown to have considerable effect on
the observed correlation. The effect would be to sup¬
press the higher frequencies and hence to increase the
correlation coefficient at a given separation of the two
wires. The magnitude of the increase would be greatest
where the scale of the turbulence is least. Such an
effect, if of sufficient magnitude, would account for the
L • x •
failure to obtain a single curve of ^ against in figure
7, part I, the curves for small screens being too high. It
is also possible that such an effect accounts for the de¬
parture of
1 -Rt'
1-Rl'
from the theoretical value 2, since
the observed value R/ would be larger than the true
value IiT by a greater amount than RL' is larger than
Rl. The required effects are, however, of such magni¬
tude as to make this explanation seem unreasonable,
since the departure from a uniform frequency weighting
is small. No adequate theory can be developed without
more information as to the variation with frequency.
The experimental problem is one of great difficulty
since, even if filters of requisite selectivity were avail¬
able, the further subdivision of the available energy
into narrow frequency bands would require still further
amplification to make measurements possible.
CONCLUSIONS
The results obtained may be summarized as follows:
1. The scale or “average eddy size” of turbulence
may be obtained from the measurement of correlation
between speed fluctuations. Such measurements may
be made with the same apparatus used to measure the
intensity of the turbulence, modified slightly to accom¬
modate two hot wires.
2. A knowledge of the variation of correlation with
distance across the stream makes possible a correction
of the error introduced in hot-wire results by the lack
of complete correlation over the length of the wire.
Convenient methods for applying these corrections are
presented.
3. Screens are suitable devices for producing turbu¬
lence in wind tunnels. The scale of the turbulence is
controlled by some dimension of the screen. Since
geometrically similar screens were used in the present
study, it has not been determined whether mesh or wire
size is the controlling factor. The scale of the turbu¬
lence produced by a screen increases with distance from
the screen.
4. The intensity of the turbulence decreases with
distance from the screen, the decay being given by a
logarithmic law when the scale of the turbulence in¬
creases linearly.
5. The pressure sphere described herein has been
found a convenient device for measuring the aerody¬
namic effect of turbulence. A pressure coefficient of
1.22 corresponds approximately to a drag coefficient of
0.3. Either coefficient will serve to connect a critical
Reynolds Number with the effect of turbulence.
6. The critical Reynolds Number of spheres depends
on the scale of the turbulence as well as on its intensity.
The combined effects may be expressed by
National Bureau of Standards,
Washington, D. C., August 6, 1986.
REFERENCES
1. Dryden, H. L., and Ivuethe, A. M.: Effect of Turbulence in
Wind Tunnel Measurements. T. It. No. 342, N. A. C. A.,
1930.
2. Dryden, Hugh L.: Reduction of Turbulence in Wind Tunnels.
T. R. No. 392, N. A. C. A., 1931.
3. Millikan, C. B., and Klein, A. L.: The Effect of Turbulence.
Aircraft Eng., August 1933, pp. 169-174.
4. Bacon, D. L., and Reid, E. G.: The Resistance of Spheres
in Wind Tunnels and in Air. T. R. No. 185, N. A. C. A.,
1924.
5. Taylor, G. I.: Statistical Theory of Turbulence. Proc.
Roy. Soc. of London, series A, vol. 151, no. 873, September
2, 1935, pp. 421-478.
6. Dryden, H. L., and Kuethe, A. M.: The Measurement of
Fluctuations of Air Speed by the Hot-Wire Anemometer.
T. R. No. 320, N. A. C. A., 1929.
7. Mock, W. C., Jr., and Dryden, H. L.: Improved Apparatus
for the Measurement of Fluctuations of Air Speed in
Turbulent Flow. T. R. No. 448, N. A. C. A., 1932.
8. Taylor, G. I.: Diffusion by Continuous Movements. Proc.
London Math. Soc., vol. 20, August 1921, pp. 196-211.
9. Schubauer, G. B.: A Turbulence Indicator Utilizing the
Diffusion of Heat. T. R. No. 524, N. A. C. A., 1935.
10. Schubauer, G. B., and Dryden, H. L.: The Effect of Tur¬
bulence on the Drag of Flat Plates. T. It. No. 546,
N. A. C. A., 1935.
11. Prandtl, L.: Der Luftwiderstand von Kugeln. Nachr. d. K.
Ges. d. Wissensch., Gottingen, Math. phys. Kh, 1914,
p. 177.
138
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
12. National Advisory Committee for Aeronautics: Twentieth
Annual Report, 1934, pp. 16 and 23.
13. Dryden, Hugh L.: Frontiers of Aerodynamics. Jour. Wash.
Acad. Sci., vol. 25, March 1935, p. 101.
14. Platt, Robert C.: Turbulence Factors of N. A. C. A. Wind
Tunnels as Determined by Sphere Tests. T. R. No. 558,
N. A. C. A., 1936.
15. Hoerner, S.: Tests of Spheres with Reference to Reynolds
Number, Turbulence, and Surface Roughness. T. M No.
777, N. A. C. A., 1935.
16. Taylor, G. I.: Statistical Theory of Turbulence. Part V.
Proc. Roy. Soc. of London, series A, vol. 156, no. 888,
August 1936, p. 307.
17. Ower, E., and Warden, R.: Note on the Use of Networks to
Introduce Turbulence into a Wind Tunnel. R. & M.
No. 1559, British A. R. C., 1934.
TABLE I.— DIMENSIONS OF SCREENS FOR
PRODUCING TURBULENCE
Nominal mesh
length, inches
Average
measured
mesh
length,
inches
Deviation of in¬
dividual rneshes
from average,
inches
Average
measured
wire
diameter,
inches
Material
Mean
Maxi¬
mum
0. 248
rto. 010
f+0. 026
1 -.023
f +.017
1 -.025
f +.015
l -.015
/ +. 163
\ -.122
/ +.04
\ -.04
) 0. 050
Iron wire.
. .
14 _ _
.515
. 012
} .096
Iron wire.
1 . .
1.007
.005
J
\ . 196
Iron wire.
V/i . .
3.285
. 068
/
1 .626
Wooden cyl¬
inders.
Wooden c y 1 -
inders.
5 . .
5.016
.021
/
} .976
TABLE I L— SCALE OF TURBULENCE
X
M
Distance
from
screen
in mesh
lengths
L'
M
X
M
r
M
Distance
from
screen
in mesh
lengths
X'
M
X
M
K-inch mesh screen
1 2-inch mesh screen
18.5
0. 276
0. 183
27.0
0. 306
0. 237
41.0
“. 405
. 290
27.0
.311
.240
41.0
“. 375
. 269
42.3
. 338
. 266
41.0
“. 365
. 263
42. 3
.355
. 280
41.0
“. 387
.278
56. 7
.395
.315
53.0
.464
.342
56. 7
.366
. 292
84.0
. 566
. 429
79.5
.494
. 406
112.0
.602
.463
79.5
.445
.366
159.0
. 864
. 702
108. 0
.548
. 458
159. 0
.916
.745
108.0
.518
. 434
159. 0
.798
. 649
171. 0
“. 626
. 536
161.0
“. 805
.648
171. 0
a. 609
.521
161.0
“. 782
.631
171. 0
“. 622
.532
161.0
“. 808
.652
171.0
0. 556
.475
161.0
“. 738
.595
171. 0
“. 604
.517
161. 0
“. 752
. 606
172.0
.695
. 601
161.0
“. 770
.621
172.0
.673
.582
21 l. 0
.906
.742
226. 0
.842
. 746
226. 0
. 846
.750
226. 0
.822
.728 )
TABLE II.— SCALE OF TURBULENCE— Continued
X
Af
Distance
from
screen
in mesh
lengths
V
M
X
M
X
M
Distance
from
screen
in mesh
lengths
V
M
X
M
1-inch mesh screen
3'4-inch mesh screen
21.0
0. 293
0. 248
16.5
0 0. 190
0. 175
21.0
.277
.234
16. 5
", 202
. 187
28.0
. 291
. 246
16. 6
. 172
. 156
39. 5
. 394
.345
26.2
0. 220
.205
39.5
.377
.331
26. 2
“.219
.204
40.0
", 305
.261
26.5
.253
.237
40.0
“.314
.269
34.6
.257
.241
40.0
“. 300
.258
34.6
. 259
.243
40. 0
“.312
.268
34.8
“. 211
. 196
] 53. 0
. 413
.363
34.8
“. 212
. 197
53.0
.366
.321
39.7
0. 250
. 234
53.8
0.352
.306
39. 7
“. 228
.212
53.8
“. 368
.319
40.0
“. 235
.220
53.8
“. 344
. 298
40.0
“.230
.215
53.8
0. 335
.292
40.0
“. 235
.220
53.8
0.335
.292
40 0
“.241
.226
53.8
“.316
.274
40.0
“. 258
. 242
53.8
0.312
.271
50. 5
. 266
.249
53.8
“. 323
.280
50.5
. 242
. 226
85.0
.451
.405
50. 8
“. 258
. 242
85.0
.406
.365
50.8
“. 261
.245
113.0
. 520
.468
50.8
“. 248
.233
113.0
.426
.383
61.4
“. 303
.287
113.0
.574
.516
61.4
“. 303
.287
113.0
.480
.433
61.4
“281
.266
113.0
.462
.416
135.5
. 512
.461
135.5
.486
.438
5-inch mesh screen
135.5
.484
.436
164.0
.496
.446
164.0
.470
. 423
17. 1
“ 0. 166
0. 156
164.0
. 505
.454
17. 1
“. 166
. 156
164.3
0.551
.499
17. 1
“. 172
. 162
164.3
0. 480
.435
22.7
“.201
. 190
164.3
o.488
.442
22. 7
“.210
.200
164. 3
“. 504
. 457
22. 7
“. 189
. 180
164.3
0. 527
.478
33.0
“. 202
. 192
164.3
“. 500
.453
33.0
“. 199
. 189
39.9
“. 199
. 189
39.9
“.203
. 193
39.9
“. 220
.209
39.9
“. 201
.191
39.9
“. 230
.220
39.9
“.236
.225
39.9
“. 253
.242
39.9
“. 237
.227
“ Signifies wires of length 4.75 mm. All other values obtained with wires of length
5.0 mm.
Turbulence in free tunnel 15.5 feet from rear of honeycomb: X' =0.303 inch, X = 0.260
inch. No noticeable increase with distance was found, although not thoroughly
investigated.
TABLE III.— EQUATIONS FOR CURVES OF FIGURE 7
a b
li-ineh mesh _ _ _ =0.1559+0.00301 7 ^
T £
14-inch mesh _ _ ^>=0.1753+0.002307
T r
l-inchmesh _ _ _ _ ..—=0.229 1 +0 . 001 493
3'4-inch mesh _ _ _ _ _ W=0' 1471+0 002000 J/
5-inch mesh _ _ _ _ _ _ -^.= 0.1316+0.002016 j{
T j
All data taken together . . . . . . . -^.=0.1467+0.002501 j j
INTENSITY AND SCALE OF WIND-TUNNEL TURBULENCE
139
TABLE IV. — INTENSITY OF TURBULENCE
TABLE IV.— INTENSITY OF TURBULENCE— Continued
New Data
Old Data
X
M
Distance
from screen
in mesh
lengths
h[d‘)w
r
(uncor¬
rected)
V"*
U
(corrected)
M
Distance
from screen
in mesh
lengths
( V u * ) w
U
(uncor¬
rected)
Sf‘
U
(corrected)
H -inch-mesh screen
Length of wire,
4.7 inm
Length of wire, 8.4 mm
16
0. 0350
0. 0550
48
0.0111
0.0187
24
.0262
. 0397
144
. 0080
.0110
39
.0188
. 0270
288
.0052
. 0063
72
.0118
. 0156
100
.0098
.0124
152
.0084
.0101
209
.0078
.0090
284
.0070
.0079
J-2-inch-mesh screen
Length of wire,
4.
7 mm
Length of wire, 8.4 mm
14
0. 0411
0. 0531
24
0. 0189
0. 0276
26
.0246
.0310
72
.0096
.0127
46
.0171
. 0208
144
. 0069
.0084
74
.0120
.0141
110
.0100
.0114
163
. 0080
. 0089
246
.0064
.0069
1-inch-mesh screen
Length of wire, 4.75 mm
Length of wire, 8.4 mm
25.3
0. 0290
0. 0324
36
0.0183
0. 0218
54. 0
.0168
.0185
72
.0122
.0142
85.3
.0117
. 0127
108
.0095
.0109
113.3
.0097
.0104
133.5
. 0086
. 0092
164.5
.0073
.0078
New Data
Old Data
X
(V U‘)w
(V «■
X
(V^'du’
V >'■
M
U
U
M
U
U
Distance
Distance
from screen
in mesh
(uncor¬
rected)
(corrected)
from screen
in mesh
(uncor¬
rected)
(corrected)
lengths
lengths
«•
3H-inch-mesh screen
Length of wire, 4.7 mm
Length of wire, 8.4 mm
15. 5
0. 0434
0. 0457
14.8
0.0423
0. 0464
20. 1
.0341
. 0358
25.9
.0270
. 0293
27. 4
. 0253
.0265
36.9
.0201
.0220
37.8
.0210
.0219
53.8
.0161
.0167
60. 8
.0145
.0150
5-inch-mesh screen
Length of wire, 4.7 mm
Length of wire, 8.4 mm
14.6
0. 0470
0, 0488
15. 4
0. 0384
0. 0414
21.7
. 0336
.0348
26.8
.0254
. 0269
29.0
.0260
.0269
39.4
.0210
.0216
For Che free tunnel, 15.5 feet from the rear of the honeycomb,
0.007 taken
with wire 8.4 mm long. The value corrected for wire length is 0.0085. No noticeable
change through the length of the working section of the tunnel was found, although
not thoroughly investigated.
TABLE V.— CONSTANTS OF EQUATION (17)
Mesh of screen
u
(V“)0
c,
)4-inch _ _ _
0. 57
0. 483
i^-inch _ _ _ _
2.81
.516
1-inch . . .
4. 28
.577
344-inch . - _
2. 6.3
.487
5-inch . _ _ - _ _ _
1. 25
.446
TABLE VI— CRITICAL REYNOLDS NUMBER OF SPHERES
M
Mesh cf
screen, inches
X
M
Distance
in mesh
lengths
100
L
Scale of
turbulence,
inches
5-inch sphere
8.55-inch sphere
U
Intensity of
of turbulence,
percent
Rc
Critical
Reynolds
Number
lOOv'a2 (R>\ It
u \l)
Rc
Critical
Reynolds
Number
100 Vm’ (D\ H
u \l)
5
15.4
4.63
0.813
116,000
6. 66
108,000
7.41
o
26.8
2. 92
.928
151,000
4.09
145, 000
4.55
3. 25
14.8
4. 55
.574
101, 000
7.01
96, 000
7.81
3.25
25.9
2.90
. 646
142, 000
4.37
137, 000
4.86
3. 25
36.9
2. 19
.718
163, 000
3.23
159, 000
3.59
1
36
2. 52
.283
151,000
4.48
134, 000
4.98
1
72
1. 45
.337
189, 000
2. 49
178,000
2. 77
1
108
1.07
390
221,000
1.78
215.000
1.98
. 5
24
3.39
.115
° 129,000
7.21
° 116,000
8.03
. 5
72
1.48
. 171
171,000
2.91
107, 000
3 24
.5
144
.94
.254
216,000
1.71
203, 000
1.90
.25
48
2. 16
.075
» 147,000
5. 00
° 155,000
5. 57
.25
144
1.07
. 148
190, 000
2. 16
184, 000
2.41
.25
288
.76
.256
240, 000
1.38
229, 000
1.53
None
85
.260
268, 000
1. 54
a These values were obtained at a distance of 1 foot from the screen. From figures 16, 17, 18, it is evident that these values are not concordant with the others. See
text for discussion.
140
REPORT NO. 581— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE VII— DISTRIBUTION OF VELOCITY PRESSURE q BEHIND SCREENS
M mesh
of screen,
inches
X/M
Distance
in mesh
lengths
Number of
stations
Distance
between
stations,
inches
Number of
readings
Approxi¬
mate
speed,
ft./sec.
Average
ratio of g
to wall
plate
Maximum
deviation
from
average,
Mean
deviation
from
average,
percent
Regular
pattern
present
pressure
percent
5
4.8
24
1.0
24
65
0. 686
17.7
8.6
Yes
7.2
23
1.0
23
60
.626
9.3
4.2
Yes
9.6
24
1.0
24
60
.622
7.4
3.3
Yes
12. 0
42
1.0
42
60
.611
6.0
2.9
No
14.4
23
1.0
23
/ 60
\ 80
.614
.618
4.6
4.6
2.3
2.3
j No
16.8
25
1.0
2 b
00
.612
4.6
2. 2
No
15.4
60
(“)
120
68
.605
6.0
2.2
No
26.8
60
V)
120
68
.618
4.7
2.2
No
3.25
3.69
19
0.5
19
65
.689
27.0
14.5
Yes
5.54
20
.5
20
60
.648
13.8
6.8
Yes
7. 38
45
.5
45
60
.632
11.2
4.6
Yes
9.23
f 42
.5
42
60
.620
6.5
2.6
} Yes
l 34
.5
34
75
.619
7.0
2.7
11.07
22
.5
22
60
.614
5.8
3. 1
Yes
12. 92
41
.5
41
60
.596
6.0
3. 1
No
| 50
.601
6.2
2.9
]
14. 76
54
(°)
108
\ 65
.600
6. 2
2.3
) No
80
. 600
6.6
2.6
J
1 50
.605
4.7
1.7
i
25. 83
54
(“)
109
\ 65
.606
4.7
1.9
!■ No
l 80
.603
5.1
2. 1
1 50
.618
4. 1
1.4
1
36.9
54
W
108
{ 65
.617
4.6
1. 7
} No
l 80
.615
5.2
1.8
1
1.0
4
23
0.125
23
60
". 607
15.6
8.7
Yes
6
26
. 125
26
60
680
12.7
5.6
Yes
8
30
. 125
30
60
". 651
7.4
3.5
Yes
12
28
. 125
28
60
b. 634
2.4
1.2
No
16
30
. 125
30
60
". 631
2.2
1.3
No
24
29
.125
29
60
b. 627
1.4
1. 1
No
1 72
]
143
35
.622
3.2
.8
36
1 72
} (°)
143
70
.620
2.6
.6
No
( 60
1
120
80
.615
2. 1
.5
[ 35
.636
2.6
.8
)
72
54
(“)
108
j 70
.633
1.6
.4
} No
[ 80
.627
1.3
.4
1
| 35
.646
2.1
.7
]
108
54
(')
108
-J 70
.644
1.3
.4
) No
( 80
.639
1.5
.4
1
0.5
6
23
0. 125
23
50
b. 668
13.8
7.7
Yes
8
23
. 125
23
50
".637
7.5
4. 1
Yes
10
23
. 125
23
50
-". 636
4.9
2. 1
Yes
12
23
.125
23
50
".632
4. 1
1.8
Yes
14
23
. 125
23
50
".631
2.9
1.4
No
16
23
. 125
23
50
".630
2.8
1. 1
No
24
60
(“)
120
70
.652
4.0
1.3
No
72
60
(»)
120
70
.644
2.4
1.0
No
144
60
(“)
120
70
.641
2.8
.9
No
0. 25
4
24
0.063
24
55
".790
66.7
28.1
Yes
6
23
.063
23
55
". 852
26.6
10.9
Yes
8
24
.063
24
55
". 678
19.2
9.7
(0
12
24
.063
24
55
".594
7.9
4. 1
(")
16
24
.063
24
55
". 584
5.1
2.8
(e)
20
23
.063
23
55
". 586
3.0
1.4
No
48
60
C)
120
70
.614
4.8
1.2
No
144
60
(“)
120
70
.607
4.9
1.2
No
288
60
(“)
120
70
.604
3.6
1.0
No
° For these positions traverses were made at a number (usually 12) equidistant points along circles of radii 2, 5, 8, 12, and 18 inches from the tunnel axis. At other posi¬
tions the traverse was made along a line which was parallel to the horizontal wires of the screen and in a horizontal plane passing midway between two wires of the screen.
" These traverses were made with a small impact tube, the reference pressure being the wall plate static pressure. The values are approximately but not accurately
comparable with values of the velocity pressure.
c There was evidence of a regular pattern but the pattern did not correspond to the spacing of the wires of the screens.
TABLE VIII.— FACTORS FOR CORRECTING HOT-WIRE
RESULTS FOR EFFECT OF WIRE LENGTH
l
L
Ki
Ki
0
1.000
1.000
.4
1.067
1. 105
.8
1. 133
1. 182
1.2
1. 198
1.241
1.6
1.263
1.289
2.0
1. 327
1.327
2.4
1.390
1.359
2.8
1.451
1.384
3.2
1.512
1. 406
TABLE IX.— DISTRIBUTION OF INTENSITY WITH
FREQUENCY
[Measurements 26 inches behind 1-inch-mesh screen]
TABLE X.— VARIATION OF WITH FREQUENCY
Measurements 25)4 inches behind 1-inch screen with wires 5 mm long and 2 mm
apart.
Frequency
cycles per
second
20 ft./sec.
40 ft./sec.
No filter
1.41
1.37
0-250
2. 67
4.89
250-500
1.50
2. 50
500-1500
.75
1.40
1500-3000
.83
>3000
.70
Frequency
cycles per
second
20 ft./sec.
40 ft./sec.
0-250
0.80
0. 65
250-500
. 14
. 16
500-1500
.05
.16
>1500
.01
.03
REPORT No. 582
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
By Eugene E. Lundquist and Claude M. Fligg
SUMMARY
A theory oj 'primary jailure oj straight centrally loaded
columns is presented. It is assumed that the column
cross section and the load are constant throughout the
length.
Primary failure is defined as any type oj jailure in
which the cross sections are translated, rotated, or trans¬
lated and rotated but not distorted in their own planes.
In the derivation oj the general equation jor the critical
stress, the cross sections are assumed to rotate about any
axis parallel to the column. When the location oj the
axis oj rotation varies from zero to infinity in every
direction, all combinations oj translation and rotation oj
the column cross section are obtained.
For illustration, the theory is applied to a column oj
I section. The conclusions, however, are generalized to
include any column with a cross section symmetrical
about its principal axes. It is shown that, jor such
columns, the theories jor bending jailure and twisting
failure are special cases oj this general theory and that
primary jailure will occur by bending about the axis oj
minimum moment oj inertia or by twisting about the
centroid, depending upon which gives the lower critical
stress.
When a column is attached to a skin, the great stiffness
oj the skin in its own plane causes the axis oj rotation to
lie in the plane oj the skin. When the column cross
section is symmetrical about its two principal axes, one oj
which is normal to the skin, the axis of rotation ivill be
either at the point where the principal axis crosses the
skin or at infinity in the plane oj the skin , depending upon
which location gives the smaller stress.
It is shown how the effective width oj skin that may be
considered to act with the column and carry the same
stress as the column alters the section properties oj the
column and how the bending stiffness oj the skin resists
twisting oj the column and raises the critical stress.
Finally, the effective moduli that apply when the column
is stressed above the proportional limit are discussed.
An illustrative problem in the first appendix (A) shows
how the theory for primary jailure may be used to con¬
struct the column curve for a skin-stiffener panel.
Appendix B shows how the theory may be applied to
columns oj closed section. For closed sections, however,
the large torsional rigidity precludes anything but bending
failure.
Appendix C contains a derivation oj the theoretical
equation for the effective modulus of elasticity when the
column is stressed above the proportional limit.
INTRODUCTION
In the determination of the compressive strength of
sheet and stiffener combinations as employed in stressed-
skin structures for aircraft, the strength of the stiffener
is a most important factor. When failure occurs by
deflection normal to the skin, the accepted column
curve for the material applies. (See reference 1.)
When failure occurs by deflection of the outstanding
portion of the stiffener in a direction parallel to the
sheet, however, there is a combined action of bending
and twisting in the stiffener that requires for its solution
a more general theory for primary failure in columns
than has been available heretofore.
Primary jailure, as used in this report, is any type
of column failure in which the cross sections are trans¬
lated, rotated, or both translated and rotated but not
distorted in their own planes (fig. 1). In keeping with
this definition of primary failure, any failure in which
the cross sections are distorted in their own planes but
not translated or rotated is designated “secondary”
or “local” failure. (See fig. 2.) Consideration is given
herein only to primary failure.
I i
I i
(a) (b)
Figure 1.— Primary failure.
(a) Translated. (b) Translated and rotated.
Figure 2.— Secondary, or local, failure.
Wagner in reference 2 has presented a theory for
torsion-bending failure of open-section columns formed
from thin metal. A part of this theory is summarized
in reference 3, which also includes the results of tests
made to substantiate the theory. In his theory,
Wagner considers the cross sections to rotate about an
141
142
REPORT NO. 582 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
axis which is parallel to the column and which passes
through the center of twist for the section. (See refer¬
ence 4, p. 194, art. 41, for location of center of twist.)
When the column is attached to the skin of a stressed-
skin structure, the stiffness of the skin in its own plane
and the anchorage of the skin at the sides of the panel
are controlling factors in the location of the axis of
rotation. If the stiffness of the skin in its own plane
is assumed to be infinite, the axis of rotation is forced
to lie in the plane of the skin. Rotation of the cross
sections about any axis not lying in the plane of the
skin would require a movement of the skin in its own
plane. Such a movement is prevented by the stiffness
of the skin in its own plane and the anchorage of the
skin at the sides of the panel. Consequently, for the
solution of the skin-stiffener problem the Wagner
theory must be extended to include rotation of the cross
sections about axes other than the one passing through
the center of twist.
The purpose of this report is to present extensions
of the Wagner theory, as given in reference 2, to include
rotation of the cross sections about any axis parallel
to the column. These extensions together with the
Wagner theory constitute the general theory of primary
failure of straight centrally loaded columns presented
in this report. This theory is applicable to any thin-
wall metal column of uniform section and contains the
Euler theory for bending and the Wagner theory for
twisting as special cases. The application of the general
theory to columns of open section is illustrated by use
of an I section column, both when the column is free
and when it is restrained by the attachment of one
flange to the skin of a stressed-skin structure. The
application of the theory to a design problem involving
an open-section column attached to a skin is given in
appendix A. The application of the theory to columns
of closed section is of less practical importance and is
given in appendix B. Appendix C presents the deriva¬
tion of the theoretical equation for the effective modulus
of elasticity when the column is stressed beyond the
proportional limit.
THE THEORY OF PRIMARY FAILURE
THE WAGNER EQUATION
The critical compressive load for primary failure of
an open-section column that is both straight and cen¬
trally loaded when the axis of rotation passes through
the shear center, in this report called ‘‘center of twist’’,
is given by equation (9) of reference 2, which written
with American notation is
P„„=f(GJ+~E CBT )
If both sides of this equation are divided by the cross-
sectional area A, the following equation for the critical
stress is obtained:
_GJ Cbtt2E
Jcrit ' t I T T 2
V Ip -Go
where
E
is the tension-compression modulus of
elasticity. 1
G— ^
shear modulus of elasticity.
6 2(1+/*)
M,
Poisson’s ratio for the material.
polar moment of inertia of the cross section
about the axis of rotation.
effective length of column.
J,
torsion constant for the section. The
product GJ in torsion problems is
analogous to the product El in bending
problems. (See reference 5.)
Get >
torsion-bending constant, dependent upon
the location of the axis of rotation and
the dimensions of the cross section. A
complete discussion of how to evaluate
C Bt is given in a later section.
In equation (1) the term
is that part of the
-L 7)
critical compressive stress caused by the resistance of
the column to pure twisting.
The term
CBT t2E .
i , u 18
that part of the critical compressive stress caused by
the resistance of the column to bending. In the deriva¬
tion of ecpiation (1) the angular displacement of the
cross section about the axis of rotation was found to
vary as a half sine wave along the length of the column
in the same w'ay that the lateral displacements in an
Euler column vary as a half sine wave along the length.
Therefore the term — is analogous to -r in the Euler
1 v A I
column formula
__ I t r2E
Urn- A L0 2
where / is the moment of inertia about a centroidal
axis.
In order for a column to fail in the manner shown '
in figure 3 (a) the end cross sections must be free to
rotate about the axis of rotation and there must be no
restraint of longitudinal displacements at the ends of
the column. Thus, when primary failure occurs in the
manner shown in figure 3 (a), the twist per unit length
is the same at all stations along the length and the )
column is said to be in a condition of pure twisting.
In a pure twisting failure there are no longitudinal
bending stresses, with the result that the second term
of equation (1) is zero. The critical stress for a pure ;
GJ
twisting failure is therefore given by -y-> which is in
agreement with the value given by equation (4a) of
reference 6. In order that the second term of equation
(1) shall be zero the effective length of the column must ?
be infinite ( L0—co ).
In order for a column to fail in the manner shown «
in figure 3 (b) the end cross sections must be held
(1)
CENTRALLY LOADED COLUMNS
143
A THEORY FOR PRIMARY FAILURE OF STRAIGHT
against rotation about the axis of rotation but there
must be no restraint of longitudinal displacements at
the ends of the column. When primary failure occurs
in the manner shown in figure 3 (b), the twist per unit
length is variable along the length of the column with
rotation about the axis of rotation and when buckling
occurs, there must be complete restraint of longitudinal
displacements at the ends of the column. Because
the end conditions for the type of primary failure shown
in figure 3 (c) correspond to built-in ends in an Euler
Figure 3. — End conditions for different effective lengths, La.
, _ GJ , Cb t v2E
<ri,= /p IP U‘
the result that longitudinal bending stresses are present
m addition to the shearing stresses of twisting. The end
conditions lor this case correspond to pin ends in an
Euler column with the result that L0=L in equation (1).
In order for a column to fail in the manner shown in
iigure 3 (c) the end cross sections must be held against
column, i0=9 f°r this case. Similarly, for any degree
of restraint against longitudinal displacements of the
end cross sections the same effective length applies as
for an Euler column with the same condition of end
restraint.
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
GENERALIZATION OF WAGNER THEORY
In the paragraph immediately following equation
(2b) on page G of reference 2 it is stated, “The longi¬
tudinal stresses aba should not give a resulting bending
moment (since there is no such moment acting on the
member). It may easily be shown that this condition
may be satisfied if and only if the magnitudes ru and rn
refer to the shear center; that is, when the section twists
about the shear axis, also in the case where longitudinal
stresses arise.” These statements are correct when
there is no moment acting on the member. A general
derivation, however, should include a moment acting
on the member.
The Wagner theory is therefore based on the assump¬
tion that only torque moments are acting on the member
at any station x along the column. From this assump¬
tion it follows that at failure all but the end cross sec¬
tions of the column rotate about an axis parallel to
the column and passing through the center of twist of
the section. When it is assumed that both torque
moments and bending moments are acting on the col¬
umn at any station x, the combined effect is such as to
cause the cross sections to rotate about some other axis
parallel to the column. In this case equation (1) will
give the critical stress provided that CBT and Ip, which
depend upon the location of the axis of rotation, are
properly evaluated. The Wagner theory, together
with this extension of it, of which the purpose is to in¬
clude rotation of the cross sections about any axis paral¬
lel to the column, constitutes a more general theory
for primary failure in columns. The development of the
general theory is necessary for calculating the column
strength of stiffeners attached to skin when failure
occurs by deflection of the outstanding portion in a
direction parallel to the skin.
EVALUATION OF Car
The torsion-bending constant CBt is a section proper¬
ty similar to moment of inertia. Like moment of inertia
it is dependent upon the axis about which the section
property is calculated. Wagner has shown that, in its
practical evaluation, CBT niay be divided into a major
and a minor part, the latter of which may be neglected
for most open sections formed of thin metal. In ref¬
erence 3 it is shown that the major part can be expressed
by a simple integral involving certain areas swept by
a radius vector. In the evaluation of CBT for some
stiffener sections used in aircraft structures, however,
the authors of the present report found it expedient
to use the basic considerations of displacement from
which the simple integral involving swept areas was
derived. In this procedure certain concepts, not given
in references 2 and 3, were introduced to clarify the
method of calculating CBT in the general case.
In order to evaluate CBT by the general method, a
portion of the column of length dx is allowed to twist
about the axis of rotation an amount such that one
end cross section is so displaced that it forms an angle
dip with respect to the other end cross section. The
longitudinal displacement of any point on the end cross
section with respect to a reference plane, normal to the
axis of rotation, is proportional to the angle of twist
per unit length hereinafter designated 6. The reference
plane is then located so that the average longitudinal
displacement of the elemental areas dA of the end sec¬
tion from this plane is zero; i. e.,
fDdA fDdA
f dA A
where D is the longitudinal displacement from the ref¬
erence plane of the elemental area dA. Physically the
reference plane establishes the neutral axis of the longi¬
tudinal bending stresses that result when the end cross
section is restrained. The general expression for CBT,
which includes both the major and minor parts previ¬
ously mentioned, is (reference 2, equation (6))
CBT=fuHA (4)
where u is the longitudinal displacement, from the ref¬
erence plane, of the elemental area dA when ^=0=1-
The general method of evaluating CBT described in
the preceding paragraph will now be applied to an I
section column with the axis of rotation located at a
distance r from tlie centroid in any direction. Wagner
and Pretschner (reference 3) have shown how to com¬
pute CBT for an I section when the axis of rotation is
at the center of twist, which is at the centroid for the
1 section. When tlie axis of rotation has some other
location, certain terms must be added to allow for the
shift in the axis of rotation. In the derivation of CBt
for any location of the axis of rotation, it is convenient
to resolve the displacement of the one end cross section
(fig. 4 (a)) into two displacements of translation (1 and
2 of fig. 4 (b)) and one displacement of rotation about
the center of twist (3 of fig. 4 (b)). The longitudinal
displacements of the different parts of the cross section
caused by the three component displacements of the
cross section (fig. 4 (b)) are then added to obtain the
total longitudinal displacement. In the following tabu¬
lations the longitudinal displacements at the center lines
of the web and flanges are given. The algebraic sign
of the displacement is positive when a point on the cross
section moves in the positive direction of x and negative
when it moves in the negative direction of x (figs. 5, 6,
and 7). Also note in the expressions for longitudinal
displacement (LD-1, 2, 3, etc.) that ^
= 0.
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
y
Figure 4.— Displacement of one end cross section with respect to the other when
rotated about the point P, Q.
Displacements for rotation about the center of twist
(fig. 5). — The longitudinal displacement from the
original plane of the end cross section at a distance s
measured from
B toward A is
B toward C,
O toward B,
O toward B',
B' toward C',
B' toward A',
~4
4
o
0
~0~s
4
(LD-l)
Displacements for translation normal to the web
(fig- 6). — The longitudinal displacement from the
Figure 5.— Displacements for rotation
about the center of twist.
Figure 6.— Displacements for translation
normal to the web.
original plane of the end cross section at a distance s
measured from
(LD-2)
Displacements for translation parallel to the web
(fig. 7). — The longitudinal displacements from the
original plane of the end cross section at a distance
s measured from
B
toward A is
-eQs)
B
toward C,
dQs
0
toward B,
0
0
toward B',
0
B
' toward C',
dQs
B
' toward A',
—0Qst
B toward A is
B toward C,
6P\
0 toward B, dPs
O toward B', —dPs
B' toward C',
B' toward A', -6P~
(LD-3)
Figure 7. — Displacements for translation parallel to the web.
146
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Total displacement for rotation about the point P, Q
(figs. 4, 5, 6, and 7). — By addition of the displacements
LD-1, LD-2, LD-3, the total longitudinal displacement
from the original plane of the end cross section at a
distance s measured from
B toward A is —
B toward C , 0^ . s 0 ■ + Q^- + P-|l
O toward B,
O toward B',
B' toward C',
B' toward A',
dPs
—OPs
A
>(LD-4)
[*(|-«)+pl]
«|-c)-P]
Therefore the longitudinal displacement of the end
cross section with respect to the reference plane at a
distance s measured from
B toward A is g— 6
B toward C, <7+0
X4+«)-p3
»(4+«)+p4]
(LD-5)
O toward B, gAOPs
O toward B', g—dPs
B' toward C', g—
B' toward A', 0+0^$^— Q^ — P-^J
Now g, the distance of the reference plane from the
original plane of the end cross section, is determined by
the conditions of equation (3). The term tds may be
substituted for clA because the longitudinal displace¬
ments vary linearly across the thickness tw of the web
and tb of the flanges. Then, if the longitudinal dis¬
placement of the center lines (LD-5) is substituted for
D, equation (3) becomes, after multiplying by A,
0= Jd(*= (^-«[s(4+e)-p!l
thds
+J»{5'+{s(t+<3
+Jof^+H thds
r*h
+ \ 2
J 0
+ P t>""| \hds
g—dPs\ thds
+
from which
/iH<4-e)+p{]h
Sf=0
(5)
From the symmetry of the I section, it might have
been foreseen that <7=0. The formal proof, however,
has been presented to show the method that would be
necessary for the determination of g for other sections.
Wagner has shown that for sections formed of thin
metal it is convenient to divide CBt into a major part
CB and a minor part CT so that
CBt—Cb-\~Ct (6)
In the major part of CBT the longitudinal displacement
is assumed to be uniform across the thickness of the
plate and equal to the value at its center line. For the
major part, dA in equation (4) is therefore written tds.
Hence
CB= fuHds (7)
Substitution of the longitudinal displacements (LD-5)
for u in equation (7), with 0=1 and g— 0, gives for the
I section
Cb= fo2[s(5+C)-PfJUs
+/02[s(!+e)+p!]k*
+
from which
CB=YiiVt"+
%
P2+~Q2
(8)
The minor part of CBT is in the nature of a correction
to the major part to allow for the variation in longitu¬
dinal displacement across the thickness of the web or
flange. When the thickness is constant along the web
or flange, the general expression for the minor part is
(reference 2, equation (6b))
CV=jH«Vs (9)
In order to evaluate f s2ds in this equation, the origin
of s must be at the point on the center line of the web
Axis of rotation
Figure 8.— Method of measuring s for evaluation of equation (9).
or flange, extended if necessary, from which a perpen¬
dicular may be erected to pass through the axis of
rotation. (See fig. 8.) When the thickness varies with
A JHEOIU FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
14;
s, t3 should be placed under the integral sign and equa¬
tion (9) evaluated by either an analytical or graphical
method.
As applied to the I section, equation (9) becomes
r
Cr= 2
from which
CT=
b3U 3
72
W
144
bt„3^ , htn3
—!L pi _L Q2
6 ^ 12 V
(10)
\\ hen the thicknesses tb and th are small as compared
with b and h, respectively, CT will be very small as com¬
pared with Ci j and may be neglected in the computation
of CBT. Substitution in equation (6) of the values of
CB and CT, however, as given by equations (8) and (10)
gives
a
bah2tb , b%3 , h%3
BT 24 ' 72 + 144
h2btb . h3th . bt ^
+
+
fb%
V 6
hth3
' 12
12 ' 6
Q 2
r)pi
or
CbT — (C bt) p =oT 1 \P2 -f- 1 UQ~
<2=0
(11)
where Iv and Iz are the moments of inertia of the cross
section about the principal axes y and z, respectively,
(fig. 4).
CRITICAL STRESS FOR AN I SECTION COLUMN
In order to show the effect of variation in y on the
h
critical stress for the I section in a later part of this
report, it is convenient to write equation (1) in the
following form
f _ 7.y r ^ 1 JS TT2Eth~
Jcril — JXVT T~
(12)
A2
where G^j is the critical compressive stress for a pure
twisting failure of the web alone when the
axis of rotation is at one edge of the web,
that is, the critical compressive stress for a
long outstanding flange simply supported
at its base. (See reference 7, equation
(91).)
EEt,2 the critical compressive stress for the web
12 W alone acting as an Euler column.
r- b2 J)
E = — — constants that vary with the dimensions of
the cross section and the location of the
axis of rotation.
E Ip
12 CBT
'-BT
Ip G1 ,
On the assumption that the torsional stiffness GJ of
the I section is equal to the sum of the torsional stiff¬
nesses of the web and flanges (reference 4, p. 76, art. 20)
the approximate equation for J is
J=-^hth3 + ~btb3
(13)
For any location of the axis of rotation, the value of
Ip for the I section is
I, = y2hnh + \h*btt+\b%+(htk+2bh)(P1+Q‘) (14)
Substitution of the values of J and Ip given by equa¬
tions (13) and (14) in the equation that defines K gives
for the I section
K=-
1 +
Ka’+ffi:
+12
1+2
b U
h th
(15)
For the same reason that CBt has been divided into a
major part CB and a minor part CT (see equation (6)),
Kbt will likewise be divided into a major part KB and a
minor part KT so that
Kb=
Kbt — Kb+Kt (16)
Substitution of the values of CB and CT as given by
equations (8) and (10) for CBT in the equation that
defines KBT, gives for the I section
(17)
60i+12
(CT
+24(
;-0
YQ\%
\tj th
1+
L'a <j
N
Or-
1 _ 1
+ 12
[1,2-
:a
a
to
+
ifO
l _ J
and
l+2(
;{)’( f:)‘+
<d:
1\-T —
1 +
L ~h (J
MV
]+i2[
-4 a
[Q+
m
DISCUSSION
Location of the axis of rotation for a free column.
When the axis of rotation is located at a distance r from
GJ
the centroid of a section, the value of in equation (1)
(18)
is independent of the direction in which r is measured.
C J
Because — is analogous to . in the Euler column
1 v A
formula, it seems reasonable to expect that, as the axis
C
of rotation moves around a circle of radius r, will
* 7)
148
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
vary from a maximum at one of the principal axes to a
minimum at the other principal axis. Because Ip is
independent of the direction in which r is measured, all
the variation in
a
L
BT
will occur in Ci
BT-
It will now be
shown that, for a section symmetrical about each of its
two principal axes, CBt is a maximum or minimum when
the axis of rotation is on the principal axis about which
the moment of inertia is, respectively, maximum or
minimum.
It follows from the symmetry of the expressions for
longitudinal displacement and the limits of integration
The first derivative set equal to zero shows that CBT is
either a maximum or minimum when P = 0°, 90°,
,/2 / <
180°, or 270°. When /3=0° or 180°, — is negative
provided that Iy<GIz, in which case P—0° or 180°
locates the axis of rotation for CBTmax. If then
B—0° or 180° locates the axis of rotation for CBT ,
Similarly, when (3=90° or 270°, it may be concluded
that CBT is a maximum or minimum when the axis of
rotation is on the principal axis about which the moment
of inertia is. respectively, maximum or minimum.
i ■ ' _ _ _ _ _ i _ _ _ _ _ _ _ _ _ — i
0 .5 1.0 f.5 2.0 2.5 3.0
b/h
Figure 9 — Variation of the critical stress with b/h for different locations of the axis of rotation along the principal axes of an I section column with pin ends. Curves
drawn for 6=2 inches, n=U=0.1 inch, length=17.1 inches, and E= 107 pounds per square inch.
that CB T for any section symmetrical about its two prin¬
cipal axes will have the form given by equation (11).
From figure 4
P—r cos p
Q—r sin P
Substitution of these values in equation (11) gives
CBT= (CBT) p=o+ I>2 cos2/3+/j,r2 sin2/3
Q= 0
The first and second derivatives of CBr with respect to $
are, respectively,
dCBT
dp
d2CBT
dp2
=r2(Iv — Iz ) sin 2 p
=2r2(Iy—Iz) cos 2 p
When a free column of symmetrical section with no
bending restraint at its ends (pin ends) is of such pro¬
portions that it develops a primary failure, the axis of
-otation will be either at infinity on one of the principal
uxes or at the center of twist. Figure 9 illustrates this
'act for a family of I section columns by means of
. I
curves for critical stress plotted against the ratio jt
’or different locations of the axis of ratation along each
of the two principal axes. Inspection of figure 9 shows
that, for values of t between 0 and 1.4, the critical
stress is lowest when the axis of rotation is at infinity
along the principal axis parallel to the web. For
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
149
values ol ^ between 1.4 and 2.0, tlie critical stress is
lowest when the axis of rotation is at the center of
For values of t
h
P 0
oo or -r= 00 • ~ = 0
h ’ fi
twist (centroid, for the I section)
greater than 2.0, the critical stress is lowest when the
axis of rotation is at infinity along the principal axis
normal to the web. Had a different set of dimensions
been selected for the family of I section columns in
figure 9, the crossing points A and B would, in general,
have been at different values of Regardless of the
dimensions used, however, the lowest critical stress
would always be given by one of the three locations of
the axis of rotation previously mentioned; i. e., at the
center of twist ^jr=0; ^=0^ or at infinity on either of
the two principal axes =
In figure 9 the critical stresses are, for the most
part, greater than the yield point for the present
engineering materials having the same value of E as
was assumed in the calculation of the curves. ( E=
107 pounds per square inch.) This fact does not detract
from the conclusions drawn from figure 9 because, when
a column is stressed above the proportional limit,
equation (1) may be considered to apply with a re¬
duced modulus of elasticity thereby giving a reduced
critical stress. The reduced modulus is discussed in a
later section of this report.
It will now be proved that for a free column oj I sec¬
tion the axis of rotation will be at infinity along the
principal axis parallel to the web provided that
lh
and
<14.7
8/*A
h<- V h
Because the axis of rotation might be at the center of
twist or at infinity on the principal axis normal to the
web (fig. 9), the two following conditions must hold if
the axis of rotation is to be at infinity on the principal
axis parallel to the web:
( fcrit ) P=0<(/cri<)p=0
(3=00 <?= 0
(fcrit) P=0<! (fcrit) P— co
<2= 00 Q= 0
The first of these conditions will be satisfied if
(fcrit) p= (
Q= c
\1
[
CBt PE
P = 0 —
0=0 1
1
<N
<
1
P= 0
<2=0
or if
h^E
A V
Jv
A
f CBT P ET\
lh vj
L_ _l(2=o
P= 0
Q= 0
\b%
hth-\-2bth
<
24
from which
h
<
3/k
\h
The second condition will be satisfied if
h<h
or if
12
Multiplication of both sides bv ,37- gives
n t & 1
<£>< X
from which
l<-
All th b
■V2 h+3h
This condition holds as long as does not become too
large. If ^ is as large as -y/ — ; then the following condi¬
tion must be satisfied
3/ h / silh
V tb <V 2 u
This latter condition will be fulfilled provided that
A3Vu
|*<14.7
<6
(19)
th
a value of j much larger than will be found in any I
tb
section column of practical dimensions. It may there¬
fore be concluded that primary failure in a free column
of I section will occur by bending with the neutral axis
parallel to the web when
i< lh
(20)
When ^ is greater than
an VI
the critical stress for the
axis of rotation located at the centroid should be
computed and compared with the critical stress for
bending about the axis of minimum moment of
150
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
inertia. The smaller of these two values will be the
stress at which failure occurs.
When the critical stress is to be computed for the
axis of rotation at the centroid, the curves given in
figures 10 and 11 may be used to determine the values
of K and KB in equation (12).
Proof that bending failure is a special case of the
theory presented in this report. — When the axis of
rotation is at infinity, equation (1) reduces to the
Euler column formula. In this case, Ip and CBT are
GJ
both infinite. Hence ~j~= 0 and it remains to be shown
* p
n T
,i , C/bt r
that t a
lp A.
If ,3 = 90° or 270°
Cbt _ ly
I9 ~A
Location of the axis of rotation for a column attached
to a skin. — When a column with pin ends is attached
to the skin of a stressed-skin structure, the stiffness of
the skin in its own plane and the anchorage of the skin
at the sides of the panel are controlling factors in the
location of the axis of rotation. In this discussion it
is assumed that the skin provides only lateral support
at its point of attachment to the column. Rotation
of the cross sections about any axis not lying in the
plane of the skin would therefore require a movement
b/h
Figure 10. — Variation of K with b/h for different values of th/tb when the axis of rotation is at the centroid of an I section column.
Equations (11) and (14) show that as the axis of
rotation approaches infinity along a radius r the terms
involving both P and Q, if P and Q both approach
infinity, become very large in comparison with the
remaining terms. Thus, when P and Q become infinite,
CBT IzP2-\-IyQ2
Ip A(P2+Q 2)
or
CBT __Iz cos2 j8+Z„ sin2 ft
IP A
When y and z are the principal axes of the section,
Iz cos2 |3+/j, sin2 ft is the moment of inertia of the
cross section about a line that passes through the
centroid and the axis of rotation. If /3=0° or 180°
of the skin in its own plane. The stiffness of the skin
in its own plane and the anchorage of the skin at the
sides of the panel tend to prevent such a movement
and the axis of rotation is forced to lie in the plane of
the skin.
For a column the cross section of which is symmetrical
about its two principal axes, one of which is normal to
the skin, the axis of rotation will lie in the plane of the
skin and be either at infinity or at the point where the
principal axis crosses the skin. This statement is
illustrated in figure 12 in which values of fCTit for a
family of I section columns having the same dimen¬
sions as those of figure 9 are plotted against for differ¬
ent locations of the axis of rotation in the plane of the
skin. For simplicity, the skin is assumed to be at the
center of one flange. Inspection of figure 12 show's
Critical stress, /b./sq. in.
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
151
152
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
that, for values of r between 0 and 1.90, the critical
stress is lowest when the axis of rotation is at the web.
For values of jr greater than 1.90, the critical stress is
lowest when the axis of rotation is at infinity in the
plane of the skin.
As in the case of free columns (fig. 9), the location of
the crossing point A in figure 12 will depend upon the
particular dimensions selected for the family of columns.
Regardless of the dimensions used, the lowest critical
stress will always be given by one of the two locations
of the axis of rotation previously mentioned; i. e., in
the plane of the skin either at infinity (j^= 00 ) or at the
point where the principal axis crosses the skin
Again, as in figure 9, the necessary use of a reduced
modulus at stresses above the proportional limit does
not invalidate the conclusions drawn from figure 12.
When a column of I section is attached to a skin, it
is not practicable to give a simple criterion by which
the location of the axis of rotation may be determined.
In view of the fact that the axis of rotation will be either
at infinity in the plane of the skin or at the point where
the principal axis crosses the skin, the critical stress for
these two locations should be computed and the lower
value regarded as the failure stress. When the axis
of rotation is at infinity in the plane of the skin, the
critical stress is given by equation (2) with I=IZ. In
order to facilitate the computation of fcrU when the
axis of rotation is at the point where the principal axis
crosses the skin, figures 13 and 14 have been prepared
from which the values of K and Ks may be obtained
for substitution in equation (12).
Effect of the skin in changing the section properties
of the column. — In the preceding section it was assumed
that the only effect of the skin was to provide lateral
support to the column. Inasmuch as the skin is at¬
tached to the column, however, it will also carry a part
of the compression load on the column and the stress
in the skin at its point of attachment will be the same
as that in the column. Usually the stiffener spacing
in terms of the sheet thickness is such that the skin
will buckle between stiffeners and only a small width
adjacent to each stiffener will be effective. In refer¬
ence 1 it is shown that, when failure occurs by bending
of the stiffener normal to the skin (axis of rotation at
infinity in the plane of the skin), the effective width,
which is dependent upon the column stress, may be
considered to be a part of the column cross section and
is to be included in the computation of section properties.
When the axis of rotation is at the point where the
principal axis crosses the skin, twisting of the stiffener
about this axis will cause a rotation of the skin near the
stiffener. If it is assumed that the effective width of
skin rotates with the stiffener, the following increments
must be added to J, Ip, and CBt as evaluated for the
stiffener when the skin was assumed to provide only
lateral support for the stiffener,
where
(21)
(22)
A B T — AC* t
(23)
ACr-^un*
(24)
In these equations ts is the thickness of the skin and V
is the effective width of skin that acts with the stiffener,
carries the same stress as the stiffener, and is assumed
to be continuous across the stiffener and symmetrically
located with respect to the web of the I section. The
evaluation of U is included in the illustrative problem
of appendix A.
Effect of the skin in providing restraint to twisting of
the column. — When a column is attached to a skin and
the axis of rotation is at a point other than infinity in
the plane of the skin, the rotation of the column cross
section at failure is resisted by bending of the skin pro¬
vided that the skin is supported by adjacent stiffeners
or other structure. A theoretical analysis of this effect
has been reserved for a future report. Only a brief
summary of the subject is given herein.
It may be stated that the effect of the bending stiff¬
ness of the skiu in providing resistance to twisting of
the column attached to the skin is such as to increase
the critical stress given by equation (1) or (12) by an
amount
A/,
KxEt? £02
crit '
then
6(1 — fj.2)dlp 7 r2
/<
GJ
crit
CBT 7 dE,
f 2 I
KxEt?
L 2
(25)
(26)
where d is the stiffener spacing.
Ku a constant depending upon the conditions of
support of the skin at the adjacent stiffener
or other structure.
It will be noted that in equation (26) G and Id have
been substituted for G and E, respectively, in equation
(1). The substitution of E for E at this time was made
to distinguish between the value of E associated with
longitudinal stresses in the stiffener and its effective
width of sheet and the value of E associated with bend¬
ing of the skin between stiffeners. The desirability of
distinguishing between these two values of E will be
explained in a later section of this report in which the
evaluation of E and G is discussed.
If the two ends of the stiffener are held against rota¬
tion about the axis of rotation and the end cross sec-
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
153
Figure 13.— Variation of K with b/h for different values of /*//» when the axis of rotation is at the intersection of the center lines of the web and flange of an I section column
154
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
tions are free to have longitudinal displacements, L0
cannot exceed the length L. For a skin approaching
zero thickness L0 will be ecpial to L. (See fig. 3 (b).)
In general, however, LQ=— where n has integral values
(n= 1, 2, 3, 4, etc.). Thus, when L0= - there will be a
Ti
particular value of n for each skin-stiffener combination
that will cause fcru to be a minimum. A trial calcula¬
tion should be made with n= 1, 2, 3, 4, etc. to deter¬
mine which value of n gives the lowest critical stress.
This critical stress should then be compared with that
for bending in a plane normal to the skin (reference 1)
and the lower of these two stresses regarded as the stress
at failure for the stiffener and its effective width of
skin.
No information has thus far been given regarding the
value of K\ to be used in equation (26). For a stiffener
that has one principal axis normal to the skin and that
is also symmetrical about this principal axis, the value
of Ki may be taken from the curve given in figure 15
provided that the total compression load is equally
divided among several stiffeners of the same dimensions
spaced at equal intervals along the skin. This curve
for Ki was calculated by the energy method (reference
8, p. 584, art. 39) on the following assumptions:
(a) The full width of skin between stiffeners provides
resistance to twisting of the stiffener.
(b) The skin is not under edge compression and is
therefore flat until twisting of the stiffener occurs.
(c) When the stiffener twists, the skin takes the shape
of a circular arc between stiffeners and a sine curve of
half wave length L0 parallel to the stiffeners.
Because the width of the effective skin that acts with
the stiffener is small, any error that may result from
assumption (a) is likely to be small. Of the three
assumptions, (b) is probably the most questionable.
Under load the skin is always subjected to edge com¬
pression and usually buckling of the skin occurs prior
to twisting of the stiffeners. Because L0 is usually
several times the half wave length that forms wdien the
skin alone buckles, any buckling of the skin prior to
twisting of the stiffener tends to increase the effective
thickness of the skin and hence the resistance of the
skin to twisting of the stiffener. The increase in strength
caused by the increase in effective thickness of the skin
tends to offset any reduction in strength caused by the
edge compression. The assumptions made under (c)
are the most reasonable that could be made following
(a) and (b) without greatly complicating the mathemat¬
ics of the problem.
Until the curve for K{ given in figure 15 has been
checked by tests, it should be used only as a guide to
design. As such, it will point the direction toward a
ore efficient proportioning of material between skin
and stiffeners. (See appendix A.) In the skin-stiffener
combinations that are likely to be used in practice
h
d
will usually be greater than 3. For these cases it will be
satisfactory to use Ki = 2, the asymptote for the curve
of figure 15.
0 2 4 6 8 10 co
dor nd
Figure 15— Values of Ki for use in equations (25) and (26).
-[waylay]
Effective modulus of elasticity. — For columns that
fail by bending, the critical stresses depart from the
theoretical values given by the Euler formula at low
values of the slenderness ratio. Consequently, an
empirical straight line or parabolic curve is frequently
drawn on the column chart to give the critical stress
in this range. Likewise, for the general theory there
will be a similar departure of the critical stress from the
theoretical values given in this report and empirical
curves must be found to give the strength for short
lengths.
For a column that fails by bending, the reduced
strength at short lengths is explained by the double¬
modulus theory of column action (reference 8, p. 572,
art. 37, and references 9 and 10). This theory follows
briefly: When a straight, centrally loaded column is
stressed above the proportional limit for the material
and deflected, the stress on the concave side increases
according to the tangent modulus E' for the material
(the slope of the stress-strain curve at the stress con¬
cerned) while the stress on the convex side decreases
according to Young’s modulus E for the material. The
critical stress is then given by the Euler formula when
an effective modulus E is substituted for E. The
effective modulus is dependent upon the shape of the
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
155
column cross section as well as upon E' and E and is
given by the following general expression (references 9
and 10):
K__E'IX + Eh
I '
(27)
where, according to Osgood (reference 9), “if is the
moment of inertia about the axis of average stress
[zero bending stress, see fig. 16] of the part of the cross-
Bertding stresses :
Figure 16.— Stress distribution for double-modulus theory.
sectional area which suffers an increase of stress at the
instant of failure of the column, I2 is the moment of
inertia about the axis of average stress of the part of
the cross-sectional area which suffers a decrease of
stress at the instant of failure of the column, and / is
the moment of inertia of the total cross-sectional area
of the column about the centroidal axis normal to the
plane of bending. The position of the axis of average
stress is defined by the relation E'Si—ES? where S,
and S2 are the statical moments about the axis of
average stress, respectively, of the two parts of the
cross-sectional area just mentioned in connection with
1 1 and J2.”
The effective modulus has been evaluated for a num¬
ber of cross sections. For a rectangular section (refer¬
enced, p. 242, equation (161))
_ _ 4 EE'
E~(-yjE+^E')2
from which
(28)
E 4
E~
($)
<E'
\ E
(29)
For an I section with a web of negligible thickness and
with bending in the plane of the web (reference 9,
equation (4))
E=2 EE/_ (30)
E+E'
from which
In the theory for primary failure as herein presented
there is a double-modulus action, similar to the double¬
modulus action in bending, when the column is stressed
above the proportional limit for the material. In view
of the fact that this double-modulus action is concerned
only with longitudinal bending stresses, an effective
modulus E will be substituted for E in the second term
of equations (1) and (12). It is shown theoretically in
appendix C that this value of El s
^J?CBTl + ECBTi
a
BT
(32)
where CBTl is the value obtained from equation (4)
when the integration is made over the part of the cross
section that suffers an increase of stress at the instant of
failure of the column, CBT2 is the value obtained from
equation (4) when the integration is made over the part
of the cross section that suffers a decrease of stress at
the instant of failure of the column, and CBT is the value
obtained from equation (4) when the integration is
made over the entire cross section as previously out¬
lined. In order to locate the points of average stress
(zero bending stress), which define the limits of integra¬
tion for CBt1 and CBT2, the reference plane must be so
located that
E' fDydA + EfDdA = 0 (33)
where l)\ and D2 are the longitudinal displacements
used in the evaluation of CBTl and CBt2, respectively.
Physically, equation (33) means that the summation of
the forces on the cross section that result from the
longitudinal displacements is zero.
When the column is stressed above the proportional
limit for the material, the shear modulus G, which is
related to E, must be corrected to correspond to the
reduced modulus E for the column. A theoretical
treatment of this problem does not appear to have
been published. Bleich (reference 11) used for the
effective shear modulus
(34)
(35)
It was reasoned that the percentage reduction in G was
not so great as in E. Because r is always equal to or
less than unity, Bleich selected VT G as a convenient
! expression for the effective shear modulus.
where
G — V tG
E
t~~E
150
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
After analyzing the results of some 500 tests on angle
columns where failure occurred by twisting, Ivoll-
brunner (reference 12) concluded that the effective
shear modulus was best given by the equation
q^T+Jsg (36)
As this value of G is based upon test data, it is recom¬
mended that it be used in preference to the value given
by equation (34) to express the reduced shear modulus.
Thus, when the column is stressed above the pro¬
portional limit, the value of G given by equation (36)
should bo substituted for G in the first term of equa¬
tions (1) and (12).
When the axis of rotation is at infinity on either of
the principal axes, equation (32) reduces to equation
(27). It can be shown that, when the axis of rotation
is at the centroid of an I section, the value of E is the
pleted, it appears that the shift of the axis of rotation
in the plane of the skin is small, for columns of prac¬
tical dimension, and that the values of E are near those
given by equations (28) and (30).
In figure 19 it is shown that the values of E as given
by equations (28) and (30) are very nearly the same
as the values for a thin circular ring or a tube. In
view of this fact it appears justifiable for practical
use to assume that E for the I section is the same as
If for the thin-wall tube in bending. Dr. W. R. Osgood
of the National Bureau of Standards suggested that
the column curves constructed by the theory of this
report be made consistent with the curves now used
for tubes, which are determined from column tests,
by evaluating E according to the following procedure:
1. Assume a series of values for the slenderness
f. U
ratio —
P
i.O
.8
.6
E/E
.2
O
Ret
zfar
SC tl
igu/
on
or
Ret
zfar
?cti
igui
ar
I s
ect
iOfly
St
St
on N
A
| \
'sy/y
AO?
Rt
3 etc
'ect
mgu
ion
'/or
/
///
//
&
/
I &
zecl
ion
Li
o i
I ^
zed
bon
i
V/V/Z
////
0.2
".5
//a
v/y/
////
//Ay
Web thickness = 0
Bendino in plane
/
/
Web thickness = O
Bending in piane
i b
w
of
web
/
P
of web
I 1
///
//
0.0
3.0
h
///ft
I/ff'
0.2
3.0
3.0
b
T
sec
tion
th
= tb
-ft
//-
Th
in c
v ret
/ tor
rn
og
I fr
/ 'l
u!
Ji
h\
l
f
E'/E
Figure 17. — Variation of El E with E'/E for
an I section column when the axis of
rotation is at the centroid or at infinity on
the principal axis parallel to the web.
E'/E
Figure 18.— Variation of E/Ev/ith E'/E for
an I section column when the axis of
rotation is at infinity on the principal axis
normal to the web.
E/E
Figure 19. — Variation of E/E with E'/E for
a rectangular section, a thin circular ring,
and an I section in bending.
same as when the axis of rotation is at infinity on the
principal axis parallel to the web. For these two
locations of the axis of rotation the value of E can
conservatively be assumed to be the same as that
given by equation (28) for the bending of a rectangular
cross section. This close agreement is shown in
E
figure 17 where values of -g, are plotted against •
When the axis of rotation is at infinity on the prin¬
cipal axis normal to the web of an I section, the value
of E will in all cases lie between that given by equations
(28) and (30), as shown in figure 18. It will therefore
be conservative to assume that E is given by equation
(30) for this case.
When the axis of rotation is at the point where the
principal axis crosses the skin, the considerations of
the double-modulus action result in a lack of symmetry
for the I section. This lack of symmetry may cause
the critical stress to be a minimum when the axis of
rotation is slightly shifted in the plane of the skin.
Although a study of this condition has not been com-
2. By means of the accepted column curve for tubes
of the material under consideration, determine the
critical stress /cr».
3. Substitute the assumed values of — and the
p
corresponding values of fCTit in the following^equation
to obtain E and plot a curve oijent against E\
CTlt ^2
(37)
4. Correct this value of E for the cross-sectional
shape being used (figs. 17 to 19), if desired.
In the construction of a column curve for a particular
I section, the following procedure should be used:
1 . Select the location of the axis of rotation for which
the column curve is to be drawn.
2. Assume a series of values oijcrit.
3. From the curve of E jtgainst_ jcrU previously
derived, tabulate the values of E and G that correspond
to the assumed values oifcrU.
4. Evaluate J, Iv, and CBt>
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS J 57
5. Substitute J, Ip, CBT, the assumed values of fCTit,
and the corresponding values of E and G in equation
(1) or (12) and solve for the length L0.
6. The column curve is obtained by plotting the
assumed values of/cr^ against the computed lengths L0.
If the column is attached to a skin, the values of
J, lp , and CBT calculated under 4 should be increased by
the amounts A J, Alp, and A CBT, respectively. These
values together with the assumed values of jCTil and the
corresponding values of E and G are then substituted in
equation (26), which is solved for the length L0. A
curve is then drawn by plotting the assumed values of
font against the computed values of L0. This curve
will be found to have a minimum point at some par¬
ticular value of L0. Because where n is an in-
7~i
tegral value (n= 1, 2, 3, 4, etc.), the strength for any
particular length L is obtained by choosing such a value
of n as will cause the critical stress to be a minimum.
(See appendix A.)
CONCLUSIONS
The following conclusions apply when primary col¬
umn failure is defined as any type of failure in which
the cross sections are translated, rotated, or both
translated and rotated but not distorted.
1. When primary failure occurs in a pin-end col¬
umn that is straight and centrally loaded, the general
equation for the critical stress is
r GJ CBT tGE
Jcril T 1 T r 2
lp lp Mjq
In the derivation of this equation it is assumed that
the cross sections rotate about an axis parallel to the
column. The factors Iv and CBT depend upon the loca¬
tion of this axis, which is called the “axis of rotation.”
~QJ
The first term gives the critical stress for a pure
ip
twisting failure about the axis of rotation. The second
term
CBT -n2E
L
T 2
-Go
is in the nature of a correction for the
effect of length caused by longitudinal bending stresses
when the end cross sections are held against rotation.
All possible combinations of translation and rotation
of the column cross section are obtained by letting the
location of the axis of rotation vary from zero to
infinity in every direction.
2. The theory for primary failure shows that, for a
Iree column with a cross section symmetrical about its
two principal axes, the axis of rotation will be at either
of the two following locations depending upon which
location gives the lower stress:
(a) The center of twist, which is at the centroid of
the section.
(b) Infinity on the principal axis about which the
moment of inertia is the smaller.
Location (a) gives the condition for twisting failure;
location (b), the condition for bending failure.
3. For a pin-end free column of I section symmetrical
about its two principal axes the critical stress will be a
minimum when the axis of rotation is at infinity on
the principal axis parallel to the web, provided that
the two following conditions are met:
When these conditions are not satisfied, the critical
stress should be computed for the axis of rotation
located at the centroid and compared with the critical
stress for bending about the axis of minimum moment
of inertia. The smaller of these two values will then
be the stress at which failure occurs.
4. When a column is attached to a skin, the great
stiffness of the skin in its own plane causes the axis of
rotation to lie in the plane of the skin. When the
column cross section is symmetrical about its two prin¬
cipal axes, one of which is normal to the skin, the axis
of rotation will be at either of the two following loca¬
tions depending upon which location gives the smaller
stress:
(a) The point where the principal axis crosses the
skin.
(b) Infinity in the plane of the skin.
Location (a) gives the condition for twisting failure
when the column is attached to a skin; location (b),
the condition for bending normal to the skin.
5. When a column is attached to a skin and the axis
of rotation is at a point other than infinity in the plane
of the skin, the rotation of the cross sections about the
axis of rotation is resisted by the bending stiffness of
the skin. The effect of this restraint is to increase the
critical stress by an amount
,, KxEt* L 2
- hrit 6(1 -n2)dlp nV
and the critical stress becomes
GJ CBT n2ir2E K\Ets2 U
Jcrit /J,i~ Ip L2 +6(1~mWprV
In this equation 7i=l, 2, 3, 4, etc., the number of half
waves that develop in the stiffener in the length L. A
trial calculation is necessary to determine which value
of n gives the lowest critical stress. This critical stress
should then be compared with that for bending in a
plane normal to the skin and the lower of these two
stresses regarded as the stress at failure for the stiffener
and its effective width of skin.
6. When the column length is small, there will be a
departure of the critical stresses from the theoretical
values given by this theory that is similar to the depar¬
ture from the Euler values in standard column curves^
It is because of this fact that the effective moduli E
and G have been substituted for E and G, respectively,
158
REPORT NO. 5S2 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
in certain terms of the equations for the critical stress.
So long as the column is not stressed above the propor¬
tional limit, E and G are equal to E and G, respectively.
Above the proportional limit the substitution of E for E
follows from the double-modulus theory of bending
where
VC
I - EC
BT,
BT
For the evaluation of G, the following empirical expres¬
sion is recommended:
where
+ V Tr
9 '
7. When the axis of rotation of a symmetrical I
section column is at the center of twist (centroid) cm at
infinity on one of the principal axes, the value of E is
very nearly the same as that for a tliin-wall tube of the
same material in bending. When the axis of rotation
is at the point where the principal axis crosses the skin,
the considerations of the double-modulus action result
in a lack of symmetry for the I section. This lack of
symmetry may cause the critical stress to be a minimum
when the axis of rotation is slightly shifted in the plane
of the skin. Although a study of this condition lias not
been completed, it appears that the shift of the axis of
rotation in the plane of the skin is small for columns of
practical dimensions and that the values of E are also
near those for a thin-wall tube in bending.
8. The value of E varies with the critical stress and
should be computed from the accepted column curve
for the material bv use of the following equation:
~E—f
If desired, this value of E may be corrected for different
cross-section al shapes .
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., August 17, 1036.
APPENDIX A
ILLUSTRATIVE PROBLEM
Problem: To construct the column curve for an I
section column of 24S-T aluminum-alloy material
(£'=10,537,000 pounds per square inch), with the di¬
mensions shown in figure 20, used as a stiffener on skin
b - I.OO"
Detail A
ih - 0.050"
Centroid of column
( Stiffener and
effective shin )
4 - 0.025"
0.050"
4
th -0.050"
Centroid of
stiffener
h I.OO"
I* 1/E"
U
I n i"
Qi Z 2
AK
d 4
it - 4"
See detail A ’
Figure 20. A skin-stiffener combination.
0.025 inch thick. It is assumed that the stiffeners are
spaced at 4-inch intervals along the skin and that all
stiffeners are equally loaded in compression.
Effective moduli E and G for 24S-T aluminum alloy.
It is assumed that the pin-end column strength of 24S-T
tubes is given by the straight-line equation
/crJ<=5 8,000-527— (38)
p
for values of the slenderness ratio — between 9.5 and
P
73. Below — =9.5 it is assumed that the critical stress
P
is 53,000 pounds per square inch. Above — =73 the
stress is assumed to be given by the Euler formula
f crit
(39)
The calculations for the effective moduli E and G are
made as follows, the results of which are given in table I:
1. Assume a series of values of —
p
2. Compute fcrit from
/er«=58, 000-527- for 9.5<— '<73
P P
f cr i l
IT
2E
for — >73
p
3. Using the computed values of fCTih compute E,
from
.2
77-_ A*> L
7T
(37)
4. Computer from
E
r=~, £=10,537,000
5. Compute G from
G=
r+ -Jr
G, <7=0.3S5£=4,057,000
Effective width of skin that acts with the column.
It is assumed that the column is attached to the skin
with two lines of rivets one-lialf inch apart. The width
of the skin between the rivet lines is therefore 204.
The effective width outside the rivet lines is assumed to
be given by the von Karman equation for the effective
width with the coefficient of 1.70, established in ref¬
erence 1
Professor Joseph S. Newell and Mr. Walter H. Gale in
an unpublished report of aircraft materials research
at the Massachusetts Institute of Technology for 1931—
32 recommend the value of 1.73 for the coefficient in
the von Karman equation.
As the width 204 between the two rivet lines is less
than the smallest value of 2 bs given by equation (40)
when fern— 53,000 pounds per square inch, all the ma¬
terial between the twTo rivet lines must be considered
as effective and the total effective width of skin that
acts with the column and carries the same stress as the
column is
U=0.5+26s (41)
l.r)9
38548 — 38 - 12
160
REPORT NO. 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The effective width of skin is calculated as follows,
the results of which are given in table II:
1. Assume a series of values of jCTit. (For con¬
venience, use the same values as given in table I.)
2. Compute 2 bs by equation (40).
3. Compute U by equation (41).
Axis of rotation at infinity in the plane of the skin
for bending failure. — In the report proper it has been
shown that, when an I section column is attached to a
skin, the axis of rotation will be either at infinity in the
plane of the skin or at the point where the principal
axis crosses the skin. The column curve must there¬
fore be drawn for each location to determine which
location gives the lower critical stress.
When the axis of rotation is at infinity in the plane
of the skin, the critical stress is given by the Euler
formula, equation (2) or (39), with E substituted for E.
For this case equation (2), is calculated about a cen-
troidal axis parallel to the skin considering the effective
area of the skin Uts as a part of the column cross section.
The calculations for the construction of the column
curve are made as follows, the results of which are given
in table III:
1. Assume a series of values of jCTu- (For conven¬
ience use the same values as in table I.)
2. Compute area of effective skin, Uts. (For U see
table 11.) 6=0.025.
3. Compute total area of column cross section, from
A— Av
where 2ls<i//=area of stiffener=0.15 sq. in.
Au^area of effective skin= 0.025 U
4. Compute the centroid of the column cross section
(including the effective skin) and tabulate the distance
Qi from the center line of the skin to the centroid,
2 ) A, tiff (0.5375)
A
(See fig. 20.)
5. Compute the moment of inertia, of the complete
column cross section (area A), about the centroid al axis
parallel to the skin
/=T(jA3+2Ms|+[26is+A(J][|+^-a]!+!7(<Q12
= 0.004167 + 0.025+0.15 (0.5375- &)2+ UtsQx2
6. From table I obtain the values of E that cor¬
respond to the assumed values of fCTil.
7. Compute the lengths L0 that correspond to the
assumed critical stresses by use of the Euler formula
where E has replaced E ,
In figure 21 the assumed values of jCTU are plotted
against the computed values of Z0. For a column with
pin ends, L0=L. Hence figure 21 is the column curve
for the axis of rotation at infinity in the plane of the
skin (bending failure). This direct calculation for ob¬
taining the column curve when failure occurs by bend¬
ing normal to the skin is preferable to the trial and error
procedure recommended in reference 1.
Axis of rotation at the intersection of the center
lines of the web and skin — twisting failure. — The
calculation for the construction of the column curve
when the axis of rotation is at the intersection of
Figure 21. — The column curve for bending failure of the skin-stiffener combination
shown in figure 20. The axis of rotation is at infinity in the plane of the skin.
the center lines of the web and skin are similar to those
for the axis of rotation at infinity in the plane of the
skin. The calculations are made as follows; the results
are given in table IV.
1. Assume a series of values for jCTU- (For conven¬
ience use the same values as in table I.)
2. Compute Aj from
Ut,’
G
(21)
3. Compute J from
J—JsiarYAJ
1 2
where
(13)
4. Compute Alp from
a/„=T un.
(22)
5. Compute Ip from
h—hsnffA^Ip
where
+ (14)
^In the evaluation of equation (14), note that
P=0 and Q=§+^^= 0.5375.)
A THEORY FOR PRIMARY FAILURE
OF STRAIGHT CENTRALLY LOADED COLUMNS
161
G. Compute A CBr from
ACbt=ACt=
7. Compute CBt from
CBT=CBTsliff
where
C sr suff — Cb-\-Ct
cB==h^hHb+\jY
L0—
144 m‘
(24)
+ A CBT
‘+’i |“]p2+x®2
(6)
(8)
b3t-3
IiHh3 , htb3 T19 , hth3
°’=72 +TS+ e p2+ Tt-«!
(10)
(In the evaluation of equation (6), note that P— 0
and Q= 0.5375.)
8. From table I obtain the values of E and G that
correspond to the assumed values of/cr<,.
9. Solve equation (26) for L0.
I r a
Sc,u_
*v
GJr
J JcrU
2
-4
CBtTT“E
- h _ _
2 KxEt3
KxEt3 "I
_6(1 — ^)dP2Ip\
(42)
f 6(1
Evaluate equation (42) using values of J, IP) CBr,
G, and E that correspond to the assumed values of
fcriti and
n= 0.3
£'=10,537,000 lb. per sq. in.
d= 4 in.
4=0.025 in.
#i=2
In figure 22 the assumed values of jcrit are plotted
against the computed values of L0. From this figure
the column curve for twisting failure is derived in the
following manner. Put L0 equal to — and then plot
7 1/
curves of jcrU against L for ?i= 1, 2, 3, 4, etc. The
column curve is then given by the lowest portions of
the several curves and is shown by full lines in figure 23.
Column curve for primary failure. — It has been pre¬
viously shown that primary failure will occur either by
bending or by twisting, depending upon which type of
failure gives the lower critical stress. The column
curves of figures 21 and 23 are therefore combined as
shown in figure 24 to obtain the column curve for
H2)dTT2lp
Figure 22.— Critical stress plotted against Lu for twisting failure of the skin-stiffener
combination shown in figure 20. The axis of rotation is at the intersection of the
center lines of the web and the skin.
Figure 23.— The column curve for twisting failure of the skin-stiffener combination shown in figure 20. The axis of rotation is at the intersection of the web and the skin.
162
REPORT NO 582 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
primary failure. It will be noted that, at lengths less
than 27.4 inches, failure occurs by twisting; whereas, at
lengths greater than 27.4 inches, failure occurs by
bending.
Discussion. — In the computed tables for this illus¬
trative problem it will be noted that some of the factors
are small and might have been neglected. All of the
factors, however, have been included to show their
relative numerical values and the method of evaluation.
The designer may therefore shorten the calculations
here outlined by neglecting the unimportant factors, if
desired.
Figure 24.—' The column curve for primary failure of the skin-stiffener combination
shown in figure 20.
In the foregoing calculations for twisting failure
it was assumed that Ki=2 regardless of the value of
~t' This value of Kx was selected because of the
possible uncertainty in establishing a more definite
value, as discussed in this report. If it had been
desired to use the values of Kx given by the curve of
figure 15 rather than the asymptotic value K\=2,
the calculation of L0 would of necessity have been by
trial and error because Kx varies with
When a skin-stiffener combination is loaded in com¬
pression, buckling will first occur in the skin provided
that the stiffener spacing divided by the skin thickness
j is sufficiently large. Because the skin is attached
to the stiffeners, the buckling of the skin will twist the
stiffeners and form small waves in them, the lengths of
which are the same as those in the skin. In this con¬
dition the stiffeners are not ready to buckle of them¬
selves but are forced to buckle by the skin. The stiff¬
en ers therefore resist buckling of the skin.
Now, if the load on the skin-stiffener combination is
increased, the waves in the skin and the corresponding
waves in the stiffeners grow larger. Finally a load is
reached at which the stiffeners buckle of themselves.
The type of buckling that occurs in the stiffeners will
be that associated with the lowest critical stress. On
the assumption that local buckling does not occur, the
stiffeners will either buckle by deflection perpendicular
to the skin in the manner of an ordinary column or
will twist about an axis in the plane of the skin. If
twisting occurs, the skin will resist twisting of the stiff¬
eners. The column curves derived by the methods of
this report give the critical stress at which the stiffeners
begin to buckle (bend or twist) of themselves. Because
the stiffeners are the main strength element in a
skin-stiffener combination, it seems quite proper that
the strength of the combination should be based on
the strength of the stiffeners.
When the stiffeners fail by twisting, it is quite possi¬
ble that tests’ will show the ultimate load for a skin-
stiffener panel in compression to be greater than the
critical load at which twisting begins. The reason for
this belief is that when the stiffener twists, the material
adjacent to the axis of rotation is not laterally dis¬
placed and is therefore capable of further compression.
The amount by which the ultimate load will exceed
the critical load at which buckling begins is dependent
upon a number of factors the consideration of which is
beyond the scope of this report.
Until the results of extensive tests made especially
to check the theoretical behavior of skin-stiffener
combinations in compression become available, the
designer should conservatively assume that failure
occurs when the buckling load is reached. The methods
outlined in this report and illustrated in this appendix
may therefore be used to derive column curves for
different skin-stiffener combinations. By comparison
of the strength-weight ratios the most efficient combi¬
nation of skin and stiffeners can be selected.
APPENDIX B
APPLICATION OF THE THEORY FOR PRIMARY FAILURE TO A
COLUMN OF CLOSED SECTION
or, if E= 107 pounds per square inch,
Equation (1), which has heretofore been applied to
columns of open section, can also be applied to columns
of closed section provided that all the factors appear¬
ing on the right-hand side of the equality sign can be
evaluated. It will be shown how these factors can
be evaluated for a thin-wall column of closed rectangu¬
lar section, symmetrical about its two principal axes.
(See fig. 25.)
B r
b J . b
2
2 1
n
1
h
Z -
-th
t
4
4-
-
A A
ft
z
]
4
l
D
(
1
_
B‘
T
-P-
C'
H
y
Axis of roioiion
Figure 25. — A thin-wall rectangular tube.
Evaluation of GJ/Ij,. — Except for J and CBt all of
the factors that enter into equation (1) are readily
evaluated by standard methods. For the closed section
t 4A2
J Cds (43)
where A is the area enclosed by the center lines of
the wall of the rectangular tube.
ds, differential element of the perimeter.
t, wall thickness of ds.
lor a square tube of constant thickness equation
(43) becomes
J = bH
Because the square tube is symmetrical about its two
principal axes, the critical stress will be a minimum
"hen the axis of rotation for the free column is either
at the centroid (center of twist P— 0, Q=0) or at
infinity on one of the principal axes. The critical
stress when the axis of rotation is at the centroid will
be greater than that given by the first term of equation
(1) or
(/ r.<)/J=o>2,88’5,000 pounds per square inch
Q= o
As this value of the critical stress is much greater
than the yield-point stress for any engineering material
with E= 1()7 pounds per square inch, it may be con¬
cluded that the large torsional rigidity of a closed
section precludes any type of primary failure except
bending failure; i. e., axis of rotation at infinity on
one of the principal axes.
Evaluation of CBt ■ — In order to show that CBr can
be evaluated for a closed section, the expressions for the
longitudinal displacement at the center lines of the wall
of the tube will be derived. In view of the conclusion
in the preceding paragraph, the value of this work will
be more in the possibilities offered in the calculation of
the stresses in monocoque shells, such as airplane wings,
fuselages, floats, and hulls than in the solution of the
column problem.
First, the longitudinal displacements caused by the
twisting of the section about its centroid will be deter¬
mined (P= 0, Q— 0 in fig. 25). If the tube is assumed
to be slit longitudinally on the 0 axis at A— A', the
closed section becomes an open section. Now imagine
a portion of length dx to be twisted an amount dtp about
the centroid (center of twist for the closed section).
The longitudinal displacements of the points on the end
cross section caused by such twisting can then be deter¬
mined in the same manner as for an open section.
These displacements with respect to the original plane
of the end cross section are, at a distance s measured
from
B toward A,
C toward B,
D toward C, —
D toward C',
C' toward B',
B' toward A',
(LD— 6)
(f ) A GJ~
J- Ti
Q=0
0.38 bEbH
4
- bH
3
|(0.385jE)
The longitudinal displacement of A (just above the
slit) is
—e[hb]
163
REPORT NO. 582 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
164
and of A' (just below the slit) is
6[hb]
The longitudinal displacement of A' with respect to A
is therefore
6[2hb]
In order to transform the open section, slit at A— A',
into a closed section, equal and opposite shearing forces
F are introduced in the slit to draw A and A' together.
The magnitude of these shearing forces is determined
by equating the integral of the shear strain in the
section between A and A' to the longitudinal displace¬
ment of A' with respect to A when the section is slit
%A[ F^ds_
A tG (lx
8[2hb]
which becomes for the section shown in figure 25
from which
(44)
The longitudinal displacement with respect to the
original plane of the end cross section caused by the
shearing force F in the slit is at a distance s measured
from
B toward A,
F lj"l h b si
dx G\_2 tntbt, J
C toward B,
1) toward C,
I) toward C',
C' toward IT,
IT toward A',
(LI) -7)
Adding of these longitudinal displacements to those of
(LI)— 6) and substituting the value of F/dx from
equation (44) gives at a distance s measured from
B toward A, — 0
C toward B, — 0
D toward C, — 0
D toward C', 0
C' toward B', 0
B' toward A', 6
3 hb bs hb / h . h s
4 + 2 ~ h , 6\2b, 6,
tnh
hb . hs hb / h s V
4' + 2 ~ h.b\2tntj
tnh
~bs hb / s\
2 ~ k,b\fh)
hs hb / s A'
2 -h.bKu)
h\ h
~hb h s h b / k s V
T+2 '~r7l\2fh+Tj
t*tb
•Gib , bs hb / h , b
4 + •>
b j b
t»h
h, 0 , £\
2tntF tj
(LD-8)
The longitudinal displacements of (LD 8) apply to
the closed section of figure 25 when the portion of
length dx is twisted an amount dip about the centroid.
If the axis of rotation is now shifted from the centroid
to the location defined by P and Q, in figure 25, certain
terms must be added to (LD-8) that are analogous to
the longitudinal displacements of (LD-2) and (LD-3)
for the I section. These longitudinal displacements
caused by translation are, at a distance s measured
from
B toward A, 0
1
I -
O' L *
1
cc
1
Ms
i
C toward B, 0
/MR]
D toward C, 0
[ps+<4]
D toward C', 0
-ps+e|]
C' toward B', 0
B' toward A', 0
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
165
Addition of the longitudinal displacements given by equations (LD-8) and (LD-9) give at i
measured from
"3 hb . bs hb ( h . b . s\ Jh \ , Ob'
rrV2ir+rt+d-U2"s)+2
B toward A, —6
2
C toward B, — 6
D toward C, —6
D toward C', d
C' toward B', d
B' toward A', 0
ib^hs hb fh , s \ Ph n(b
i + 2 h,b\2h + rj 2 yV2 1
rh+u
(£>-*
©-
~bs hb
2 h + h
tnU
bs hb
2 h b
. tnh
~hb hs hb
4 +y~iTT
thtb
~Shb , bs
4 : 2 ~h
Qb '
Ps + <2
iHKMH
!+£KH
lh lb
Qb'
9
(LD-10)
Because the rectangular tube of figure 25 is symmet¬
rical about its two principal axes the reference plane
coincides with the original plane of the end cross section.
(See derivation of CBt for the I section.) Hence,
(LD-10) gives the longitudinal displacements with
respect to the reference plane. These
displacements when substituted for u in <
with 0 = 1 give the major part of Cut- TIk
of Cut is calculated in the same manner as
section.
i distance s
longitudinal
equation (7)
■ minor part
for an open
APPENDIX C
DERIVATION OF THE THEORETICAL VALUE OF THE EFFECTIVE
MODULUS E
If CBtx is the value obtained from equation (4) when
the integration is made over the part of the cross sec¬
tion that suffers an increase of stress at the instant of
failure of the column, and E' is the modulus of elasticity
for increasing stress, the work done by the increase in
compressive stresses is (see equation (3) of reference 2)
}2E’CBT^\v"ydx
If CBt2 is the value obtained from equation (4) when
the integration is made over the part of the cross sec¬
tion that suffers a decrease of stress at the instant of
failure of the column, and E is the modulus of elasticity
for decreasing stress, the work done by the decrease in
compressive stresses is
~ EcBTA\<p"ydx
The total work done by the longitudinal bending
stresses is therefore
\(E’CBTl + EOBT2) £(‘p"y<te (a)
When the modulus of elasticity is the same for in¬
creasing stress as for decreasing stress, as it is in the
elastic range, the total work done by the longitudinal
bending stresses is
±ECBT\\<e"ydx (b)
If a modulus E is substituted for E in (his expression,
the total work given by expression (b) can be made to
have any desired value depending upon the value as¬
signed to E. If E is allowed to have only such values
as will cause the total work given by (b) to equal that
given by (a), it is found that
>r
C/ BT
This value of E is called the “effective” modulus when
the column is loaded above the proportional limit.
The total work done by the longitudinal bending
stresses when the column is loaded above the propor¬
tional limit is therefore given by the expression
\~ECst \\v")2dx
Thus when the column is loaded above the proportional
limit, E should be substituted for E in Wagner’s
equation for the critical stress, i. e., equation (1) of this
report.
REFERENCES
1. Lundquist, Eugene E.: Comparison of Three Methods for
Calculating the Compressive Strength of Flat and Slightly
Curved Sheet and Stiffener Combinations. T. N. No.
455, N. A. C. A., 1933.
2. Wagner, Herbert: Torsion and Buckling of Open Sections.
T. M. No. 807, N. A. C. A., 1936.
3. Wagner, H., and Pretschner, W.: Torsion and Buckling of
Open Sections. T. M. No. 784, N. A. C. A., 1936.
4. Timoshenko, S.: Strength of Materials, Part I. D. Van
Nostrand Co., Inc., 1930.
5. Trayer, George W., and March, H. W.: The Torsion of
Members Having Sections Common in Aircraft Construc¬
tion. T. R. No. 334, N. A. C. A., 1930.
6. Pugsley, A. G.: Torsional Instability in Struts. Aircraft
Engineering, vol. IV, no. 43, Sept. 1932, pp. 229-230.
7. Trayer, George W., and March, II. W.: Elastic Instability
of Members Having Sections Common in Aircraft Con¬
struction. T. R. No. 382, N. A. C. A., 1931.
8. Timoshenko, S.: Strength of Materials, Part II. D. Van
Nostrand Co., Inc., 1930.
9. Osgood, William R.: Column Curves and Stress-Strain
Diagrams. Research Paper No. 492, Bur. Standards
Jour. Res., vol. 9, Oct. 1932, pp. 571-582.
10. Osgood, William R.: The Double-Modulus Theory of
Column Action. Civil Engineering, vol. 5, no. 3, Mar.
1935, pp. 173-175.
11. Blcich, Friederich: Theorie und Berechnung dcr eisernen
Briicken. Julius Springer (Berlin), 1924, S. 218-219.
12. Kollbrunncr, Curt F.: Das Ausbculen des auf Druck bean-
spruchten freistehenden Winkcls. Gcbr. Lccmann & Co.
(Zurich & Leipzig), 1935.
TABLE I
EFFECTIVE MODULI E AND Ti FOR 24ST ALUMINUM
ALLOY
u
p
ferit
lb./sq. in.
E
lb./sq. in.
T
2
G
lb./sq. in.
9. 49
53, 000
483, 600
0. 0459
0. 1301
527, 600
13.28
51, 000
911,300
.0865
. 1903
771,900
17.08
49, 000
1,453,000
. 1379
.2382
966, 400
20. 87
47, 000
2, 074, 000
. 1968
. 3203
1,299,000
24.67
45, 000
2, 775, 000
.2633
.3883
1,575, 000
28.46
43, 000
3, 529, 000
. 3349
. 4568
1,853,000
32. 26
41, 000
4, 323, 000
.4103
. 5254
2. 132, 000
36. 05
39, 000
5, 135, 000
.4874
.5891
2, 390, 000
39. 85
37, 000
5, 953, 000
. 5650
.6583
2, 671, 000
43. 64
35, 000
6, 754, 000
.6409
.7208
2, 924, 000
47.44
33, 000
7, 525, 000
.7141
.7796
3. 163, 000
51. 23
31,000
8, 244, 000
.7823
.8334
3, 381, 000
55. 03
29, 000
8, 898, 000
.8444
. 88t7
3, 577, 000
58. 82
27, 000
9, 465, 000
.8982
.9230
3, 744, 000
60. 72
26, 000
9, 713, 000
.9215
.9407
3.817, 000
62. 62
25, 000
9, 933, 000
. 9426
. 9568
3. 881, 000
66. 4 1
23, 000
10, 278, 000
.9754
.9815
3, 982, 000
70.21
21,000
10, 489, 000
. 9954
. 9965
4, 043. 000
73.00
19, 520
10, 537, 000
1.0000
1.0000
4. 057, 000
75. 00
18, 490
10, 537, 000
1. 0000
1. 0000
4,057, 000
80. 00
16, 250
10, 537, 000
1.0000
1.0000
4, 057, 000
85.00
14, 3S0
10, 537, 000
1. 0000
1.0000
4, 057, 000
90. 00
12, 840
10, 537, 000
1. 0000
1. 0000
4, 057, 000
95.00
11,520
10, 537, 000
1.0000
1.0000
4, 057, 000
100. 00
10, 400
10, 537, 000
1. 0000
1. 0000
4, 057, 000
166
A THEORY FOR PRIMARY FAILURE OF STRAIGHT CENTRALLY LOADED COLUMNS
167
TABLE II
TABLE III
FECTIVE WIDTH
OF SKIN THAT ACTS WITH THE
COLUMN
CRITICAL STRESS FOR BENDING
FAILURE
fcTlt
lb./sq. in.
uts
sq. in.
A
sq. in.
Q.
inch
I
in*
lb./sq. in.
u
inches
53, 000
0.0275
0. 1775
0. 4542
0. 0359
483, 600
4.27
51, 000
. 0278
. 1778
. 4535
. 0359
911,300
5. 97
49, 000
.0281
. 1781
. 4527
. 0360
1,453,000
7.69
47, 000
.0284
. 1784
.4519
.0361
2, 074, 000
9. 38
45, 000
. 0288
. 1788
. 4509
. 0362
2, 775, 000
11.09
43, 000
.0291
. 1791
. 4502
. 0362
3, 529, 000
12.80
41,000
. 0295
. 1795
. 4492
. 0363
4. 323, 000
14.51
39, 000
. 0300
. 1800
.4479
. 0364
5, 135, 000
16.21
37, 000
. 0304
. 1804
.4469
. 0365
5, 953, 000
17. 92
35, 000
. 0309
. 1809
. 4457
. 0366
6, 751, 000
19. 62
33, 000
.0315
. 1815
. 4442
. 0367
7, 525, 000
21.33
31,000
. 0321
.1821
.4128
. 0368
8, 244, 000
23. 03
29, 000
.0328
. 1828
.4411
. 0369
8, 898, 000
24.73
27, 000
. 0335
. 1835
. 4394
.0371
9, 465, 000
26. 44
20, 000
.0339
. 1839
. 4384
. 0372
9, 713, 000
27. 29
25, 000
.0343
.1843
.4375
. 0372
9, 933, 000
28. 15
23. 000
. 0353
. 1853
.4351
. 0374
10, 278, 000
29. 84 1
21,000
. 0363
. 1863
. 4328
. 0376
10, 489, 000
31. 55
19, 520
.0372
. 1872
. 4307
. 0378
10, 537, 000
32. 79
18, 490
. 0379
. 1879
.4291
. 0379
10, 537, 000
33. 68
16,250
.0396
. 1896
. 4252
. 0382
10, 537, 000
35.91
14, 390
.0413
. 1913
.4215
. 0385
10, 537,000
38. 15
12, 840
.0430
. 1930
.4177
.0388
10, 537, 000
40. 36
11,520
. 0416
. 1946
.4143
. 0391
10, 537, 000
42. 60
10, 400
.0463
. 1963
.4107
.0394
10, 537, 000
45. 80
ferit
2 b,
U [
\ lb./sq. in.
inches
inches
53, 000
0.599
1.099
51, 000
.611
1. Ill
i 49, 000
.623
1. 123
47, 000
. 636
1. 136
45, 000
. 650
1. 150
43,000
. 665
1. 165
41,000
.681
1. 181
39. 000
. 699
1. 199
37, 000
.717
1.217
35, 000
.737
1.237
33, 000
.759
1.259
31,000
. 784
1.284
29, 000
.810
1.310
27, 000
.840
1.340
26, 000
.856
1.356
25, 000
.873
1.373
23, 000
.910
1.410
21,000
. 952
1.452
19, 520
. 988
1.488
18, 490
1.015
1.515
16, 250
1.082
1 . 582
14, 390
1. 150
1.650
12, 840
1.218
1.718
11,520
1.285
1.785
10, 400
1.353
1.853
TABLE IV.— CRITICAL STRESS FOR TWISTING FAILURE
ferit
A J
J
A/p
Ip
A Cbt
°Cbt
G
K
z.
0
| lb./sq. in.
in.4
in.*
in.*
in.4
in.6
in.6
lb./sq. in.
lb./sq. in.
in.
in.
53,000
0. 0000057
0. 0001307
0. 00277
0. 08360
0. 0000001
0. 00450
527, 600
483, 600
53.4
2.2
1 51, 000
. 0000058
. 0001308
. 00286
. 08369
. 0000001
. 00450
771,900
911,300
52. 1
3. 1
49, 000
. 0000059
. 0001309
. 00295
. 08379
. 0000002
. 00450
996, 400
1,453,000
50. 9
4. 0
47, 000
. 0000059
. 0001309
. 00306
. 08389
. 0000002
. 00450
1, 299, 000
2. 074, 000
19. 4
... (i
45, 000
. 0000060
.0001310
.00317
. 08401
. 0000002
. 00450
1,575,000
2, 775, 000
48.0
5. 0
43, 000
. 0000061
.0001311
. 00330
. 08413
. U000002
. 00450
1, 853, 000
3, 529, 000
46. 5
6. 9
41,000
. 0000062
.0001312
. 00343
. 08427
. €000002
. 00450
2, 132,000
4, 328, 000
44.9
7. 9
39, 000
. 0000062
. 0001312
. 00359
. 08442
. 0000002
. 00450
2, 390, 000
5, 135. 000
43. 2
8. 9
37, 000
. 0000063
.0001313
. 00376
. 08459
. 0000002
.00450
2, 671.000
5, 953, 000
41.5
III. (1
35. 000
. 0000064
. 0001314
.00395
. 08478
. 0000002
. 00450
2, 924, 000
0, 754, 000
39. n
1 1 . J
33, 000
. 0000066
.0001316
. 00416
. 08500
. 0000002
. 00450
3, 163, 000
7, 525, 000
37. 5
l'.’. )
31, 000
. 0000067
. 0001317
.00441
. 08524
. 0000002
. 00450
3.381,000
8, 244, 000
35. 3
13. 9
29, 000
. 0000068
. 0001318
. 00468
. 08552
. 0000002
. 00450
3, ,577, 000
8, 808, 000
32. 8
1 5. 5
27, 000
. 0000070
. 0001320
.00501
. 0S584
. 0000003
. 00450
3, 744, 000
9, 465, COO
29. i
17. 7
20* 000
. 0000071
. 0001321
. 00519
. 08603
. 0000003
. 00450
3,817,000
9, 713, 000
27. 7
1 9. 2
25 000
. 0000072
.0001322
. 00539
. 08622
. 0000003
. 00450
3, 88 1 . 000
0, 933, 000
23. 6
22. 8
23,000
. 0000073
.0001323
. 00584
. 08667
. 0000003
. 00450
3, 982, 000
10, 278, 000
imaginary
C'b =0.00 119- CT =0.000006.
REPORT No. 583
THE ROLLING FRICTION OF SEVERAL AIRPLANE WHEELS ANI) TIRES ANI) THE
EFFECT OF ROLLING FRICTION ON TAKE-OFF
By J. W. Wetmore
SUMMARY
Tests were made to determine the rolling friction of
airplane wheels and tires under various conditions of
wheel loading , tire inflation pressure, and ground surface.
The effect of wheel-hearing type was also investigated.
Six pairs of wheels and tires were tested including two
sizes of each of the types designated as standard {high
pressure), low pressure, and extra low pressure. The
results of calculations intended, to show the effect of varia¬
tions in rolling friction on take-off are also presented.
The values of rolling-friction coefficient obtained on a
concrete runway raided from 0.009 to 0.035; on firm turf,
from, 0.023 to 0.054; and on moderately soft turf, where
only the high-pressure tires were tested, from 0.064 1°
0.077 . Of the variables investigated, the ground-surface
condition was the most important in its effect on the rolling-
friction coefficient. For comparable conditions, both on
a concrete surface and on firm turf, the standard wheels
and tires offered the least resistance to rolling. Slightly
higher values were obtained with the low-pressure wheels
and, tires, and the extra low-pressure type gave the highest
values. The variation in rolling-friction coefficient with
wheel loading and, inflation pressure was generally quite
small. The value of rolling-friction, coefficient for wheels
equipped with plain bearings was appreciably greater than
that for the same wheels provided with roller bearings.
The effect on take-off of all the variables, with the exception
of ground-surface condition, was sufficiently small to be
neglected in rough calculations of take-off performance
but should be considered in more, accurate work.
INTRODUCTION
In many cases when comparisons have been made
between measured and calculated values of the ground-
fun distance in the take-off of an airplane, the results
have shown considerable disagreement. A part of the
discrepancy can be attributed to the inadequacy of
available information concerning the forces and condi¬
tions existing during the take-off. An investigation of
the rolling friction of airplane wheels and tires, one of
the uncertain factors, was undertaken as a step toward
augmenting this information and lienee toward im¬
proving the reliability of the prediction of take-off
performance.
The measurement of the rolling friction was accom¬
plished by recording the pull between a towing vehicle
and a loaded trailer equipped with the wheels and tires
to be tested. The resistance thus measured included, of
course, that due to the wheel bearings as well as that
of the tires.
The tires and wheels tested included two sizes of each
of the types generally classified as standard (high pres¬
sure), low pressure, and extra low pressure. The tests
were run at various speeds under several conditions of
wheel loading and tire inflation pressure. The ground-
surface conditions investigated were concrete, firm
turf, and soft turf.
As an indication of the probable effect on take-off
of the differences in rolling friction occasioned by the
various conditions, calculations were made of the
distances required to leave the ground for two hypo¬
thetical airplanes of different loading characteristics;
for each case several values of rolling-friction coeffi¬
cient, covering the range determined by the tests, were
assumed.
APPARATUS AND METHODS
The trailer used in the tests (fig. 1) was a 2-wheel
carriage with provision for interchanging stub axles
to accommodate the various wheels. It was capable
of carrying up to 3,000 pounds of load in the form of
200-pound lead weights, which, with the weight of the
carriage itself, provided a maximum load on the wheels
of 3,500 pounds. The carriage was equipped with
airplane-type hydraulic shock absorbers to simulate
an airplane landing chassis. The axles were so arranged
that there was no toe-in of the wheels. A light truck
was used as the towing vehicle.
The pull between the truck and the trailer was meas¬
ured with a dynamometer consisting essentially of a
helical spring, the deflection of which, proportional
to the force, was recorded by a standard N. A. C. A.
instrument of the type ordinarily used to record the
position of airplane controls in flight. The force was
transmitted from the trailer drawbar to the spring
through a cylindrical shaft running in ball-bearing
guides that confined the motion of the shaft to an axial
direction. All these components were mounted in a
169
170
REPORT NO. 583 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 1.— Trailer and test equipment.
Q)
s!
H
Extra low pressure
Low pressure
Standard
Extra low pressure
Low pressure
Figure 2. - Cross sections and dimensions of the airplane tires and wheels tested.
36 X 8
Standard
= 12.8
THE ROLLING FRICTION OF AIRPLANE WHEELS AND TIRES
171
heavy frame to form a unit which, in turn, was bolted
to the bed of the truck.
A standard N. A. C. A. recording inclinometer was
mounted on the trailer to determine the horizontal
acceleration. A timer was used to synchronize the
records of the two recording instruments and also, in
conjunction with an electrical-contact mechanism on
the front wheel of the truck, to provide a means of
evaluating test speeds.
Sketches of the wheels and tires used in the tests are
shown in figure 2. The wheels and tires tested included
three types: Extra low pressure or airwheels, low pres¬
sure, and standard or high pressure. Two sizes of
each type were tested. The sizes of extra low pressure
tires tested were 22X10-4 and 30X13-6; the recom¬
mended tire inflation pressure for both sizes was 12.5
pounds per square inch. The recommended inflation
pressure was 20 pounds per square inch for the two
Each pair of wheels and tires was tested under three
loads with the tires inflated to the recommended pres¬
sure. The heaviest load in each case was determined
either by the recommended maximum static load for
the tires or by the capacity of the trailer; the other
loads were chosen arbitrarily to provide a convenient
range.
With 940 pounds per wheel, a load common to all
the test series, the rolling-friction measurements were
made at two inflation pressures below and in addition
to the recommended value, the lowest pressure being
about 50 or 60 percent of the recommended pressure.
The 26X5 tires were run only at recommended infla¬
tion pressure.
All the foregoing conditions were covered in tests on
a concrete runway designed for airplane operations, the
surface of which had been scarified to improve its
tractional qualities. Tests were likewise run for all
2000
. 1500
£
o IOOO
'A
£ 500
<
C
0)
Q.
O
1500
■K.
IOOO
500
O
Extra
i
22 xlO-4
low-pressu
re tii
e
/ /
/ /
T7
/ / /
’''X It
lflatio
— 12V.
— 10
-- 8
n pre
18. /s
II
II
ssure
q. in._
Extra
30 xl3~6
low-pressu
re tir
e
/V
0/
7
/ .
Ir
if latio
— 12 Vs
— 10
— 8
n pre
>lb./s
H
ssure
q. in . _
V~
—
12 3 4 5 6
!
Low-j
7.50-K
iressu
3
re tir
e
/
(' /
'A
Inf
///
1 at ion
- 20 1
-16
-12
press
b./sq
II
II
>ure
in —
//
///
/
—
Lc
8.5
TW-pre
>0-10
ssure
tire
/ /
//
7
/ /
///
r/
^ In
f latio
— 20
n p ret
lb./s
it
ii
ssure
in._
//
//
'X
—
— 16
— 12
_
O 12 3 4 5 6
Radio! deflection , inches
Figure 3.— Static load-deflection curves of tires. The highest pressure in each case is the recommended inflation pressure.
sizes of low-pressure tires, 7.50-10 and 8.50-10. The
recommended inflation pressure for the 26X5 standard
tire was 50 pounds per square inch; for the 36X8
size the recommended pressure was 60 pounds per
square inch. All the tires had smooth treads except
the 26X5 size, which had a nonskid tread. Static
load-deflection curves for all the tires are shown in
figure 3.
The bearings of all the standard and extra low-pres¬
sure wheels were of the plain type, i. e., bronze bushings
grooved for lubrication and running on steel journals.
Both sizes of the low-pressure wheels were equipped
with antifriction roller bearings. The tests of the
8.50-10 low-pressure wheels and tires, however, were
repeated for two loads with the roller bearings replaced
by plain bearings in order to provide an indication of
the effect of bearing type.
conditions on a turf surface of probably average smooth¬
ness, having a clay topsoil and covered with fairly thick
grass about 6 or 8 inches in height. Most of the tests
were made when the surface was very dry and firm,
probably representative of the best field condition likely
to be encountered. For the tests with varying load on
the 26X5 and 36X8 standard wheels and tires, how¬
ever, the surface was wet and moderately soft so that
the truck tires left tracks between one-half and 1 inch
in depth, representing fairly unfavorable conditions for
normal operation but by no means the worst possible.
The measurements of rolling friction were made for
each condition according to the following procedure:
3- or 4-second records were taken at several speeds
between 5 and 45 miles per hour on the concrete sur¬
face or between 5 and 30 miles per hour on the turf
surface, with the speed held as nearly constant as pos-
172
REPORT NO. 583— — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
sible during each run. The value ol‘ the mean gross
pull Pm between the truck and trailer was determined
from the record of dynamometer spring deflection.
Because it was impossible to maintain the speed dur¬
ing the runs sufficiently steady to preclude relatively
large errors due to the inertia force of the trailer, the
recording inclinometer was used to provide a correction
for this force. Before and after each series of runs,
several records were taken of the inclinometer angle
with the truck and trailer standing on a fairly level
surface and heading in various directions so that the
average of the readings provided a reference angle 0O,
the angle for no horizontal acceleration. Then the dif¬
ference between this value and the mean angle 0 m re¬
corded during a run defined the mean direction of the
resultant force acting on the inclinometer pendulum
relative to the direction of the gravity component, or
0m— 0o=tan-1 —
9
where am is the mean acceleration in the direction of
travel. The mean inertia force P/ was then deter¬
mined from the relation
Pi = W tan (dm—d())
where W is the weight of the loaded trailer.
Owing to the deflection of the truck springs resulting
from the drag of the trailer, the attitude angle of the
trailer — hence of the inclinometer base — while running
differed sufficiently from the static reference angle to
cause an appreciable error in the acceleration as deter¬
mined by the foregoing method. Moreover, a similar
effect was caused at higher speeds by a reduction in the
deflection of the trailer tires due to centrifugal force.
The necessary corrections were found by mounting a
second inclinometer between the truck axles where it
was not subjected to the described effects and compar¬
ing the records of the two instruments for a sufficient
number of runs under various conditions to establish a
relationship between the correction and the influencing
factors. The correction angle dc was then the difference
between the mean angles recorded by the inclinometer
on the truck and the inclinometer on the trailer, and
the corrected inertia force became
Pi = W tan (dm+9c-d 0)
The air resistance D of the trailer was determined as
the difference between the over-all resistance measured
with the trailer covered by a hood and that with the
trailer uncovered. The hood consisted of a fabric-
covered framework completely enclosing the trailer
but entirely free of any mechanical connection with it,
being supported by direct connection with the truck
and running on skids. The air drag was measured in
this manner at several speeds within the range covered
by the tests.
The rolling friction or resistance R was evaluated
from the test results according to the relation
R=Pm~W tan (dm + dc-eQ )-D
Then the rolling-friction coefficient, the form in which
the results are presented, is
R
PRECISION
The mean gross force was measured by the dynamom¬
eter to within ±1 pound for individual runs. The
mean acceleration was determined from the inclinom¬
eter records to within ±0.06 foot per second per
second. From this the inertia force is correct to
within ±2 pounds for the lightest load and within
±6 pounds for the heaviest load. Inasmuch as each
of the values presented in the table and the figures was
averaged from the results of 18 runs, all but small
consistent errors are largely eliminated.
In the case of the tests run on the turf surface, there is
a possibility of some lack of uniformity in the condition
of the surface between the different series of tests,
which was not indicated by its appearance and might
introduce an error into the effects attributed to the
applied variables. Likewise, inasmuch as the plain
bearings used in airplane wheels are of the imperfectly
lubricated type and hence of somewhat uncertain
frictional characteristics, it is possible that there was
some difference in bearing friction between the several
wheels equipped with plain bearings so that the differ¬
ences observed between the over-all friction coefficients
of the wheels and tires for similar conditions may not
be due solely to tire size and type. These effects are
believed, however, to be too small to invalidate the
comparisons and conclusions drawn from the results
of the tests.
RESULTS
The values of rolling-friction coefficient for all the
conditions covered in the tests are presented in table I.
Figures 4 and 5 give the results obtained on the con¬
crete runway for all the wheels and tires. Figure 4
shows the effect of wheel load on the rolling-friction
coefficient and also the difference between the coeffi¬
cients with plain and roller bearings as determined on
the 8.50-10 low-pressure tires. Figure 5 shows the
variation of rolling-friction coefficient with tire infla¬
tion pressure for all but the 26X5 tires. The coeffi¬
cients measured on the turf surface are plotted in
figures 6 and 7. Figure 6 shows the variation of the
coefficient with wheel load. For the tests of the
standard-type wheels and tires, i. e., the 26X5 and
36X8, the surface was wet and fairly soft, whereas for
THE ROLLING FRICTION OF AIRPLANE WHEELS AND TIRES
173
c
QJ
.0
$
<u
o
o
c
.0
y .06
o
Q:
J;
3 v !
n - i
W I c?
o—
— 0
Plain bearing's!
r -
2 1 ^
1 *
3
OxlC
5-6 v
vhee
Is
Pr
r
ess
i a 1 1
are
1
= 12 1
4 lb
1 5 J
. / sq. in
o—
- c
7.50
-10
er I
■e = .
whe
>ear
20 1
e 1 s
ing-s
>./S(
q.in.
°rez
ssur
-o-
o—
- c
£
. 50
- 1C
wh
eel.
3
—
Pre.
ssure =
20 1
b./sq.tn
lLj _
t -
/ P 1 a i r
/ -J _ 4,
i be
_
1
arings
~5t—
r\
- - r
o—
"Roller bear
ngs
1
. 2B
1
x 5 v
/heels
1- —
Pre
Plain bearing's
ssurfi^ 50 lb./sa.in
"l
/ -
36
- PI
x 8
ain
re =
whe
be<
60
els
ir ir
b./s
lgS-
q.in
Pre
ssu
0
‘
o
Load per wheel, pounds
Figure 4— Variation of rolling-friction coefficient with load per wheel; concrete
surface; recommended inflation pressure.
.08
<5
<0
.0"
$
dJ
O
0
c; '
.0
\
.U
£
>.
$
o
•
r
A - 1 - 1 1
22 x 10-4 wheels.
Plain bearing's.
Recommended |
sure = 12 7. lb. Isa. i
n. —
p
res.
i
a.
b
r
30 x
13-
1,
3 w
-iee.
S.
n.
res
r i d. i ri uigo.
Recommended |
_ nw n, /o^r i
o-
p
bun
- /2 1
^ * /
J T *
—
7. 5
_ Rol
0- It
ler
} whee 1
bear insf
S.
s.
. -
Recommended |
pressure = 20 lb. /sq.m
c
u
8. 5
0-1
0 w]
reel
s.
Roller bearings.
Recommended j
J
pre
SSU
re =
L. U
u./ a
i -
>
-
1
36 x 8 v
/hee
Is.
>
r lain Dear mg
Recommended |
o -
pre
SSU
re -
T •
1
0
c:
<u
■ s
<0
0 •
O
c
.o
-K
.o .
4;
£
_
2
i
2 x 1 0- 4 wh
ain bearii
are =12‘/2 lb
eX
Pr
P
essi
ig's.p
./sq. in
. _
Fi
rm
tur
f
•< -
— Cr
~ -
OU X lu U WUCCJ3.
Plain bearings!
i o i / i-i- / ~ ^
Pr
e ssure = i c /2 io./b
1 Firm turf
7. 50- 1 0 whee 1 s
Roller bearing's
a-
i
Pressure = 20 lb./sq.in.
C
■o firm tun_
£
. 50
toll
- 10
sr b
J
wh
ear
20 1
Lur:
eels
mgs
Q —
—
o-
Pre
- 1
ssure -
Firm
L> . ] £>
4- Ill
n _
D
26x5 whee 1 s •
Plain bearing
s.
q.in
Pres
isure = 50 lb./s
I Sof t turf
/ -
36 x 8
Plain b
>vhe
ear
els.
ing
b./s
s.
q.ir
L.
l
Pre
ssure = 60 1
|
L_
500
8000
1000
Load per wheel, pounds
Figure 6.— Variation of rolling-friction coefficient with load per wheel; turf surface;
recommended inflation pressure.
•C
<u
■ —
^ '
<0
o •
o
c: .
o
’
.<0
V
O
Q;
0
22 x
— 1 1 r
1 0 - 4 wheels.
=d
1_ 1 - 1-
Plai
1 1
n bearings.
1 .
i
res
sure
= 1 2 y2 it
5./ £
q. 1
A
-4
a
i q _
J u A W v* *
Plain bear
ngs.
A _l _
n.
p
res sur e = 1 2 “4 1 b . / s q • i
1 I ' 1
7. 5 0 - 1 0 whee 1
11 U 1 A Is A 0
Recommended. |
nrft SUTP. - 20 1 b . / S C7. 1 n
4
r * ~
> -
8. 5
■D 1
0 - 1
0 wf
eel
s.
Recommended |
nressure = 20 lb./sq.in
c
‘i
—
—
p
—
36 X 8 wheels.
Plain bearing
S _
Recommended j
Dressure = 6 0 1 b . /s q . i r
1 . -
t
—
0 —
7
Inflation pressure, percentage
of recommended pressure
Figure 5. — Variation of rolling-friction coefficient with inflation pressure; concrete
surface; load per wheel, 940 pounds.
Inflation pressure, percentage
of recommended pressure
Figure 7. — Variation of rolling-friction coefficient with inflation pressure, firm turf
surface; load per wheel, 940 pounds.
174
REPORT NO. 583 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
all the other tires the surface was dry and firm. In
figure 7 is shown the variation of rolling-friction coeffi¬
cient with inflation pressure for all tires except the
26X5 size, the surface being dry and firm in all cases.
As explained before, for each test condition a series
of runs was made at different speeds with the intention
of determining, if possible, the effect of speed on the
rolling-friction coefficient. It is probable, however,
that the heat generated by the friction caused a con¬
siderable rise in temperature in the tires during a series
of runs which, according to the data of reference 1,
would result in an appreciable reduction in the rolling
friction. Since the runs were made with consecutive
increments of speed, the effect of speed would thus be
obscured by the temperature effect. The results of the
present tests, therefore, do not provide a true indication
of the effect of speed and are not so presented. Consid¬
eration of these results and of the data presented in
reference 1, however, indicates that the effect of speed
is probably slight in any case.
Each value of the rolling-friction coefficient given
in the table and figures is the average of the several
runs made at various speeds and with varying tire
temperature, as previously mentioned. The average
tire temperature was probably very nearly the same for
all conditions with all tires except for those of the
standard type. Tests of the standard tires were made
in generally cooler weather and, consequently, the
values of rolling-friction coefficient are possibly slightly
higher relative to the values for the other tires than
would be the case had the temperature conditions been
comparable. The speed range for the tests on the
concrete runway was from 5 to 45 miles per hour,
whereas on the turf surface the range was from 5 to
30 miles per hour. The two groups of tests, never¬
theless, are sufficiently comparable in view of the
probable small effect of speed.
The results of the take-off calculations are shown
in figure 8. Values of the take-off ground run were
calculated for two hypothetical airplanes, one of
moderate loading and the other of high loading. Sev¬
eral values of rolling-friction coefficient covering the
range encountered in the tests were assumed for each
case. Figure 8 shows the increase in ground run for
given rolling-friction coefficients as a percentage of
the distance required with no friction plotted against
the corresponding coefficients.
DISCUSSION
Rolling-friction coefficients. — On the concrete run¬
way the rolling-friction coefficients obtained ranged
from 0.009 to 0.035. The coefficients increased some¬
what with increasing load for all wheels and tires,
the variation being approximately linear and of similar
magnitude for all cases. Likewise, the coefficients
increased almost linearly with decreasing inflation
pressure, although in this case there were appreciable
mo
\ 90
3
o
3 80
C
3 70
k
u
3 60
o
c
Q>
s. 50
o
i
3
40
T 30
<0
<0
3
3
k
O
k
20
10
—
IQ
q.ft.
/hp
w
Pr
.ng" loading = 12.7 lb./s
wer loading" = 10.0 lb.
'ound run (/u= 0) = 525 ft.
1 1 1
javily loaded airplar
ing" loading" = 19.0 lb./
iwer loadings 15.0 lb.
-ound run (u = 0)- 1340
—
G i
- He
W
Pc
Gl
e
sq. ft.
/hp.
ft.
X
/
/
J
|
/
1
x
/
X
X
X
O .01 02 03 . 04 . 05 . 06 .07 . 08
Rolling- friction coefficient, /jl
.09
Figure 8.— Calculated effect of rolling-friction coefficient on take-off.
differences in the magnitude of the variation for the
different tires.
The effect of replacing the roller bearings in the
8.50-T0 wheels with plain bearings was to increase
the over-all rolling-friction coefficient by about 0.007,
the increase being sensibly independent of load and
representing more than 50 percent of the original values.
Of the three types of wheels and tires tested, the
extra low-pressure type gave the highest values of
rolling-friction coefficient and the low-pressure type
with roller bearings provided the lowest values. The
coefficients for the standard wheels and tires were
slightly higher than those for the low-pressure type.
Increasing the values for the low-pressure tires by
the difference in coefficients observed between the
values for the plain and roller bearings in order to
obtain a fairer comparison would, however, raise the
values for these tires somewhat above those for the
standard tires. For different sizes of wheels and tires
of a given type, the results do not show any consistent
relation between tire size and rolling-friction coefficient.
For the tests on the turf surface, there were, of
course, factors contributing to the over-all resistance
that were not present on the smooth hard surface, such
as the energy loss incurred by depressing the grass and
earth and also the energy loss to the shock absorbers
and tires associated with the unevenness or roughness
of the surface.
In general, the values of rolling-friction coefficient
derived from the tests on the firm turf surface averaged
about twice those obtained on the concrete runway for
corresponding conditions, the range of coefficients
found being from 0.023 to 0.054. The coefficients
THE ROLLING FRICTION OF AIRPLANE WHEELS AND TIRES
175
decreased slightly with increasing load for the low-
pressure wheels and tires and for the 30X13-6 extra
low-pressure wheels and tires. The 22X10-4 extra
low-pressure size showed a considerably greater varia¬
tion in the same sense. The effect of varying load was
not determined for the standard-type wheels and tires
on the firm turf surface.
Decreasing the inflation pressure resulted in a small
reduction in the friction coefficient in the case of the
standard and low-pressure tires. The values for the
30X13-6 tires appeared to be very nearly independent
of inflation pressure, whereas the 22X10-4 tires
showed a fairly large increase in the coefficient with
decreasing inflation pressure.
The different types of wheels and tires were in the
same order of merit, as regards rolling-friction coeffi¬
cient, for the firm turf condition as for the concrete run¬
way. In general, the larger tires of each type offered
greater resistance to rolling than the smaller size for
comparable conditions.
Only the 26X5 and the 36X8 standard-type wheels
and tires were tested on the soft turf surface and these
only for various loading conditions. The values for
this condition were about twice those obtained with the
36X8 wheels and tires on the firm turf surface and
were of approximately the same general magnitude for
both sets of tires, the coefficients ranging from 0.064
to 0.077. The larger size showed decreasing rolling-
friction coefficients with increasing load whereas the
values for the smaller tires increased slightly with
increasing load.
Effects on take-off. — Some indication of the effects
on the take-off ground run that would result from the
differences observed in the rolling-friction coefficients
corresponding to the various conditions may readily
be obtained by cross reference between figure 8 and
figures 4 through 7. It may be seen from figure 8 that
the effect of rolling friction on the take-off will be much
greater for a heavily loaded airplane than for one of
moderate loading even when considered, as in the figure,
on a percentage basis. For convenience, only the heavily
loaded airplane will be considered in this discussion.
Obviously the ground-surface condition is the vari¬
able having the greatest effect on the rolling-friction
coefficient, and hence on the take-off distance. The
distance required to take off on the firm turf would
average about 9 percent longer than on the concrete
runway, while on the soft turf surface it might be as
much as 35 percent longer.
The variation in rolling-friction coefficient on the
concrete surface between the highest and lowest loads
tested would result in a difference of only 1 or 2 percent
in the take-off distance. On the turf surfaces, the effect
of varying load on the take-off would likewise be very
small in most cases although, for the 36X8 tires on
the soft turf surface, the variation in friction coefficient
with load is sufficient to cause about 11 percent differ¬
ence in take-off distance. Inasmuch as the load on the
wheels of an airplane is continually decreasing during the
take-off ground run, the rolling-friction coefficient will
likewise be changing. In most cases, however, this
variation can be neglected in take-off calculations
without serious error or can be allowed for satisfactorily
in any case by assuming a constant value of rolling-
friction coefficient corresponding to the load inter¬
mediate between the static load and the load at the
end of the run prior to the pull-off.
The effect on the take-off of moderate differences in
the inflation pressure of a given set of tires would
obviously be very small in most cases, probably result¬
ing in a difference of only 1 or 2 percent for as much
as 35 or 40 percent underinflation. For the cases show¬
ing an unusually large variation of friction coefficient
with inflation pressure, the effect might be as high as 6
percent.
Under similar conditions on the concrete runway the
take-off distance that would be required with the extra
low-pressure tires would be between 4 and 6 percent
longer than that with the standard tires. For the
low-pressure tires equipped with roller bearings, the
take-off distances would be slightly less than with the
standard tires, within 2 percent, and with plain bear¬
ings about 1 percent greater. The same conclusions
apply approximately to the firm turf condition.
In view of the generally small effect on take-off of
all the variables with the exception of the ground-surface
condition, the assumption of an average rolling-friction
coefficient corresponding to a given surface condition
should be satisfactory for ordinary routine calculations.
Where the greatest possible accuracy is desired in cal¬
culating take-off performance, the other factors — type
and size of the wheels and tires, wheel load, inflation
pressure, and wheel-bearing type — should also be con¬
sidered.
176
REPORT NO. 5S3 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
CONCLUSIONS
1. The values of rolling-friction coefficient obtained
on the concrete runway varied from 0.009 to 0.035;
on the firm turf surface, from 0.023 to 0.054; and on
the soft turf, where only the high-pressure tires were
tested, from 0.064 to 0.077.
2. The most important factor affecting the rolling-
friction coefficient was the character of the ground
surface.
3. For comparable conditions, either on a concrete
runway or on firm turf, the standard-type wheels and
tires had the lowest values of rolling-friction coefficient;
the values for the low-pressure tires were only slightly
higher. The highest coefficients were obtained with
the extra low-pressure wheels and tires.
4. In general, the variation in rolling-friction coeffi¬
cient with either wheel load or tire inflation pressure
was fairly small.
5. The rolling-friction coefficient was appreciably
greater for wheels equipped with plain bearings than
for the same wheels having roller bearings.
6. The effect on take-off of all the variables, with the
exception of the ground-surface condition, wasgenerally
quite small; so that, for ordinary calculations of take¬
off performance, the assumption of an average value of
rolling-friction coefficient corresponding to a given
ground-surface condition would probably be satis¬
factory. Where greater accuracy is desired, however,
the other factors, although of less consequence, should
nevertheless be considered.
REFERENCE
1. Holt, W. L., and Wormeley, P. L.: Power Losses in Auto¬
mobile Tires. Tech. Paper No. 213, Bur. Standards, 1922.
TABLE I. — ROLLING-FRICTION COEFFICIENTS
Stat-
Rolling-friction
Inflation
ic
coefficient,, m
Wheels
Bearings
per
wheel
tire
de-
flec-
pressure
Con-
Firm
tion
Soft
creto
turf
turf
Pounds
Itt.sq. in.
Inch cs
Extra low pressure:
1,240
12.5
2.55
0. 029
0. 035
940
12.5
2. 06
. 030
.011
22X10-4
Plain.
640
12.5
1.58
.025
. 054
►
940
10
2.50
. 028
.047
940
8
2.92
. 033
. 050
1,740
12.5
2. 82
.027
.046
1,340
12.5
2. 29
. 024
. 046
30X13-0-
_ do _
940
12. 5
1. 74
. 023
.047
940
10
1.96
.029
.049
940
8
2. 19
. 035
. 047
Low pressure:
1,540
20
2. 26
.013
.025
1,240
20
1.90
.010
. 023
7.50-10
Roller _
940
20
1. 52
. 009
. 029
940
16
1.78
.010
. 026
940
12
2. IS
.012
.026
1,740
20
2. 52
.013
. 030
1,340
940
20
1.93
.014
. 031
do
20
1.56
.010
.034
940
16
1.83
.013
. 029
8.50-10
Plain.
940
f 1,740
1 940
12
20
20
2. 22
2. 52
1. 56
.015
.020
.018
. 030
)
1
Standard:
1,240
50
.94
.018
I
(0. 070
26X5 .
. do _
940
50
. 76
.015
1
\ .071
640
50
.58
.013
r
1 .066
1,740
60
.80
.017
i
I .064
1,340
60
.67
.011
I
f .072
36X8 .
do _
940
940
60
60
.53
.53
.015
r
.037
1 .077
1
940
50
.62
.020
. 033
1
940
40
.69
.025
. 033
1
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., September 19, 1936.
Report No. 584
STRENGTH OF WELDED AIRCRAFT JOINTS
By W. C. Brueggeman
SUMMARY
The work described in N . A. G . A. Technical Report
No. 3Jf8 showed that the insertion of gusset plates was
the most satisfactory way of strengthening a joint.
The additional tests of the present series show that
joints of this type could be improved by cutting out
the portion of the plate between the intersecting tubes.
T and lattice joints in thin-walled tubing iy2 by
0.030 inch have somewhat lower strengths than joints
in tubing of greater wall thickness because of failure
by local buckling. In welding the thin-walled tubing ,
the recently developed “ carburizing flux” process was
found to be the only method capable of producing
joints free from cracks. The “ magnetic powder ” in¬
spection was used to detect cracks in the joints and
flaws in the tubing.
The strengths of chromium-molybdenum T, lattice ,
and butt joints were materially increased by heat treat¬
ment. Butt joints in chromium-molybdenum sheet and
tubing welded with low-carbon and chromium-molyb¬
denum welding rod and those welded by the “ car¬
burizing flicx ” process had about the same strength in
the ''bis welded ” condition. The chromium-molybde¬
num and carburizing flux welds were the strongest after
heat treatment.
INTRODUCTION
This investigation is a continuation of work started
in 1928 at the request of and with the financial assist¬
ance of the National Advisory Committee for x\ero-
nautics, and published by the Committee as Technical
Report No. 348: Strength of Welded Joints in Tu¬
bular Members for Aircraft. It covers additional tests
on joints reinforced by inserted gusset plates, tests of
joints made with low-carbon and chromium-molybde¬
num welding rods, and the recently developed “car¬
burizing flux” welds, and new tests made on T joints
in which the leg of the T was loaded as a cantilever
beam. Tests were also made on joints in thin-walled
chromium-molybdenum tubing. Joints were tested in
both the heat-treated and “as welded” conditions.
MATERIAL
Steel tubing and sheet of the following materials and
sizes were used :
C hromium-molybdenum steel
Tubing — 1 inch O. D. (O. D.=outside diameter)
by 0.035-inch wall.
P/2 inches (). D. by 0.020-inch wall.
U/2 inches O. D. by 0.058-inch wall.
iy2 inches O. D. by 0.083-inch wall.
Sheet — thickness 0.031, 0.0G3, 0.125, and 0.188 inch.
Mild-carbon steel
Tubing — 11/2 by 0.058 inch.
Sheet — thickness 0.063 inch.
The tubing and sheet complied with the following
Navy Department specifications:
C hromium-molybdenum steel
Tubing— 44T 18 1
Sheet — 47S14a
Mild-carbon steel
Tubing — 49T1
Sheet — 47Sl7a
The tensile strengths of ihe tubes from which I he T
joints were made are given in table I. Each value is the
average strength of two specimens cut from opposite
ends of the tube from which the members of the joints
were taken. When the joint was heat-treated the tensile
specimens were given the same heat treatment. Results
of chemical analysis of the materials are given in
table II.
TABLE I.— TENSILE STRENGTHS OF MEMBERS OF
T JOINTS
Joint No.
Figure
Tensile
A
strength
B
lb./sq. in.
lb./sq in.
0140
10
107, 500
107,500
0200
10
109, 600
i09, 600
H140
10
148. 100
155,500
11260
10
152,500
155, 500
K140
10
85, 900
85, 900
K260
10
83, 300
83, 300
L140
11
134, 900
134, 900
1.260
11
130, 100
130, 100
.1140
11
129,400
129,400
J260
11
125,800
125,800
OM 140
14
107, 400
102, 600
O M 260
14
102,800
102, 800
O M 440
14
107, 400
102, 600
HM140
14
149, 100
161, 400
TIM 260
14
149, 100
152, 900
KM 140
15
81,300
81, 300
KM 260
15
85, 200
85, 200
i This specification has been superseded by Navy Department specifica¬
tion 44T18a and supplement 44T18b. The tubing also complied with
the new specification.
177
TABLE II.— CHEMICAL COMPOSITION OF TUBING, SHEET, AND WELDING ROD
Material
Carbon
percent
Manganese
percent
Phosphorus
percent
Sulphur
percent
Silicon
percent
Chromium
percent
Molybde¬
num per¬
cent
Tubing:
Chromium-molybdenum steel:
1 inch 0. D. by 0.035-inch wall
0. 27
0. 43
. 57
0.01
0.012
0. 89
0.20
\y> inch O. D. by 0.020-inch wall -
.27
.01
.012
.94
.20
1 \(> inch O. D. by 0.058-inch wall
.34
.54
.022
.011
1.09
. 19
1 \t> inch O. I). by 0.058-inch wall
.34
. 50
.023
.010
1.08
. 19
Mild-carbon steel:
. 28
.24
. 52
. 019
. 019
.52
.020
. 016
Sheet:
Chromium-molybdenum steel:
0 031-inch thickness . _
.30
.42
.015
.008
.89
. 18
0.063- inch thickness _ _ _ _ _ _ _
.32
. 41
.016
.004
.90
.20
Welding rod: 1
. 17
1.02
.02
.02
.024
0. 38
.41
.90
.006
.58
1. 13
.20
1 The low-carbon steel welding rod was from the same lot used in the previous investigation. The chemical composition is given in N. A. C. A. Technical Report No.
318, table VII.
PREPARATION OF SPECIMENS
INSPECTION FOR DEFECTS
Method. — Visual inspection of specimens of the pre¬
vious investigation showed that there were cracks in
some of the joints. It was found by experience that it
was impossible to detect all of the cracks by visual in¬
spection. Inasmuch as cracks may weaken the joint to
an indeterminate extent, it was considered desirable to
use a more effective method of inspection.
In 1922 William E. Hoke patented 2 a “method of and
means for detecting defects in paramagnetic material”
by magnetizing the object “while in proximity to mo¬
bile, finely divided paramagnetic material” such as iron
filings or powder. A crack lying across the magnetic
path presents a relatively high magnetic reluctance.
An appreciable difference in magnetic potential thus
exists between the two sides of the crack, and if close
to the surface there is an external leakage flux between
them. When the iron filings are brought into the field
of this leakage flux they are attracted to the edges of the
crack which is then indicated by an accumulation of the
filings. The test may be carried out by immersing the
object to be inspected in a fluid bath in which the iron
filings are suspended.
In 1927, Roux (reference l)3 described a method of
testing butt welds in steel plates by producing a mag¬
netic flux in the plate and obtaining a pattern of the
leakage flux by sifting iron filings onto a paper placed
on the weld. A defective weld having no penetration,
for example, has a higher magnetic reluctance than a
corresponding portion of the base metal. This is indi¬
cated by magnetic leakage from the metal into the air
around the defect, causing an accumulation of the
powder at the defect. The joint was magnetized by a
portable electromagnet with pole pieces which span
the weld. By properly interpreting the pattern as¬
sumed by the iron filings the operator can often detect
the presence of defects.
This method has been used in the United States by
Watts (reference 2).
Recently cle Forest (reference 3) 4 has developed a
technique for inspecting steel and iron for such defects
as cracks and other discontinuities. His technique is
similar in principle to that of Roux and Watts and
consists in suitably magnetizing the object, then
sprinkling the magnetic powder onto the surface.
The magnetic powder method appeared to offer a
solution to the problem of locating these cracks, and
arrangements were therefore made with Professor de
Forest to cooperate in the inspection of the joints used
in this investigation.
Seams. — Each piece of tubing and sheet was inspected
for defects before welding. The apparatus for detection
of seams in tubing is shown in figure 1. The tube A
was slipped over the copper rod B which was con¬
nected to the transformer C. An electric current in
the rod produced a circumferential magnetization in
the tube. Circumferential magnetization was used be¬
cause it was believed that any defects originating dur¬
ing the processes of manufacture would probably be
longitudinal. A current of from 200 to 300 amperes
was found to be satisfactory. D is an ammeter and E
is a current transformer for measuring the current.
The dust was applied from the shaker F.
Many longitudinal seams were found. Typical indi¬
cations are shown in figures 2 and 3. The seams were
usually less than 1 inch long although some were 4
or 5 inches in length. The seams generally occurred
singly, but sometimes in groups of two or more as in
figure 2.
2 U. S. Patent No. 1426384, Aug. 22, 1922.
3 A more complete description of the technique of testing welds by
the magnetographic method is given in a paper “Magnetic Testing of
Welds’’, published in the Welding Engineer, vol. 15, no. 2, February 1930,
p. 31. This paper was translated from material obtained from the
laboratory of La Soudure Autogfene Frangaise.
*• See also U. S. Patent No. 1960898, May 29, 1934.
STRENGTH OF WELDED AIRCRAFT JOINTS
179
Where defects were indicated, several of the tubes
were sectioned as indicated by the dotted lines in fig¬
ures 2 and 3, and examined under the microscope. The
seams were in approximately a radial direction and
varied in depth from about 0.003 to 0.015 inch. They
were partially filled with iron oxide. The etched cross
section at A, figure 2, shows the surface of the tube and
the seam to be decarburized. It is probable that the
Some of the tubes had grooves on the inside surface
as shown at B and C, figure 3. These grooves were
visible without using the magnetic powder and appar¬
ently were formed when the tube was drawn over a
mandrel. When the powder was applied, as in the
inspection for seams, the grooves were indicated by
longitudinal accumulations of powder extending the
full length of the tube as in tubes 5 and G, figure 3.
Ficure 1. — Apparatus for detecting seams in tubing by t lie magnetic powder method of inspection. The tube A was magnetized by a
heavy alternating current produced in the copper rod B by the transformer C. The ammeter D was used with the current transformer
E to measure the current. The magnetic powder was applied to the surface of the tube by means of the shaker F. The iron-cored coils
G were used when a portable magnetizing apparatus was desired.
seams originated during the fabrication of the steel and
were caused by surface imperfections being rolled or
drawn into the material.
There were seams on the inside as well as the outside
of the tubes. It is difficult to inspect the inside sur¬
faces, particularly of long tubes of small diameter.
However, deep seams which occurred on the inside could
usually be detected by applying the dust on the outside.
It is believed that very few of the seams could have been
detected visually without the magnetic powder.
Seams were found in the carbon-steel tubing and in
two sizes (114 by 0.058 inch and 1 by 0.035 inch) of
chromium-molybdenum steel tubing.
The tubes were not rejected because of the presence
of seams and grooves. The joints did not rupture at
these defects and there was no indication that the
strength was lowered under static loading.
The effect of seams and grooves on the torsional and
fatigue properties of the tubing was not investigated.
Cracks. — All welded joints were examined for cracks
by means of the magnetic powder method. The heat-
treated joints were inspected again after heat treat¬
ment. The technique was similar to that employed for
detecting seams.
The electromagnet shown in figure 4 was used to mag¬
netize the joints. It consists of a solenoid having about
180
REPORT XO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
500 turns of No. 18 magnet wire and two steel pole pieces
connected by a steel bar. When inspecting joints in
tubular members V blocks were used on the ends of the
pole pieces. These could be rotated about the axes of
the pole pieces. The joint was placed in contact with
the V blocks in such a manner that the flux passed
magnetic circuit is not so efficient as one in which the
core is continuous, as in figure 4. A current of about
1 ampere was found to be satisfactory for both kinds
of apparatus.
When inspecting the sheet samples the electromagnet
(fig. 4) was used, replacing the V blocks on the pole
Figure 2. — Seams in chromium-molybdenum tubes lx/o, inches O. D. by 0.058-inch wall. A microscopic exam¬
ination was made at the cross section shown by the dotted line. The seam at point A is shown in
the photomicrographs (left) in the unetched cross section and at a lower magnification (right) after
the cross section had been etched in 1-percent Nital.
through the portion of the joint it was desired to exam¬
ine. It was sometimes more convenient to use a port¬
able magnetizing apparatus, in which case the two coils
F (fig. 1) were used. These are of the same size as the
coil shown in figure 4 and are connected in series. Each
coil has a laminated iron core about 6 inches long which
is placed in contact with the members of the joint. It
was necessary to use the coils close together because the
pieces with flat blocks. No cracks, seams, or other
defects were found in the sheets either before or after
welding.
Cracks were found in all joints made in thin-walled
chromium-molybdenum tubing l1/} by 0.020 inch in
which low-carbon welds were made. Figures 5, 6, and
7 show locations of cracks as outlined by the magnetic
powder. In the photomicrographs taken at point A,
Figure 3. — Seams and grooves in other chromium-molybdenum tubes 1% inches 0. D. by 0.058-inch wall. The seam at point A, tube 3, is
similar to the one shown in figure 2. The powder accumulations on tubes 5 and 6 are caused by grooves inside the tube as shown in
the end view of tube 6. The photomicrograph C shows the cross section adjacent to groove C.
181
182
REPORT NO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
figure 5, there are cracks apparently following the
grain boundaries that existed when the steel was in
the austenitic state. There were cracks on both the
inner and outer surfaces of the tube and one goes com-
Figure 4. — Examining a lattice joint for cracks by the magnetic
powder inspection.
pletely through the wall. These cracks are partly filled
with oxide.
The majority of the cracks were less than one-half
inch long although in the y joints shown in figure 7
they extend on one side nearly half the circumference
of the tube. The cracks occurred in the base metal
of joints in thin-walled tubing made with low-carbon
welds, usually about one thirty-second inch from the
toe of the fillet, and ran parallel to the fillet.
WELDING
The specimens were welded in the same manner as
those of the previous investigation by Mr. J. C. Ivush-
ner, of the Keystone Aircraft Corporation. The weld¬
ing supervisor was II. S. George, research engineer of
the Union Carbide and Carbon Research Laboratory.
The procedure specifications were prepared for the pre¬
vious investigation by a Committee on Welding Pro¬
cedure of the American Bureau of Welding, and are
given in N. A. C. A. Technical Report No. 348. The
welder complied with the qualification tests of the pro¬
cedure specifications.
The welding supervisor witnessed all of the welding.
In his opinion the joints welded with low-carbon rod
cations had been prepared to apply only to this type
of weld).
Four sets of welding equipment were loaned by man¬
ufacturers. They are designated as A, B, C, and 1), as
shown in figure 8. The set used for each joint is indi¬
cated at the bottom of the figure showing the test results.
Figure r>, — Typical magnetic powder indications of cracks formed dur¬
ing welding in a lattice joint made from thin-walled chromium-molyd-
denum tubing (1% inches O. D. by 0.020-inch wall). The photomicro¬
graphs taken at point A show the cross section indicated by the dotted
line (upper) unetched and (middle) etched in 1-percent Nital. Low-
carbon welding rod and a neutral flame were used in welding this joint.
STRENGTH OF WELDED AIRCRAFT JOINTS
183
All tubular joints were welded in a suitable jig that
held the members in alinement. The time required to
complete the weld after the members were set up in the
jig was recorded.
It was found impossible to avoid cracks in thin-
wallecl tubing when welding with a low-carbon rod.
Several expedients that were tried in attempting to
avoid cracks were: Preheating the tubes at the joint
before welding by heating to a red heat with the torch;
removing all scale adjacent to the weld with emery
cloth; minimizing contraction stresses by heating one
side of the joint with a torch while welding the other
side; using various sizes of beads; exercising care to
prevent excessive penetration; trying both forward and
backward welding; using small sizes of torch tips and
Figure 6. — Cracks in butt joints made with thin-walled tubing (1%
inches O. D. by 0.020-inch wall) as indicated in the magnetic powder
inspection. These joints were welded with low-carbon rod and a
neutral flame.
of welding rod; and, where the end of a tube was
welded to the wall of another continuous tube, sawing
out the portion of the continuous tube which is cov¬
ered by the end of the intersecting tube. None of these
CD
expedients was successful.
After unsuccessful attempts to weld the thin-walled
tubing the welding supervisor suggested that a new
welding process recently invented by him might prove
successful. This process (reference 4) 5 utilizes the car¬
burized film caused by the absorption of carbon by
steel when the latter is heated to a temperature some¬
what below its melting point, in a carburizing at¬
mosphere.
The usual type of oxyacetylene torch may be used;
the gas flow is adjusted, however, to have an excess
of acetylene, producing a carburizing atmosphere.
The surface of the base metal when heated to the proper
temperature absorbs carbon from this atmosphere. In¬
5 See also U. S. Tatent Xo. 1973341, Sept. 11, 1934.
38548—38 - 13
creasing the carbon content of steel lowers the tem¬
perature at which it may be fused; thus a thin liquid
film of melted steel is formed on the surface of the base
metal at a temperature several hundred degrees lower
than the fusion temperature of the base metal itself.
The film, which may be recognized by its characteristic
wet appearance under the flame, forms ahead of the
Figure 7. — Cracks in T joints made with thin- walled tubing (1% in.
O. D. by 0.020 in. wall) as indicated in the magnetic powder in¬
spection. Low-carbon welding rod and a neutral flame were used
in welding these two joints.
advancing melted filler metal and acts as a flux by pre¬
venting oxidation and causing intimate union between
the base and the filler metals. The fluxing action of
this film makes it unnecessary to heat the base metal to
its melting point. The technique is somewhat like braz¬
ing in this resnect, although all of the characteristics of
a true weld are attained. A special rod containing
carbon, manganese, and silicon as alloying elements in
the iron base is used.
184
REPORT NO. 584 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 8. — The torches and equipment used. Each set was used to weld about an equal number of specimens.
STRENGTH OF WELDED AIRCRAFT JOINTS
185
It was believed that welds made in the thin-walled
tubing by this process would be less susceptible to
cracking because it would be unnecessary to fuse the
base metal. Some preliminary welds were made by
the carburizing flux process, and after several days’
practice the welder, who had little previous experience
with this process, was able to make welds in the thin-
walled tubing in which no cracks could be detected.
A series of T, lattice, and butt joints was made in
this tubing by the carburizing flux process, using a
rod having the chemical composition given in table II.
No indications of cracks could be detected by means
of the magnetic powder inspection.
A brief description of some special features that
were employed in making carburizing flux welds in
thin-walled tubing is as follows:
(1) The luminous feather in the welding flame, indi¬
cating the amount of acetylene in excess of that re¬
quired for complete combustion, was maintained at a
length of from 2 to 2 y2 times the length of the inner
cone.
(2) Backward welding (see fig. L, N. A. C. A. Tech¬
nical Report No. 348) was used; that is, the torch was
held so that the flame issued in the opposite direction
to that of the progressing bead. This was done to
retard the rate of cooling of the fillet during the critical
interval when the base metal was most susceptible to the
formation of heat cracks. It is believed that less oxida¬
tion of the unwelded base metal occurs in backward
welding and that the base metal is less likely to be over¬
heated. “Forward” welding was used for all tubes hav¬
ing a wall thickness of 0.035 inch or more welded by the
carburizing flux process and for all low-carbon welds
made by the regular neutral flame technique.
Position of torch for
''backward” welding
I igure 9. — Diagram' of bead used in making carburizing flux welds
in thin-wallcd tubing' showing how the puddle was made to
solidify in increments.
(3) An additional precaution consisted of manipu¬
lating the torch so as to confine the melted puddle to
as small an area as possible. Instead of maintaining
a continuously melted puddle as would be done on
heavier base metal the fillet was made to solidify in
increments. Starting with a puddle (fig. 9) having a
long slope from the top of the fillet a to the point of
farthest advance c, the torch was withdrawn until the
first puddle had begun to solidify on the bottom (still
maintaining the carburizing atmosphere), then more
reinforcement a c d was added. After this layer had
begun to solidify along the line c d, the next layer
d c f was added and so on. The carburized film that
was formed on the surface of the overlapping layers
as well as on the base metal insured a continuous
bead, the layers being welded to each other in the
same manner as they were welded to the base metal.
Thus the minimum amount of heat was applied to the
joint and the length of the puddle, measured in the
direction of welding, was kept as short as possible,
minimizing the amount of the contraction as the pud¬
dles cooled.
Chromium-molybdenum welding rods having the
chemical composition given in table II were used to
make some of the butt joints that were to be heat-
treated after welding.
Henceforth joints welded with low-carbon rod, chro¬
mium-molybdenum rod and those welded by the car¬
burizing flux process are termed low-carbon welds,
chromium-molybdenum welds, and carburizing flux
welds, respectively.
The butt joints in steel sheets were made with rein¬
forcements on each side about equal to half the sheet
thickness, making the total thickness of the weld about
twice that of the sheet. This type of weld was used to
provide a symmetrical specimen and, in the low-carbon
welds, to permit the maximum “picking up” of alloying
elements from the base metal. Table ITT gives the
average thickness of reinforcement (for both sides) of
the butt joints in percentage of the base metal thickness.
TABLE III.— AVERAGE TOTAL THICKNESS OF REIN¬
FORCEMENT OF BUTT JOINTS IN PERCENTAGE OF
BASE METAL THICKNESS
Sheet thickness, inch
Tube
size 1 R
Type of weld
by
0.031
0.063
0.125
0.188
0.058
inch
Low-carbon, percent.-- _ _
143
126
122
83
•113
Carburizing flux, percent _
189
121
89
85
124
Chromium-molybdenum, percent _
235
100
111
92
HEAT TREATMENT
All heat treatment was done by the Division of Metal¬
lurgy. National Bureau of Standards. For the normal¬
izing and hardening operations the temperatures given
in the chart “Heat treatment and inspection test of
aircraft metals — Naval Aircraft Factory”, serial no.
ML-79L. September 15. 1932, were used.
The lattice and T joints were hardened by heating at
1.600° F. in a gas furnace for 1 hour and quenching in
oil. They were tempered at 900° F. for 1 hour and
cooled in air. Tensile and compressive specimens of the
tubing from which the joints were made were given
the same heat treatment.
186
REPORT NO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
IDENTIFICATION OF T AND LATTICE JOINTS
The butt and cross joints that were heat-treated were
hardened by heating at 1,600° F. for 45 minutes and
quenching in oil. They were then tempered at 500°,
700°, 900°, and 1,100° F., respectively, for 45 minutes
and cooled in air. Specimens that were normalized
'/s" protrusion of plate
welded to tubes
As in the previous investigation, three specimens were
made of each joint. When reference is made to a group
of triplicate specimens of the same design a specimen
Z/6 " protrusion of plate
welded to tubes
A
-E
28:3
3(3
//a" X 0.058"
heat treated
fS tress in A , (Me/ 1),
a J " - B , (P/A), and
efficiency of b for
C). I in. set at midspan
200
.160
■%
<0
b
a
<5
o
120
80
<a 50
o
0)
* 0
-Torch
-b cd
G 14 1
G 1 4 2
G 143
to
k.
O -K
- J J .k
d
oi%
%
200
.6
6-/60
b
^ 120
q
I 80
*s
<0
(0
h 40
U>
0
o Ultimate stresses and
efficiency
200
A-
0
— c
7 t
7 C
n
T
D
GZ61
G262
G 263
PQ
Ah
S' 8
o.b b
°.G h
k;
s.
ki
■5
<0
A
Ci
05
0}
80
'■n
* 40
h
f>
0
LaC
1
Q
—t
1C
: d
-a
.
H 1 4 1
H 1 4 2
H 1 4 3
Cl
o +.
>> b
k;
s.
kj
-e
2-5
'3/2*
.2
0.063"
' T
/N
B
— V/'1
183
"XT
m
T
IZ2" x 0.058"
heat treated
240
200
•S
160
tr¬
ee
k
QJ
Q.
55 120
o
I
*60
(O
0)
h
<0 40
0
X
*1
— c
7 t
3 C
B J
u
T
H261
H262
H263
PQ
-| JOs.
o s-
C:
o o
0 0
°.o h
§
f A
1,283
s~\
B
4
H“\ i
* I/2" x 0.058"
carbon steel
/,2&3.^ ^3/24
A
Zm" protrusion
of plate welded
to tubes
-*---0.063"
B
3
T
* t/z" x 0.058"
carbon steel
4
6-/20
<o
b
h 80
4
§
<0
<0
QJ
h
k)
40
0
<566
A A 4
—deb
pc
Crd
rrr
PQ
V
O ■
jo^b
K 1 4 1
K 1 4 2
K 143
o o
k:
kj
A (A
6-/20
*0
b
h 80
4
s
§- 40-
-c da
§ dBiiU g., *
CQ
S.
k k
io
K26 1
K262
K263
.G h
I
Figuhe 10. — Results of the transverse test of T joints made wi
and low-carbon welds. Tube B was loaded in tension with
permanent set of 0.1 inch at midspan was determined, also
for both loads, also the tensile stress and efficiency for tu
were held at 1,600° F. for 1 hour and cooled in air.
To prevent oxidation a reducing atmosphere was main¬
tained in the furnace for all heating operations above
500° F.
lh chromium-molybdenum steel (upper) and carbon steel (lower)
tube A supported at a span of 15 inches. The load producing a
the maximum load. The stress Mc/I for tube A was computed
be B.
number terminating in a cipher is used, thus, 260 ; speci¬
mens numbered 261, 2(52, and 2(53 are the triplicate spec¬
imens comprising joints 260. Letters prefixed to the
specimen numbers have the following meaning:
STRENGTH OF WELDED AIRCRAFT JOINTS
187
Meaning
Letter
G Joint made with D/o by 0.058-inch chromium-
molybdenum tubing and low-carbon weld
H Joint made with 1 y2 by 0.058-inch chromium-
molybdenum tubing and low-carbon weld,
heat-treated after welding
J Joint made with 1 y2 by 0.020-inch chromium-
molybdenum tubing and low-carbon weld
K Joint made with 1 y2 by 0.058-inch carbon-steel
tubing and low-carbon weld
L Joint made with 1 y2 by 0.020-inch chromium-
molybdenum tubing and carburizing flux weld
M Cantilever loading of T-joint
increasing loads, the load producing a permanent set
of 0.1 inch at midspan was determined (loading I).
As it was believed that a determination of the bending
strength of tube A would be more valuable than the
results of loading II (see p. 25 and fig. 7, N. A. C. A.
Technical Report No. 348), in which tube A was sup¬
ported at the joint and tube B loaded until failure
occurred, loading / was continued to failure.
Unreinforced T joints, 140, were tested in the heat-
treated condition, H140, figure 10.
In an attempt to improve the design of the T joints
in the previous investigation, joints 260 were made by
inserting a T-shaped gusset plate in slots in the tubes,
allowing the edge of the plate to protrude slightly,
G260, H260, and K260 (fig. 10).
Carbon-steel joints, K140 and K260 (fig. 10) were
tested.
Since the transverse strength of tubing increases
© ©
with a decrease in the ratio of diameter to wall thick¬
ness, in order to investigate joints in tubing having a
/3z" protrusion of plate
welded to tubes
'/as" protrusion of plate
welded to tubes
•9
G-
< o
b
Q.
160
/SO
"Air
Q)
§
10
10
U)
h
80
dO
0
Torch
-c do
~B1
LI
L 1 4 2
L 143
cq
30\^
o’ ^
£
kl
0
%
L
0)
W
.160
120
C5
Q>
C5
<o
to
(U
h
80
dO
0
Al
rj
□
— c
A:
1
ib
T
>
L26 1
160
L262
L 263
CO
30 o 't-
-sb
.9) 9>
.0 0.
$
ki
o',
O
i o
V
Qj
Q.
=9
05
05
05
120
80
lo
to
0)
b
CO
dO
0
— c
it
it)
Ai
A
'
A
J141
J1 42
J 143
to
-30 o-p
ft®
0%
%
b
Q.
■9
io
b
Q.
=9
05
§
160
120
80
<0
to
<U
b
<o
dO
0
-c
—
A-1
>—
O
—t
c
' d
B--
> <
J26 1
J262
J263
CO
V
30
ftb
§
Figcre 11. — Results of transverse test of T joints made with thin-walled chromium-molybdenum steel tubing.
T JOINTS
TRANSVERSE LOADING
Drawings of the T joints are shown in figures 10 and
11. The method of testing the T joints was changed
slightly from the procedure followed in the previous
investigation. Tube A was supported on rollers over
a span of 10 diameters (15 inches) on the platen of a
pendulum hydraulic testing machine (fig. 6, N. A. C. A.
Technical Report No. 348). The free end of tube B
was gripped in the lower jaws of the machine and load
applied. By applying and releasing a succession of
greater ratio of diameter to wall thickness than is or¬
dinarily used in aircraft construction, joints J140,
J260, L140, and L260 (fig. 11) were included. Chro¬
mium-molybdenum tubing iy2 by 0.020 inch was used.
For comparative purposes two nominal stresses in
tube A of the T joints were computed, corresponding to
loads in B which produced in A a permanent set of
0.1 inch, and failure, respectively. These stresses were
computed like moduli of rupture, by dividing the bend¬
ing moment at midspan by the section modulus of the
original tube (that is, the gusset plates, if any, and tube
B were neglected) ; they are plotted in figures 10 and 11.
G1 43
ge&TT-y-.
-
0283
.
H283
J 262
K141
H 143
K 261
J]43
L 143
m
188
Figurk 12. — T joints after failure under the transverse loading.
STRENGTH OF WELDED AIRCRAFT JOINTS
189
It should be emphasized that while these stresses are a
convenient means of comparing the results obtained on
different joints of the same size and same size of tubinsr,
the extent to which they could safely be used with other
sizes of tubing and different relations of bending
moment to shear has not been investigated.
The stresses in tube B at 0.1 inch set and at failure
of tube A have been plotted in figures 10 and 11. The
ratios of these stresses to the tensile strength of tube B
have been denoted the efficiencies of tube B. They indi¬
cate the extent to which the strength of the material
of tube B has been fully utilized in the joint. The effi¬
ciencies are also shown in figures 10 and 11.
Typical failures of T joints under transverse load¬
ing are shown in figure 12. The failures are also in¬
dicated in figures 10 and 11 by the specimen numbers
1. 2, and 3 at the points of failure. Thus for joints
GUO, figure 10, the numbers 1, 2. and 3 indicate that
specimen Gill failed by buckling and specimens G142
and G143 failed at the bottom of tube A at the loca¬
tions shown. All the failures at the top of tube A
were buckling failures. The failures at other locations
were ruptures of either tube A or the weld.
The ratio of the stress for 0.1 inch set to the ulti¬
mate stress was much higher for the heat-treated joints
than for those which had not been heat-treated. Speci¬
mens H142, H143, and H263 failed before the set be¬
came 0.1 inch. The strengths of the gusset-reinforced
joints G260 under transverse loading were about 31
percent greater than those of the unreinforced joints
GUO, and the stress which produced a 0.1-inch per¬
manent set in tube A was about 37 percent higher.
I he heat-treated joints H260 were about 26 percent
stronger than the unreinforced heat-treated joints
H140.
The carbon-steel joints KUO and K260 had about
the same strength. Thus there appears to be little
advantage in adding a reinforcing gusset to a carbon-
steel T joint.
T joints LUO and L260, figure 11, made with thin-
walled tubing by the carburizing flux process, had
somewhat lower strengths under transverse loading
than joints made from heavier tubing because the thin-
walled tubing buckled under lower stresses. There
were cracks in joints J140 (see fig. 7), made with low-
carbon welds, that greatly lowered the strength of
these joints. Cracks were also found in joints J260,
made in the same way. The cracks in joints J260
were smaller and did not lie in such a highly stressed
portion of the joints as in joints J140. They appar¬
ently did not lower the strengths, which were about
the same as those of joints L260. All of the joints
made with thin-walled tubing failed before develop¬
ing 0.1-inch set.
Figure 13. — Applying the cantilever leading to a T joint. The weights
D were applied by turning the turnbuekle C. The permanent set
at E was measured by the dial micrometer.
190
REPORT NO. 584 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Me
1
computed
for these
sec tions
$
da 1.883 B
• 1 ✓
* r <•
■r/z'y 0.058'
JC .
-15"
p-q q-r
GM141 GM 1 4 ]
GM142 GMJ42
GM 14 3 GM 143
-A
,-t,8S3 B E
p-q q-r
HM142 HM142
HM143 HM 143
0 _ i _ i _ i _ i _ i _ i
HM261 HM261
HM262 HM2G2
HM263 HM263
Figure 14. — Results of the cantilever test of T joints made with chromium-molybdenum steel and low-carbon welds. The stress M c/I was
computed at section p-q in tube A (see upper left diagram) and at section q-r in tube B tor the load producing 0.1 inch permanent set
at E and for the maximum load.
STRENGTH OF WELDED AIRCRAFT JOINTS
191
CANTILEVER LOADING
It was believed that information regarding the
strength of T joints in which the leg of the T was
loaded as a cantilever beam would be valuable. Joints
were therefore tested as shown in figure 13. Tube A
was held in a vertical position between two pins, the
upper of which was fixed and the lower was fitted with
rollers, allowing movement in a vertical direction. The
load was applied by turning the turnbuckle C until
the weights D were raised. The dial F measured any
movement of the support during loading. No appre¬
ciable movement was observed. The pins supporting
tube A were spaced 15 inches apart and the length
along tube B from the center line of tube A to the
t
KMI42 KM ] 4 2
KM143 KM 1 43
any) were neglected in computing the section modulus.
Typical failures are shown in figure 16.
Joints GM260, reinforced by an inserted gusset plate,
were about 19 percent stronger than the unreinforced
joints GM140. Each failed in tube B where the tube
had been annealed during welding.
Joints GM260, reinforced by an inserted gusset plate,
were stronger than joints GM440, reinforced by trian¬
gular gusset plates.
The unreinforced heat-treated joints HM140 failed by
tube B tearing out of the wall of tube A on the upper
side. The reinforced heat-treated joints HM2G0 were
about 37 percent stronger than joints IIM140 and failed
by rupture of tube B at the end of the gusset plate.
1
KM263 KM263
Figure 15. — Results of the cantilever test of T joints made with carbon steel and low-carbon welds.
point where the load was applied was 15 inches. The
load producing 0.1-inch permanent set at the point of
loading E was determined, as well as the maximum
load. A dial micrometer was used to measure the
permanent set.
Figure 14 shows the test results for “cantilever-
loaded"' T joints made with chromium-molybdenum
steel in both “as welded” and heat-treated conditions.
Figure 15 shows test results for similar joints made
with carbon steel “as welded.”
In figures 14 and 15 the stress at section p-q in tube
A and at section q-r in tube B has been plotted for the
load which produced a permanent set of 0.1 inch at
point E. The stress at failure has been plotted also,
t he stresses were obtained by dividing the bending mo¬
ment by the section modulus. The guesset plates (if
The carbon-steel joints KM140, figure 15, failed by
bending of tube B without rupturing or buckling. In
joints KM260 tube B buckled on the compression side
at the end of the gusset plate.
LATTICE JOINTS
The form of specimen and method of testing used
for lattice joints was the same as in the previous in¬
vestigation. The angle between tubes A and B and
between B and C (figs. 17 and 18) was 60°. The ends
of tubes A and C were supported on pin bearings in the
testing machine as shown in figure 8, N. A. C. A.
Technical Report No. 348, and tube B was loaded in
tension until the joint failed.
The new type of inserted gusset reinforcement was
also used for the lattice joints. Figure 17 shows joints
38548— 3 S - 14
192
REPORT NO. 584 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 16. — Cantilever-loaded joints after failure.
STRENGTH OF WELDED AIRCRAFT JOINTS
193
GT60 made with chromium-molybdenum steel in both
“as welded” and heat-treated conditions. Figure 18
shows joints J7G0 and L760 made in thin-walled chro-
G763 G763 G763
joints, L630 and K630, figure 18, were made without
reinforcement with thin- walled chromium-molybdenum
and carbon-steel tubing, respectively.
G 1 02 2
G 1 023
G 1 0 22 G 1 022
G 1 0 23 G 1 023
H633
H633 H633
H762
H763
H762 H762
H763 H763
H 1 012
HI 013
H 1 01 2 H 1 0 12
H1013 H 1 013
Figure 17. — Test results for lattice joints made with chromium-molybdenum steel and low-carbon welds.
To determine the effect upon the strength of the
joint of tubes lying in a plane at right angles lo the
plane of the tubes to which the loads are applied, lat¬
tice joints G1020 were made (fig. 17).
mium-molybdenum tubing, and joints K760 made in
carbon-steel tubing.
The unreinforced lattice joints HG30, shown in figure
17, were tested in the heat-treated condition. Other
194
REPORT NO. 584- — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The strap-reinforced joints G1010 tested "as welded”
in the previous investigation were found to have a
high strength. To determine the strength of this type
of joint in t he heat-treated condition, joints H1010
shown in figure 17, were made.
plotted on the right side. Et is the percentage of the
tensile strength of tube B developed by the joint and
Ec is the percentage of the compressive strength of
tubes A and C (both cut from the same length of
tubing) developed by the joint. The location of the
L633
L633 L 633
L763
L763 L763
K632
K633
K632 K632
K633 K633
0.063"
K762
K763
K762 K762
K763 K763
Figure 18. — Test results for lattice joints made with carbon-steel tubing and low-carbon welds (lower) and with thin-walled
chromium-molybdenum steel tubing (upper).
The results for the lattice joints are plotted in the
same manner as in the previous investigation. In fig¬
ures 17 and 18 the maximum tensile stress in tube B
is plotted on the left side of the graphs. The tensile
efficiency Et and the compressive efficiency Ec are
failure is shown on the drawings. Failure by crush¬
ing of the tubes at the joint is indicated by X. Typical
failures are shown in figure 19.
Joints G7G0, figure 17, had about the same strength
as joints 750 and 1010 (N. A. C. A. Technical Report
STRENGTH OF WELDED AIRCRAFT JOINTS
195
Figuke 19. — Lattice joints after failure.
196
REPORT NO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
No. 348, fig. 27), which were the strongest lattice joints
tested in the previous investigation.
The three additional tubes in joints G1020 had a
reinforcing effect, as these joints were stronger than
joints G30 of the previous investigation.
The strengths of joints G30 were increased by heat
treatment, although the tensile and compressive effi¬
ciencies were somewhat lowered. Marked increases in
the strengths and slight increases in the tensile effi¬
ciencies of joints 7G0 and 1010 were produced by heat
treatment. The compressive efficiencies were slightly
lowered.
The efficiencies of the joints made from thin-walled
tubing, shown in figure 18, were low, especially those
of the unreinforced joints LG30. Joints J760, for which
low-carbon welds were used, have cracks which appar¬
ently did not appreciably lower their strengths as their
efficiencies were about the same as those of joints L7G0.
The gussets were more effective than in joints made with
thicker-walled tubing. The tubes failed by crushing at
the joints. The lower strengths of these joints are due
to low resistance to lateral crushing or flattening of the
thin-walled tubing.
Tensile tests were made of the welded-sheet speci¬
mens using either a fluid -support, Bourdon-tube hy¬
draulic machine having dials of 0 to 10,000 pounds,
0 to 50,000 pounds, and 0 to 100,000 pounds capacity or
a pendulum hydraulic machine having dials of 0 to
10,000 pounds, 0 to 25,000 pounds, 0 to 50,000 pounds,
and 0 to 100,000 pounds capacity.
Templin grips were used for all sheet specimens of
which the load did not exceed 10,000 pounds. Speci¬
mens having higher strengths were tested in the wedge
grips provided with the machine.
Figure 21 shows the four types of fractures of the
butt joints for both sheet and tubing. The type of
fracture is shown at the top of the diagram in which
the test results are plotted. Fractures of type 1 were
remote from the weld; type 2 (which occurred for
tubular specimens only) in the area where the welding
heat had caused a localized annealing effect as shown in
figure 17, N. A. C. A. Technical Report No. 348 ; type 3
at the edge of the weld; and type 4 in the weld. The
results for the butt joints in steel sheet are plotted in
figures 22 and 23. The strengths of all welds were
increased materially by beat treatment, particularly
Specimens
No.
Heat treatment
I
None
2
Normalized
3
Quenched at
1600 ° F.
Tempered at 500° F.
4
" " 700° Y.
5
'• 900 °¥.
6
« « II 00°?.
Figure 20.- — Layout of butt joints and tensile specimens of the base metal in the steel sheets.
The carbon-steel lattice joints, shown in figure 18, had
somewhat lower efficiencies than joints made with chro¬
mium-molybdenum steel.
BUTT JOINTS
SHEET SPECIMENS
Butt joints were made in chromium-molybdenum
sheet and tubing to determine the tensile strengths of
heat-treated welds.
Four thicknesses of sheet, 0.031, 0.063, 0.125, and
0.188 inch were used. Open square butt joints were
made with the 0.031-inch and 0.063-inch sheets and open
90° single V butt joints with the 0.125-inch and 0. 188-
inch sheets. All specimens were reinforced on both
sides. After welding, tensile specimens were machined
from the joints as shown in figure 20. The reduced
section was y2 inch wide and 41/2 inches long. The
weld was at the middle. One series of specimens was
made, as shown in figure 20, in each sheet thickness
with each of three kinds of welds.
those of the carburizing flux and the chromium-molyb¬
denum welds. There was considerably more scatter in
the results of the heat-treated low-carbon welds than
in the other types.
In general the full strength of the base metal was
realized in the “as welded” and normalized joints in
all four sheet thicknesses. Of the joints which were
quenched and tempered the carburizing flux welds de¬
veloped the highest strengths for all tempers in the
0.031-inch sheet thickness. In the other thicknesses
the strength of the carburizing flux welds was slightly
greater and somewhat more uniform than that of the
chromium-molybdenum welds except at the 500° F.
temper.
There was some variation in the bead reinforcement
(see table III) between specimens of different sheet
thicknesses and types of weld. However, none of the
chromium-molybdenum welds and only three of the
carburizing flux welds (one in the 0.063-inch and two
in the 0.188-inch sheet, all quenched and tempered at
500° F.) fractured in the welds, indicating that the
STRENGTH OF WELDED AIRCRAFT JOINTS
197
Figure 21. — Butt joints in chromium-molybdenum sheet and tubing after failure, illustrating the four types of failure designated in
figures 22, 23. 28, 29, and 30.
198
REPORT NO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
o Strength tow-carbon welds
A " carburizing flux welds
o " chromium-molybdenum welds
base metal
* Vickers number of weld specimens
" base metal specimens
220
200
/QO
.cf
&/60
%
^ 140
Q
120
£
^100
<u
X:
80
<o
,Seo
40
20
0
<o
J
V
J /
1
sJO
1
Js.
J
u J
Jl 5
0
rr
H-
-0
£
*
XL
_
i
“I -
o
-
-
r
L
c
57
1
0.03/ -in. sheet-
saunrp hi rH <>>
>
1
reinforced both '"sides
"7
—
— J
L
-T
—
c
"j] ~ ^
4
—
•
— i
i —
.
••
V
•
•
3
- 4
1
*
I r
1 — ri
) '
j><
j,
—
|y
u
L
i
.
i
J^i
,
■
J
->
J
r
Is
->d
ii!
x
f >
1
>
->
i
jr*
4
L
■
>
Torch
L
C
-
1
c
_
J
3
|
c
1
1
C
3
6
a
X.
l
O
X-
C
-i
t
b
c
t
b
j
c
i
b
t
—
600
400
100
0
j- • r- auu r. nuu r.
- Quenched at 1600° F. then tempered at above temperatures
600
500
400
300
200
too
0
Figuke 22. — Test results for open square butt joints in 0.031-inch chromium-molybdenum sheet (upper) and in 0.063-inch
sheet (lower). Three groups of specimens corresponding to three types of welds were used for each heat treatment. An
additional specimen of base metal representing each group of triplicate specimens was heat-treated and tested. The
points shown on the graph are the tensile strengths and Vickers numbers of the joints. The corresponding values for
the base metal specimens are shown by horizontal lines. The type of fracture of the joints is indicated at the top of the
graph ; the torch used, at the bottom.
Vickers number Vickers number
STRENGTH OF WELDED AIRCRAFT JOINTS
199
o Strength low carbon we/ds * Vichers number of weld specimens
A " carburizing flax welds 7 " " base diet a I specimens
o k " chromium -molybdenum welds
base metal
600
500
400
300
POO
k
<D
i
C
IT)
b
.o
£
too
0
220
200
180
.C
d/60
^ 140
§
^ / 20
£
^/oo
£
*> 80
4?
40
20
0
III III III _ 411 III III 44444/ III 444 III III 444 1 1 I 1 1 1 444 III I lib
/4s Welded Normalized
J
■
—
pr
r
r~
o
0
■•b
1
-
m
5 |
4
’i
1
Dpi
re
3n
0.(88 -in. sheet-
?//? forced both side
O
1
4-
...
— i
t— '
m
3 -
_
)
<
’
<
4
—
)
>
i
i
h
4
I
- d
<
4
fi
• -
Li
u
>
i a
JD
IE
>r>
h
c->
; ,
j
E
i-i
tt
! !
r
<
!>-<
M
W
_
L
—
!
-J
....
i-j
n
<-
rn
—
L->
1
u
X_
x_
L_J
LA
-e
o
u
IS
I
c
1
—
d
|
r*
c
d
c
4
C
c
J
y
c
C
C
7
c
*
c
1
c
7
c
y
c
y
c
_
7
C
y
_
500°?. 700° F. 900° F. 1100° F.
u Quenched at 1600°?. then tempered at above temperatures
600
500
400
300
200
100
0
Figure 23. — Test results for open single-V butt joints in 0.125-inch chromium molybdenum sheet (upper) and 0.188-incli
sheet (lower).
Vichers number
Vickers numb
500
Figure 24. — Vickers number of open butt joints in chromium-molybdenum sheet “as welded.” The impressions were made on the edge of the specimens.
200 REPORT NO. 5 84 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
to
STRENGTH OF WELDED AIRCRAFT JOINTS
202
EE PORT NO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
reinforcement was adequate for these welds. Frac¬
tures in the weld, type 4, showed a marked reduction
in area.
The Vickers explorations shown in figures 24, 25, and
2G were made to study the effect of the heating of the
base metal during welding, and the effect of heat treat¬
ment after welding. Vickers’ impressions were made
on the edge of the specimens. The load was varied ac¬
cording to the resistance to indentation and the thick¬
ness of the specimen. A 10-kilogram load was gener-
The Vickers number of specimens that had been
quenched and tempered at TOO0 F. are shown in figure
25. The Vickers number of the bead was greatest in
the chromium-molybdenum welds ancl lowest in the
low-carbon welds. The thinner sheets in the low-
carbon and carburizing flux welds had higher numbers.
The Vickers number of the base metal was uniform out¬
side the weld.
Vickers numbers for heat-treated low-carbon welds
are shown in figure 26.
Figure 20.- — Vickers number of open single- V butt joints in chromium-
molybdenum sheet "as welded", normalized and quenched and tem¬
pered at several temperatures.
ally used for the 0.031-inch specimens. For the thicker
specimens the load was 30 kilograms when the Vickers
number did not exceed about 250, and 50 kilograms for
higher Vickers numbers. One series of impressions
was taken along the center line of the edge by advanc¬
ing the specimens longitudinally by means of a lead
screw. These impressions were spaced from one
thirty-second to one-fourth inch apart. In addition,
impressions were made on the bead at from two to six
points (depending on its size) located as close as pos-
TUBULAR SPECIMENS
Four chromium-molybdenum tubes (l1/-? by 0.058
inch) were laid out, each as shown in figure 27. Low-
carbon welds were made in two of the tubes, carburizing
flux welds in the other two.
Butt joints were also made in thin-wallecl tubing
iy2 by 0.020 inch and in carbon-steel tubing V/2 by
0.058 inch. These were left “as welded.”
The ends of the tubular butt joints were plugged and
the specimens were tested in tension using the same
apparatus and methods as used for the sheet specimens.
Tubular butt joints (fig. 28) showed more variation
in strength than butt joints in sheet. The carburizing
flux welds had the highest strengths of any of the
quenched and tempered joints. Failure occurred either
in the weld or remote from the weld, seldom at the edge.
More of the low-carbon welds failed at the edge than in
the weld. Those joints that were quenched and tem¬
pered showed little difference in strength regardless of
tempering temperature.
Results of tests on the thin- walled tubular butt joints
are shown in figure 29. All low-carbon welds had
cracks (see fig. 7) and failed at these cracks. No cracks
were found in the carburizing flux welds. Two of the
latter joints failed in the weld, four in the annealed
portion of the tube, and one at the edge of the weld.
Those failing in the weld had low strengths.
"As welded"
Normalized at
!600°F.
<-Quenched at 1600 °F. then tempered at temperatures given below~A"As welded ‘
600 "F. | 700 °F. | 900 °F. | IIOO° F.
I I I
V-/2IJ-^-IO'-\ [~We/d
'''- Base metal specimen
Figure 27.- — Layout of the tubular butt joints and base metal specimens.
sible to the edge of the cross section. The averages of
these are shown in the figures.
Figure 24 shows that the Vickers number of the -weld
metal in the “as welded” condition varies with the kind
of welding rod used. The welding heat caused hard¬
ening of the base metal near the weld in a zone vary¬
ing in width from about 14 to % inch on each side of
the weld. In this zone the Vickers number was lower
in the thicker sheets, probably because of slower cool¬
ing of the thicker sheets.
The strengths of the carbon-steel butt joints in iy2 by
0.058-inch tubing are also shown in figure 29.
CROSS JOINTS
Cross joints (shown in fig. 30) were tested to deter¬
mine the strengths of three types of welds when used
to make heat-treated joints in tubes of different thick¬
nesses. These joints consisted of two chromium-molyb¬
denum tubes, 1 by 0.035 inch, lying in the same axis,
welded to opposite sides of the wall of a much thicker
STRENGTH OF WELDED AIRCRAFT JOINTS
203
tube, IV2 by 0.083 inch. Three types of welds were
used: (1) low-carbon welds, (2) carburizing flux
welds, and (3) a combination of the first two types
as the unreinforced joints 140 and 630 in the previous
investigation. As before, no consistent difference in
welding speed could be observed for any one torch.
Figure 28. — Test results for butt joints in chromium-molybdenum steel tubing 1% inches O. D. by 0.058-inch wall.
in which the welding rod was the same as used for the
carburizing flux welds but in which the base metal was
fused, using the neutral flame technique of type (1).
The 1 by 0.035 inch tubes were laid out as shown in
figure 27.
Tensile tests were made in a 100,000-pound pendulum
hydraulic testing machine.
The cross joints had the lowest strengths of any of
the heat-treated joints. Practically all joints except
those tested “as welded” failed at the edge of the
weld. There was no significant difference in strength
within the range of tempering temperatures used. The
low strengths of these joints were probably due to
stress concentrations near the weld caused by the sharp
changes in cross section. The joints made by the car¬
burizing flux process were slightly stronger than those
made with the same rod, and neutral flame technique.
The low-carbon welds had the lowest strengths.
TIME OF WELDING
The time required to machine and welcl the joints
and the weight of the wreld metal and gusset plates
are shown in figure 31. The gusset-reinforced joints
G260 and G760 required about twice the time to weld
Low-carbon Carburizing
we/c/s flux welds
Figure 29. — Test results for butt joints
in thin-walled chromium-molybdenum
steel tubing and in carbon-steel tubing.
MECHANICAL PROPERTIES OF BASE METAL
Tensile tests were made on heat-treated sheet and
tubular specimens of the base metal from which the
butt and cross joints were made. Stress-strain and
204
REPORT NO. 584 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
O Strength tow -carbon welds
A
x Vickers number of weld specimens
carburizing flux welds r_T' " " '' base metal specimens
" we/ds made with carburizing ^"-Strength of base metal
flux rod, but with neutral flame * Cross tube failed
technique
1.5
1.0
.5
0
Butt joints in sheet
Chromium -molybdenum
we/ds
d5
dO
35 H
T joints
Lattice joints
if
iM
ab cd ab cd
2 30
C 25
5 20
Q)"
.§ 15
£
10
0
Time to weld
.Average time
' to machine
4
I
III
li
Cross
joints
Tubular
butt
joints
see fig. 30 see fig. 28
T orch obc ,dcb cda dob bed eda dab dab eda bed adc abc abc eda
G260 K260 J260 L260 G1020 K760 L 630
K140 J140 L 14 0 G760 K630 J760 L760 A Low-carbon we/ds
B Carburizing flux
welds-
C Carburizing flux rod,
neutral flame
technique
K 1 4 0 J 1 4 0 L 1 40
G 1020 K76 0 L630
G760 K630 J760 L760
.031 .063 .125 .188
Sheet thickness, in.
% Bead welded on both sides in one operation
Figure 31. — Time required to machine and weld joints; weights of weld metal and reinforcement.
STRENGTH OF WELDED AIRCRAFT JOINTS
205
difference curves 5 (fig. 32) were obtained. The me¬
chanical properties are given in figure 33 for tubular
specimens and figure 34 for sheet specimens.
The tubes were tested in full section with steel plugs
in the ends. For the sheet the American Society for
Testing Materials’ standard sheet-metal specimen hav¬
ing a 2-inch-gage length and a width of i/2 inch was
used.
A Ewing extensometer having a 2-inch-gage length
was used to measure the strain.
The yield point was determined as required in Navy
Department Specification 44T18a, in which it is de-
tempered at either 700° F. or 900° F. The normalized
specimens had comparatively low proportional limits.
Young’s modulus increased slightly with the temper¬
ing temperature for the sheet specimens and for the
1 by 0.035-inch tubular specimens, but not for the
iy2 by 0.058-inch tubular specimens.
The elongation in 2 inches increased with the sheet
thickness.
The mechanical properties of the heat-treated chro¬
mium-molybdenum sheet are in fair agreement with the
properties of similar heat-treated sheet tested by F. T.
Sisco and D. M. W arner (reference 5).
Figure 32. — Tensile stress-strain curves for chromium-molybdenum steel tubular specimens 1% inches O. D. by 0.058-inch wall.
fined as that stress under which the specimen shows a
strain 0.002 inch/inch greater than that computed from
the formula
Strain (in./in.)
stress (lb./sq. in.)
“30000000
The i^-inch sheet specimens had the highest tensile
strengths of all quenched and tempered specimens.
When tempered at 500° F. the tensile strength was
about 238,000 lb./sq. in.
The yield points of the 1 by 0.035-inch tubular speci¬
mens were highest when the specimens were tempered
at 700° F.
The proportional limits were the most variable of the
mechanical properties. The proportional limits of the
tubular specimens were highest when the specimens were
6 See N. A. C. A. Technical Report No. 348, p. 6 ; also discussion by
L B. Tuckerman of the Determination and Significance of the Propor¬
tional Limit in the Testing of Metals, by R. L. Templin, presented at
the Thirty-second Meeting of the American Society for Testing Mate¬
rials, June 25, 1929.
Figure 35 shows the variation of tensile strength with
Vickers’ number for chromium-molybdenum sheet and
tubing.
CONCLUSIONS
1. The magnetic dust-inspection method was quite
effective in detecting seams in tubing and cracks in
welded joints. This method of inspection could be
utilized by manufacturers in the routine examination
of steel aircraft materials and welded structures.
2. Based on considerations of strength, weight, weld¬
ing time, and freedom from cracks, the inserted gusset
type of reinforcement used in this investigation for T
and lattice joints, is considered to be better than any
type tested previously. In increasing the strength of
joints this reinforcement was effective for all joints ex¬
cept the carbon-steel T joint under transverse loading.
3. In welding the thin-walled chromium-molybde¬
num tubing, only the carburizing flux process was
206
REPORT NO. 5 84 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 33. — Mechanical properties of two sizes of chromium-molyb¬
denum steel tubing for various heat treatments.
found to produce welds which were free from cracks.
T and lattice joints made from this tubing had some¬
what lower strengths than joints made from heavier
tubing because of failure by local buckling.
4. Normalizing the chromium-molybdenum steel butt
joints increased their strengths except in the case of
carburizing flux welds in 0.031-inch sheet, which showed
a slightly lower strength. Of the sheet specimens heat-
treated by hardening and then tempering at various
temperatures, the chromium-molybdenum and the car¬
burizing flux welds were approximately equal in
strength except in the case of the 0.031-inch sheet which
showed a somewhat higher strength for the carburizing
flux welds.
Vickers number
Figure 35/ — Relation between the Vickers number and the tensile
strength for chromium-molybdenum steel sheet and tubing.
5. The strength of the heat-treated butt joints, espe¬
cially those made with low-carbon welds, was in most
cases less uniform than the strength of the base metal.
Heat-treated cross joints, in which adjoining tubes had
a great difference in diameter and wall thickness, had
low strengths compared to the tubular butt joints.
6. As in the first investigation, no consistent differ¬
ence in strength or speed of welding could be attributed
to any one torch.
STRENGTH OF WELDED AIRCRAFT JOINTS
208
REPORT NO. 584 — NATIONAL ADVISORY COMMITTEE EOR AERONAUTICS
ACKNOWLEDGMENTS
Acknowledgment is made to the Air Reduction Sales
Co., the Linde Air Products Co., the Torchweld
Equipment Co., and the Bastian-Blessing Co. for lend¬
ing the torches and equipment; to the Linde Air Prod¬
ucts Co. for contributing the services of the welding
supervisor, Mr. H. S. George, who rendered invaluable
assistance during the welding; to the Keystone Air¬
craft Co. for assistance in obtaining a welder; to Mr.
R. M. Fowle r, for making chemical analyses of the ma¬
terial; to Messrs. Louis Jordan and H. E. Francis for
heat treating some of the welded joints; and to Mr.
R. E. Pollard for making a microscopic examination
of seams and cracks.
National Bureau or Standards,
Washington, D. C., August 12. 1936.
REFERENCES
1. Roux, Albert: Controle des Soudures par les Spectres Mag-
n6tiques. Comptes Rendus de L’Academie des Sciences,
vol. 185, October 24, 1927, p. 859.
2. Watts, T. R. : Magnetic Testing of Butt Welds. Jour, of the
American Welding Society, vol. 9, no. 9, September 1930,
p. 49 ; also Magnetographic Inspection of Welds. Weld¬
ing Engineer, vol. 15, no. 10, October 1930, p. 31.
3. de Forest, A. V. : Non-Destructive Tests by the Magnetic
Dust Method. Iron Age, vol. 127, no. 20, May 14, 1931,
p. 1595.
4. George, H. S. : A New Process for Making Welded Joints.
Jour, of the American Welding Society, vol. 11, no. 7, July
1932, p. 22.
5. Sisco, F. T„ and Warner, D. M. : Effect of Heat Treatment
on the Properties of Chrome-Molybdenum Steel Sheet.
Trans, of the American Society for Steel Treating, vol. 14,
August 1928, p. 177.
BIBLIOGRAPHY
In addition to the bibliography given in N. A. C. A.
Technical Report No. 348, the following technical
papers may be of interest :
1. Whittemore, H. L., Crowe, John J., and Moss, H. H. : Pro¬
cedure Control in Aircraft Welding. Proceedings of the
American Society for Testing Materials, vol. 30, Part II,
1930, pp. 140-146. ,
2. George, H. S. : The Cause and Prevention of Heat Cracks in
Aircraft Welding. Mechanical Engineering, vol. 53, no. 6,
June 1931, pp. 433-439.
3. Beissner, Hans : Einfluss der Gasschmelzschweissung auf die
Biegungsschwingungsfestigkeit von Ghrom-Molybdiin-Stakl-
rohren. Z. V. D. I., vol. 75, no. 30, July 25, 1931, pp.
954-956.
4. Reclitlieh, von Arved : Grundlagen fur die konstruktive An-
wendung und Ausfiihrung von Stahlrohrschweissungen im
Flugzeugbau. D. V. L. Yearbook, 1931, pp. 3794138.
5. Jansen, P. N., and Speller, T. H. : An Aircraft Manufac¬
turer’s Experience with Welding Quality Control. Jour,
of the American Welding Society, vol. 12, no. 10, October
1933, pp. 9-13.
6. Muller, J. : Weldability of High-Tensile Steels from Experi¬
ence in Airplane Construction, with Special Reference to
Welding Crack Susceptibility. T. M. No. 779, N. A. C. A..
1935.
REPORT No. 585
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
By H. A. Pearson
SUMMARY
Tables are given for determining the load distribution of
tapered wings with partial-span flaps placed either at the
center or at the wing tips. Seventy-two wing-flap com¬
binations, including two aspect ratios, four taper ratios,
and nine flap lengths, are included. The distributions for
the flapped wing are divided into two parts, one a zero
lift distribution due primarily to the flaps and the other an
additional lift distribution due to an angle of attack of the
wing as a whole.
Comparisons between theoretical and experimental
results for wings indicate that the theory may be used to
predict the load distribution with sufficient accuracy for
structural purposes.
Simple computing forms are included for determining,
by the Lotz method, the theoretical loadings for a combina¬
tion of any wing with any flap. A discussion of the
method is given showing: ( 1 ) the effect on the load dis¬
tribution of increasing the number of harmonics for a
wing with partial-span flaps; and (2) the effect of increas¬
ing the number of points used across the semispan for a
wing of unfair plan form.
INTRODUCTION
A knowledge of the span load distribution over a
wing is important not only from structural considera¬
tions but also because certain conclusions regarding the
behavior of the wing near the stall may be drawn from
it. Indirectly, the span load distribution also influences
such items relating to performance as the magnitude
of the induced drag, the pitching moment of the entire
wing about an aerodynamic center, and the angle of
zero lift. Because of the importance of span load
distribution, numerous methods for computing it have
been proposed but, since they are generally lengthy
and complicated, they have been little used in practice.
In reference 1 the span loading was given for linearly
tapered wings with rounded tips. The results given
therein cover a large range of aspect ratios and taper
ratios, but they are for the case of a wing in which there
is either no twist or only linear twdst. Since most
airplanes include some sort of high-lift or drag-increas¬
ing device covering only part of the span, the wing with
an abrupt twist is of particular interest. These high-
lift devices, when deflected, may be considered as
introducing an effective twist that alters the load
distribution along the span. As the actual effective
twist depends upon possible combinations of wing angle
of attack, flap type, flap deflection, flap span, wing plan
form, and the variation of the flap-chord ratio along
the span, it is apparent that the resulting load distri¬
bution depends upon many variables.
The presence of so many variables precludes the
possibility of making either sufficiently extensive theo¬
retical or experimental investigations to provide design
charts for the general case. The present report there¬
fore covers only the most commonly used series of
wings; i. e., linearly tapered wings with rounded tips
having chord distributions like those of reference 1 and
equipped with partial-span Haps of constant flap-chord
ratio. Comparisons are made of the experimental load¬
ings, taken from reference 2, and the theoretical loadings
to give an indication of the differences to be expected
when the theory is used. Finally, a method for com¬
puting the span loading is included so that those
interested will be in a position either to estimate from
the results given herein the probable loading for similar
cases or, if necessary, actually to make the computa¬
tions.
Although the present report presents only the span
loadings, later reports will deal with the effect of the
load distribution on performance and on the behavior
of the wing near the stall.
SYMBOLS
bf, flap span.
bw, wing span.
S, wing area.
A, aspect ratio, bf/S.
5f, flap deflection, positive downward.
V, wind velocity.
р, mass density of air.
g, dynamic pressure, \pV2.
£
w, induced downflow at a section.
L, lift on wing.
CL, wing lift coefficient, LjqS.
cs, chord at plane of symmetry.
с, chord at any section.
209
210
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
a0, effective angle of attack of any section.
aa, angle of attack of any section referred to
its zero-lift direction.
as, angle of attack of section at plane of
symmetry referred to its zero-lift direc¬
tion .
X, ratio of fictitious tip chord, obtained by
extending leading and trailing edges of
wing to extreme tip, to the chord at the
plane of symmetry.
E, ratio of flap chord to wing chord at any
section.
r, circulation at a section.
I, section lift (per unit length along span).
Ci, section lift coefficient, l/qc, perpendicular to
wind at infinity.
Subscripts:
0, refers to section lift coefficient
perpendicular to local relative
wind.
b, refers to basic lift (CL= 0).
a, refers to additional lift for any CL.
al, refers to additional lift for <7z = 1.0.
Cimai, maximum lift coefficient for any section.
Ac i, increment in section lift coefficient caused
by a flap deflection, 8f.
cdj, section induced-drag coefficient.
cd(>, section profile-drag coefficient.
La, additional-load parameter, ciai g-
cb
Lb, basic-load parameter, cw-qt —
b e>ACi
, (^! of entire wing, per radian.
m
dci
m0, i— of any section, per radian.
(LOLc\
ms
dcr
it, -jE of section at plane of symmetry, per
CLOCq
radian.
A CL, the part of CL at a given wing attitude due
to any flap deflection.
ACl i, the increment caused by a flap deflection
corresponding to a A cx of 1.0.
y, variable point along span.
y' , fixed point along span.
cos 6,
■An> En, C^n,
-Jjx (when y= — bw/ 2, 0 = 0; when y=bw/ 2,
6 = tv) .
coefficients in Fourier series.
THEORETICAL RESULTS FOR WINGS WITH FLAPS
According to the assumptions upon which wing
theory is based, the distribution of lift over the span
is a linear function of the angle of attack at each point
of the span. Thus it is permissible to compute sepa¬
rately either a zero lift distribution or a distribution
due only to the flaps and later to superpose them on
appropriate distributions due to an angle of attack of
the wing with flaps neutral.
Deflecting flaps on an untwisted wing that previously
was at zero lift produces the angle of attack and load
distributions shown by the solid lines in figure 1. If
the angle of attack of the wing without flaps is reduced
so that the area under the dashed load curve is equal to
that under the solid curve, their addition will result in
a zero-lift curve. It can be seen that the load distri¬
bution due to the flap alone (solid curve) does not follow
Wing
Flap
T~
+ fa
_ E _
—Flap
- cca Wing^
Angle-of -attach. d i str i but ion
Load distribution
Figure l.— Angle of attack and load distribution for a wing with flaps.
the abrupt angle-of-attack change but, owing to in¬
duction, is distributed along the remainder of the span
where there is no apparent angle of attack. At these
stations there is, however, an effective angle of attack
due to the upwash produced by the portion with flaps.
Numerically the effective angle of attack at any section
is equal to the section cz divided by the slope of the
section lift curve, or it can be given by
ao =<xa—-y (!)
In order to determine the theoretical distribution of
the forces and angles for a particular case, it is necessary
to obtain a solution of the fundamental formula for
induced downflow
The graphical and analytical methods for solving
this complicated integral tend to be lengthy and none
is exact. In the general case where the wing plan
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
211
form or angle-of-attack distribution cannot be expressed
as simple analytical functions, either the Lotz or Lip-
pisch methods (references 3 and 4) are particularly
applicable, although other methods may be used. An
adaptation of the Lotz method, which has been used to
compute the theoretical load distributions given herein,
is given in a later section of this report in a form suitable
for routine computation. These load distributions are
listed in tables I and II for 72 wing-flap combinations
that include two aspect ratios (6 and 10), four taper
ratios (1.0, 0.75, 0.50, and 0.25), and nine llap lengths.
The flap lengths, expressed as a fraction of the semi¬
span, are:
Flaps at
Flaps at
center
tip
0. 233
0. 240
. 383
. 351
. 649
. 617
. 760
. 767
1. 000
Table I gives the ordinates of the curves of the addi¬
tional load distribution at 10 selected span wise stations
in terms of the parameter
La — Clai-g (3)
and table II gives the ordinates for the basic-load
distribution in terms of the parameter
(4)
The additional-load distribution, given for a wing CL
of 1.0, is independent of wing twist (flap displacement)
and maintains the same form throughout the useful
range of the lift curve. The basic distributions are
zero lift distributions that depend principally on the
wing twist.
The values of La and Lb were computed by the Lotz
method; 10 points across the semispan were used and
10 harmonics of the series were retained. In these
computations the slope of the section lift curve was
assumed to be equal to 5.67. The odd flap lengths
given result from the use of a Fourier series in the solu¬
tion for the load curves; in the case of a wing with an
abrupt twist the discontinuity occurs, mathematically,
in the interval including the end of the flap.
Since the parameter La has been given for the con¬
venient wing CL of 1.0, the relation between the addi¬
tional section lift coefficients c,a and ct(ll becomes
Cia=CLclal (5)
The total lift coefficient at each section is
Ci=Cib-{-CLCial (6)
and the lift at a section is
(7)
In the application of the results given in tables I
and II, interpolation will generally be necessary. For
structural purposes a linear interpolation between the
different variables is probably justified. The results
may also be extrapolated with reasonable accuracy to
aspect ratios 4 and 12, although values of La may be
obtained from reference 1 for aspect ratios from 3 to 20
without the necessity of any extrapolation.
.020
■V,
O
< .0/6
c
,<h
©
0
0
O)
Cl
b
i •
•S
’ >.
o
£
0/2
\
\
\
_ V
\
\
\
\
\
\
. \
O.
/ Cdc
fo f
6f
= 30
o
\
— v -
\
\
S - N
\
\
\
A-U
-y--
■ y
s
C
A fc
<r 6j
= O
o
\ X
\ct
*
_
T
/
6. /
cdQ
for
it
❖
for
6f
= 30
o
4^
CD
*
.o
24 b
c
<0
8-
/6 o
u
.C
<*-
c
8 ■
c
o
-X
0
o
-8
o
c
■'C
0
/.6
2.0
.4 .8 /.2
Lift coefficient , c,0
Figure 2.— Typical characteristics of a section equipped with a flap.
In order to illustrate the procedure to be followed in
the use of the tables, the span loading of a wing with
the following characteristics will be found:
CL= 1.72
\ = 0.625
A=6
y^=0.3S3.
r/=5 7.5 pounds per square foot
#=0.20
5,= 30°
A table, such as table III, is prepared in which the
values of the chord at the various stations are first
entered, interpolations are made for taper, etc., and the
values of La and Lb from tables I and II are entered in
columns 3 and 4, respectively. From La, the values of
C[al and c}.a are found by the use of equations (3) and (5)
and entered in columns 5 and 6.
Before cXh can be found, however, it is necessary to
determine from experimental data the value of Ac;
corresponding to the flap-displacement angle of 30°.
This increment is generally found by correcting the
residts of tests made of a finite wing with full-span
flaps of proper type and proper flap-chord ratio to
l = cxqc
212
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
obtain section characteristics. It is assumed that such
section characteristics are available (fig. 2) ; the value of
A Ci to be used may then readily be found. Theoretically,
flaps.
the effect of displacing a flap would be to displace the
lift curves parallel to each other so that A ct would be
independent of the effective angle of attack. Experi¬
mental results, however, indicate that Act depends on
the effective angle of attack and some averaging is thus
necessary to determine its value. Since the example is
for a high-angle-of-attack condition, the value of A ct
is arbitrarily taken in this range at an angle correspond¬
ing to a Ci of 1.2 for the plain section. By the use of
equation (4) together with a value of A ct equal to 0.6,
from figure 2, the values of cih are computed and entered
in column 7 of table III. The total section ct (column
8), from which the load distribution (column 9) is
determined, is the sum of columns 6 and 7.
Standard section characteristics for the plain section
and the section with a flap are sometimes tabulated in¬
stead of being plotted as in figure 2. In such a case the
value of Act may be found from the formula
where ci0 is the slope of the section lift curve per degree
and a,0 the angle of zero lift measured from the chord
line in degrees. The subscript / refers to the character¬
istics with the flap deflected. If desired, the slopes and
angles could also be given in radians.
If the induced-drag distribution corresponding to a
given load distribution is specifically required, it may be
found by the use of the equation
Cl—ACLiAci\^cjl
K m ) m0.
(8)
which gives the variation of the section induced-drag
coefficient over the portion of the span without flaps,
and the equation
CAi=Ci
L(
Cl AClxACi
m
(9)
which holds over the portion of the span with flaps. The
increment of wing lift coefficient A CLl and the slope of
the lift curve of the finite wing m to be used in these
equations are given in figure 3 for the series of wings con¬
sidered in this report. The value of A CLy (fig. 3) repre¬
sents the increase in lift coefficient based on the entire
wing area due to a flap deflection corresponding to a Act
cb
of 1.0. Figure 4 gives typical distributions of Ci-t? and
Ci for various wing-flap combinations corresponding
to a Ac i of 1.0. These distributions are thus directly
related to the results given in figure 3.
COMPARISONS OF EXPERIMENTAL AND THEORETICAL
RESULTS
Previous comparisons (reference 5) ol experimental
and theoretical span loadings for a 2:1 tapered U. S. A.
airfoil equipped with partial-span flaps of three different
lengths indicated a satisfactory agreement. The first
conclusion given in reference 5 is: “A satisfactory de¬
termination, for all conditions of test, of the span load
distribution for an airfoil equipped with a partial-span
split flap may be made by applying the Lotz method of
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
213
calculating the aerodynamic characteristics of wings.
The increments of load due to the deflection of the flap
are computed by the Lotz method and added to the
span load distribution for the plain airfoil.”
Since the publication of reference 5 additional pres¬
sure-distribution tests (reference 2) have been made
over a rectangular wing having a 0.6-span constant-
chord split flap. The wing used was of Clark Y section
with a 20-inch chord and a total span of 120 inches.
Some of the span-loading curves taken from reference 2
are compared, in figure 5, with corresponding theoretical
curves for a wing with square tips.
section the method will be discussed in more detail and
a scries of computing forms will be given which, it is
believed, will make the computations simpler and more
direct than if the method of reference 8 were followed.
Outline of theory. — As is customary in aerodynamic
theory, the wing is replaced by a single line vortex whose
strength at every section along the span is equal to the
circulation F at that section. The lift per unit length
of span is then
dL—pVrdy (10)
and the problem is to find F for any point on a wing of
Figure 6 shows comparisons of computed and experi¬
mental values of A Ch for various flap locations. The
experimental values of A CL are those given in refer¬
ences 6 and 7 at 8° angle of attack. Reference 6 gives
the results of force tests of a rectangular Clark A wing
with partial-span flaps placed at the center and at the
wing tips; reference 7 gives similar results for a 5:1
tapered wing. In the comparisons given in figure 6 the
experimental results were obtained from tests of wings
with straight tips; whereas the computed results are
those for wings with rounded tips.
any shape. The relations between I', c,, and «0 are
given by the equations
CiCV_a0m0cl
1 9 9
(11)
where a0=aa~w/V. Since the induced angle at a
particular station y' is
b
THE LOTZ METHOD FOR CALCULATING THE
AERODYNAMIC CHARACTERISTICS OF WINGS
The following method was proposed in 1931 by Miss
Lotz (reference 3), who gave the basic theory involved.
Shenstone (reference 8) gave a brief discussion of the
method and a simple procedure to be used in obtaining
the various constants required in the solution. In this
the circulation r may be expressed by the integral
equation
2T
T 7
m0c v
(13)
214
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
This equation is to be solved for F, and the method used
is to replace the circulation by a Fourier series where
and hence
An sin nd
_2T_ _ms c_s
m0cV m o c
~2An sin nd
(14)
(15)
Figure 5.— Comparison between experimental and theoretical load distribution
for a wing with partial-span flaps. (Data from reference 2; X=1.0; .1=6;
square tips.)
As a result of expressing the circulation by the foregoing
series, the induced angle becomes
w cs m. , / sin nd\
V=~WlnA'\^re )
By substitution, equation (13) is transformed into
(16)
changing the values of the coefficients already com¬
puted. When the wing plan form is symmetrical about
the center line, the cosine series contains only even
values; whereas, if the angle-of-attack distribution is
symmetrical, as it is with flaps, only odd values of n
are retained. Equation (17), after the foregoing series
have been substituted, becomes
ZC2n cos 2nd sin nd+^j^ZnAn sin nd~
- Bn sin nd (18)
Figure 6.— Comparison of experimental and computed values of ACl.
lien n is temporarily replaced by the indices k and /,
the double series on the left of equation (18) is trans¬
formed into
—sin 6 HAn sin nd=aa sin Q— c-^^nAn sin nd (17)
mo C 4 0
The new feature introduced by Miss Lotz is to replace
771 C
! — sin d and aa sin d by the two series 'ZC2n cos 2nd
mQ c
and E/E sin nd, respectively. As the coefficients in
these series are independent of the load distribution,
they may be separately computed, and it is possible to
increase the accuracy by taking more terms without
'h^2lAuAjc Ci [sin (/c — f- Z) 0 — 1— sin ( k — l)d]
By the substitution of the foregoing series and consid¬
erable rearrangement, equation (18) may be expanded
into the following form. In its exact form there are
an infinite number of equations and terms. For the
purpose of calculation, however, the circulation may
be computed at a finite number of points with a finite
number of equations.
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
A B C
2PiA\Jr(C2—Ci)As-\-(Ci — Cn)A'l-\-(Ct—Ci)Arsr(Ci—CM)A'i+(C\o—Cn)A\\+(Cn-Cu)Au+(C\i—C\z)A\$\-{Cis—C\i)Au+{Cu—Cm)AH=
(Ci— Ci)A\+2PsAi->r(Ci— CsMs+CUi— C7io)-47-j-(<?6— Cn)Ar>r{Ci — Cu)A\\+{C^—Cn)An+{Cn—Cii)A\i-\-{Cn—C^)A\T\-(C\a—C22)A\a-
(Ci—Ci)A\Jr(Ci—Cs)Ar\-2PsAh-\-(Ci—Cn)Av1r(.Ci—Cu)At+(Cs -Cn)Au-\-{Ca — CisMia-KCio— C20M15-KC12— C22)A\-+(Cn— Cu)Au=
(C0-C,8)^.l + (G-Cl0)^3 + (C’2-C12)^5-|-2P7^7f (C2-Cl6)^9+(C4 -CnMu+(C6 -C2oMl3+(C8 - C22M15 + (CI0-C24)n17+(Cl2-C2eM19 =
(Cz-Cui)A\+(C6—Ci2)Az-\-(Ci—Cii)As+(C2—C\t)A7+2P9Ai+(C2 — C20MU-HC4 — C22M13-HC6 — C24M15-KC8 — C20M17-KC10— C2t)An=
(CiQ—Ci2)A\+(Cs—Cu)Az-\-(C6—Cm)As+(Ci—C\s)AT+(C2—C2o)A2-}-2PuAu+(C2—Cu)A\2+(C4—C2s)Ais+(C(i — C2a)Aa+(Ca — C3oMis =
(C12 — Cn)Al-(-(ClO— Cie)A3+(C8— Cl8)A5-(-(C6 — C2o).-l7-(-(C,4— C22)A9+(C2— C27)ylil+2Pi3^4l3-HC2— C28)yll5-)-(C4 — Cjo)Ai7 + (C6 — C32Ml9 =
(Ch— Cl6)v4l+(C]2— Clg)-43+(ClO— C,2n)A5-|-(C8— C22)^l7+(C6— C24)Ag + (C4 — C26)A|1 + (C2 — C28)yll3+2Pi5Ai5-f (C2 — Cn)A\l-\-{Ci — C34) 1 9 =
(C16— C'l8)Al-(-(Ci4 — C2o)A3+(C'l2— C22)/l5-i-(C!0— C24)/l7 + (C8— C26)/l9+(Ce— C28)All+(C4— C3o)Al3+(C2— Ca2)Al5+2Pl7Al7-i-(C2— C36)Al9 =
(Clg— C2o)^4i + (C.16— C22).43-(-(Cl4— C21) A5+(Cr2— Go) A7 + (C’iO— C26)A9 + (C'8— C30) Au-f (Cs— C;2)/li3+(C4 — C34)A|5+(C2— C3f.)Al7+2Pi9^.i9 =
2fii
2 Bz
2Bs
■2B:
-2 Be,
2Bu
2BI3
2Bis
■2Bn
2Bi9
215
09)
P„=Co~~-C2n+nc-^
These equations form a system of normal simultaneous
equations, and it will be seen later that in the nth
equation the unknown An has the greatest coefficient,
the others decreasing rather rapidly. Because of this
circumstance, the system is most easily solved by a
method of successive approximations.
In the first equation, since the value of all the terms
is small compared with Pi Ah, an approximation to A\
is obtained by assuming all terms except Ax equal to
zero. Then in the next equation, since P3 Az is large
with respect to all terms except (C2—Ci) Alt which is
known, an approximation to A3 is obtained by assum¬
ing the remaining terms equal to zero. Thus by the
substitution of the approximated values in the other
equations, approximate values of the remaining coeffi¬
cients are obtained which, when substituted back in
the first equation, result in a closer approximation for
Ax. A repetition results in closer approximations for
all the coefficients. In this way the process can be
carried on until the approximations of the coefficients
cease to differ. Usually the second approximation is
fairly close, and the third may be considered as exact.
(See illustrative example.)
Forms for computing B„ and C2n coefficients.- -Before
the system of simultaneous equations (19) can be solved,
the Bn and C2n coefficients must be found. Forms for
determining these coefficients are given by plates I to
IV, inclusive. Plates I and II are for the case when
the circulation is to be determined at 10 points across
the semispan and plates III and IV are for 20 points.
It is only necessary to tabulate on each of the forms
the values of yn and yn' and to follow the steps indi¬
cated. The values of yn are the ordinates for the a sin 6
curves taken either every 9° or 4)2° (starting with the
tip as zero), depending upon whether 10 or 20 points
are used. The values of yn' are the ordinates of the
TYl C
~ ~ sin 6 curves taken at the same intervals as before.
Mo c
The checks indicated at the bottoms of these forms
merely serve as checks of the numerical work performed
on that sheet and, if only a few harmonics are to be
retained, the arithmetic may be decreased by comput¬
ing only the coefficients necessary and omitting the
checks.
Number of harmonics or points to be retained. — In
the series of simultaneous equations given by equation
(19) the question naturally arises as to how many
equations should be used and how many points across
the semispan are required. The system shown is for
10 points, but it may easily be extended to more than
10 points by following the indicated trend. In the
case given (equation (19)), the conditions are satisfied
at only 10 points when the whole system of equations
is solved simultaneously; if the system is cut off, as at
A, B, or C, where 4, 5, and 8 harmonics are retained,
the circulation may still be found at 10 points but with
a greater degree of approximation.
0 !0 OO 30 40 50 60 70 80 90 IOO
Percent semi span
Figure 7.— Effect of the number of harmonics on the span of ci distribution of a
wing without flaps. (Angle of attack, a, 1 radian.)
As a criterion for gaging the number of harmonics
to be retained, the span c; distribution has been com¬
puted (fig. 7) for an untwisted rectangular wing
(straight tips) of aspect ratio G at 1 radian angle of
attack, using 4, G, and 10 harmonics. The calcula¬
tions were repeated (fig. 8) for the same wing with a
r —0 .649 flap extending out from the center. The
O w
angle of attack for the portion with flap is 1 radian
and that of the remainder of the wing is zero. In
both cases 10 points have been used across the semi¬
span. The An, or circulation, coefficients from which
the distributions of figures 7 and 8 were computed
are given in table IV. In figure 9 the distribution
has been computed for a wing with double taper.
Distributions are given for the case using 10 points
38548—38 - 15
216
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
and retaining 4 anti 10 harmonics of the series and
also for the case with 20 points and 4 harmonics. For
convenience the distributions have been computed for
an untwisted wing at an angle of attack of 1 radian.
Example. — In order to illustrate the method of
calculating the wing characteristics, an example for a
wing with partial-span flaps is worked through the
forms to determine the Bn and C2n coefficients. The
calculations are made for one of the wing shapes
given in this report (A = 0.50, 21 = 10, 6//6w=0.489) at
an angle of attack of 1 radian from 0 to 0.489 and 0
from 0.489 to 1.0. The additional types of forms and
tables necessary to compute the load distribution for
a given case are also included.
Table V is a tabulation of the known geometric
quantities of the wing for which the load distribution
is desired. Column 1 of this table merely designates
the points along the span, the numbers increasing
O 10 20 30 40 50 60 70 80 90 IOO
Percent semi span
Figure 8.— Effect of the number of harmonics on the span ci distribution of a wing
with flaps. (Angle of attack, 1 radian from 0 to 0.649 and 0 from 0.049 to 1.000.)
numerically from the wing tip; column 5 represents
the angle of attack measured from zero lift at the
points along the span given in column 2. 'Where an
abrupt twist exists, the discontinuity will fall within
the portions of the span given in column 2. The final
computations, however, will be for the case of a flap
whose end lies halfway between these points. Because
of this fact a slight discrepancy in length may occur,
which can be reduced by increasing the number of
points. In the present case only the distribution due
to the flaps is found. In order to obtain a complete
determination of the distribution at other flap angles
and wing angles, it would also be necessary to find the
distribution corresponding to the plain wing. For this
case the C2n coefficients remain unchanged and Bx=aS)
all other Bn values being zero. Column 7 is the slope
of the section lift curves along the span which, in
this case, is assumed as 5.67. Column 8 is the ratio
of the slope of the section at the plane of symmetry
to the slopes of the sections at each station. Column
9 is the ratio of the chord at the plane of symmetry
to the chord at each section.
The values of columns 6 and 10 (yn and yn') are
then tabulated as shown in table VI and the instruc¬
tions of plates I and II, or of plates III and IV as in
the present example, are followed until the Bn and C2n
coefficients are found. If this method were used and
only four harmonics were to be retained, it would be
only necessary to compute Bx to B7 and C0 to CXi (see
A, equation (19)); computing the remaining coeffi¬
cients would be necessary only to obtain the check.
Figure 9.— Effect of the number of points and harmonics on the span ct distribution
for a wing with double taper.
A calculating form similar to table VII is then pre¬
pared. This form, as given, is complete for the case
of 10 harmonics irrespective of the number of points.
It will be noted that each major horizontal division
represents one of the simultaneous equations occurring
in equation (19). In column 1 of table VII are given
the operations required to obtain the coefficients and
in column 2 are tabulated the values of the coefficients,
etc., just found. In column 3 (a) are listed the values
of the An coefficients when they are known. Since
none are known at the start, Ax is determined as though
the others were absent arid listed in column 4 (a). The
value of A3 is next approximated in the same way,
except that the value of Ax just found is used as in-
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
217
dicated. The same procedure is followed for Ah , A7,
etc., and these values are listed in column 4 (a). After
all the An 8 have been approximated in this way, they
are written in column 3 (b) and the whole process
repeated, using the latest approximated value for each
coefficient as it appears. It can be seen that the
third approximation shows very little change from the
second, indicating that a solution has been obtained.
If it is desired to use fewer equations and harmonics,
the corresponding computing form can be obtained
from the present table VII simply by omitting all
computations dealing with the higher harmonics. Thus
if four harmonics were retained onty portions of the
form between the braces would be retained and the
computations would proceed as before.
It will be noted, in the present example, that, although
the Bn and C2n coefficients were determined for 20
points, it is not necessary that ct be computed for every
point to obtain the final load curve. Even though the
computations of the load distribution may be some¬
what shortened in this manner, the value of c* should
not be computed at points other than those first selected.
An examination of equation (19) will indicate that,
if n harmonics are retained, n values of B and 2 n
values of C are required. Hence, if it were decided to
use 10 harmonics and compute the circulation at 10
points, the Bn and C2n values can be determined for
20 points and the process shortened as indicated, or
the Bn coefficients could be determined from plate I
and the C2n coefficients from plate IV.
After the An coefficients have been determined, the
Ci values (in the present case c,—Cia) are found from
c-rMi^An sin nd (20)
c
These computations for Ci are given in table VIII for
only 10 points. The wing CL is found from
CL=7rA^A1 (21)
When this value is known, the distribution at any other
CL is obtained by direct proportion.
If desired, the induced-drag distribution may also
be computed by using the An coefficients
„ rnscs\}nAn sin nd , 00*
(>i 1 46 2-J sin 0
as shown in table VIII; however, an easier method
would be to compute it at each point from the equation
DISCUSSION
Although the computed span-loading curves show a
qualitative agreement with the experimental wing
curves (fig. 5), it, is not so good as might be inferred
from the results for the 2:1 tapered wing of reference 5.
In the present comparison, however, the disagreement
at the tip may be somewhat discounted since the square
tip on a rectangular wing is known to give a high tip
load. Comparisons of experimental and theoretical
distributions for plain wings have indicated better
agreement either as the tip was rounded or as the value
of X was decreased.
Rib-pressure curves taken from reference 2 (fig. 10)
show a drop in positive pressure near the trailing edge
for a section just beyond the end of the flap. This loss
in lift may partly account for the fact that the exper¬
imental distributions give sharper breaks than the cor¬
responding computed curves. An improvement in the
Figi-re 10.— Rib pressure distribution on a Clark Y wing with a partial-span split
flap. (Reference 2; a= 15°; 5/=45°.)
agreement at the end of the flap may also be obtained
by using more points and more harmonics in the series
for deriving the theoretical distributions.
For the rest of the span the agreement between the
computed and experimental curves would have been
slightly improved if jet-boundary corrections had been
applied to the data of reference 5. This correction,
which varies along the wing span, would effect a better
agreement in the present case.
The number of harmonics to be used in computing
the span loading depends both on the wing plan form
and on the type of wing twist. For wings with a con¬
tinuous taper and twist, four harmonics may be suffi¬
cient (fig. 7); whereas, for wings with either a sharp
double taper or a discontinuous twist, it may be neces¬
sary to increase the number of harmonics and points
(figs. 8 and 9), depending, of course, upon the desired
accuracy.
Although the data given herein are intended primarily
for structural purposes, they may also be useful in rela¬
tion to the stalling of tapered wings with flaps. When a
partial-span flap is deflected, there is an increase in
effective angle of attack and in the value of Cimax for
the sections with the flap; whereas, for the sections
beyond the flap, the effective angle of attack is theoret¬
ically increased without any increase in the value of
chnax- Thus, according to lifting-line theory, the tip-
stalling tendency of the tapered wing should be aug¬
mented by the use of flaps that extend out from the
218
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
center, while the center-stalling tendency of the rec¬
tangular wing should be increased by flaps at the tips.
Experimental results from reference 2 (fig. 11), how¬
ever, indicate that the pitching-moment coefficient (or
effective camber) of sections considerably beyond the
flap are actually increased by a flap deflection. This
increase may prevent these outboard sections from
stalling as early as would be indicated by the use of
lifting-line theory. Furthermore, since theory neglects
any transverse flow, any stalling characteristics based
upon it may be at best only qualitatively correct.
This statement is particularly true of a wing with a
partial-span flap, where a relatively large transverse
flow exists owing to the abrupt change in lift distribu-
Figure 11.— Increment of pitching moment Acmc/t caused by deflecting a 0.6-span
split flap on a rectangular Clark Y wing (reference 2).
tion produced by the flap. Lachmann’s tests (refer¬
ence 9), in which the action of wool tufts was observed,
seem to indicate that the transverse flow delays the
stall of sections immediately adjacent to the flap, thus
causing the initial stalling point to move outward away
from the flap end.
In regard to the application of the calculations to
structural design, fore-and-aft forces as well as vertical
forces must be taken into account. An examination
of equation (8) indicates that when A CLl A et is equal
to CL (case given by solid lines in fig. 1) the portion
of the wing without flaps has its lift vector displaced
forward owing to the upflow produced by the flapped
part. This forward component may be large enough
to cancel the profile drag. Thus, for a wing with flaps
at the center, the drag force is concentrated over the
flap portion, and there may be an antidrag force over
the outer portion of the wing. Hence, in design these
conditions should be taken into account in some
rational manner.
For structural purposes the ct values obtained by use
of tables I and II, or by computations, may be con¬
sidered equal to clo, the lift coefficient perpendicular
to the local relative wind. The values of C/0 and cdo,
which are perpendicular and parallel to the local rela¬
tive wind, may then be resolved into either chord and
beam or any other directions; the fore-and-aft loads
are thus obtained without the explicit use of a section
induced drag. The angle that the local relative wind
makes with the zero-lift direction is obtained by divid¬
ing C;0 by m0. In actual practice a portion of the wing
is intercepted by the fuselage so that the actual span
load distribution may be modified, depending upon
whether or not the fuselage carries its proportionate
share of the load. As so fevT data on fuselage loads
are at present available, it may be assumed that for
conventional cases the fuselage carries an amount of
load equal to the load that would be carried by the
wing it displaces.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., November 21, 1936.
REFERENCES
1. Anderson, Raymond F.: Determination of the Character¬
istics of Tapered Wings. T. R. No. 572, N. A. C. A., 1936.
2. Wenzinger, Carl'J., and Harris, Thomas A.: Pressure Distri¬
bution over a Rectangular Airfoil with a Partial-Span Split
Flap. T. R. No. 571, N. A. C. A., 1936.
3. Lotz, Irmgard: Berechnung der Auftriebsverteilung beliebig
geformter Fltigel. Z. F. M., vol. 22, no. 7, April 14, 1931,
S. 189-195.
4. Lippisch, A.: Method for the Determination of the Spanwise
Lift Distribution. T. M. No. 778, N. A. C. A., 1935.
5. Parsons, John F.: Span Load Distribution on a Tapered
Wing as Affected by Partial-Span Flaps from Tests in the
Full-Scale Tunnel. Jour. Aero. Sciences, vol. 3, no. 5,
March 1936, pp. 161-164.
6. Wenzinger, Carl J.: The Effect of Partial-Span Split Flaps
on the Aerodynamic Characteristics of a Clark Y Wing.
T. N. No. 472, N. A. C. A., 1933.
7. Wenzinger, Carl J.: The Effects of Full-Span and Partial-
Span Split Flaps on the Aerodynamic Characteristics of a
Tapered Wing. T. N. No. 505, N. A. C. A., 1934.
8. Shenstone, B. S.: The Lotz Method for Calculating the Aero¬
dynamic Characteristics of Wings. R. A. S. Jour., vol.
XXXVIII, no. 281, May 1934, pp. 432-444.
9. Lachmann, G. V.: Stalling of Tapered Wings. Flight, vol.
XXIX, no. 1410, Jan. 2, 1936, pp. 10-13.
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
219
PLATE I.— COMPUTING FORM FOR EVALUATING ANGLE COEFFICIENTS, Bn
10 POINTS
vi vi v * v* Vi vt i/7 y% vv Av io
i/H-03— vs— yi+y»=ri 02—09+34010=72
Multiply
by
Sin 9 = 0.1564 _ _
0i
“07
-03
09
Sin 18=0.3090 . .
02
05
06
02
Sin 27=0. 4540 . .
yz
0i
-09
-07
Sin 36=0. 5878 . . .
V*
-Ve
ye
~Vi
Sin 45=0. 7071 . . .
Vi
05
7 1
-03
05
Sin 54=0.8090 _ _ _
2/e
02
02
06
Sin 63 = 0.8910 .
2/7
-09
01
-03
Sin 72=0. 9511 . .
Vs
Vi
-Vi
-Ve
Sin 81=0. 9877 . .
09
03
07
01
Sin 90=1.0000 . .
}40io
— 340m
72
— 34010
34010
Sum col. 1 . . .
Sum col. 2 _ _
Col. 1+col. 2 _ _
= 5£i
=553
= 5 S5
= 5£j
=5 B«
Col. 1— col. 2 _
= 5£i?
«3
*o
II
= 5S,5
= 5Bi3
= 5£„
Check: Si — £3+ Bs — £?+ Ss — Bn + Si 3 — £15+ £i? — £i 9 = 0i o.
Note.— If <*„ is constant along the span, Si = a, and S3 to £u areO.
PLATE II.— COMPUTING FORM FOR EVALUATING PLAN FORM COEFFICIENTS, C2n
10 POINTS
340io'
0l'
02.'
Vi'
Vi'
05'
VC
01
»2
09'
0b'
y~'
ye'
Vs
04
f3
Sum . .
-..TO
»1
?;2
vz
Vi
7’5
Po
P>
Pi
Difference.
- 777 0
wi
W2
wz
U’i
00
01
02
10 Co =po+Pi+P2
5 Cio=Wo— «/j+«/<
10 C2O = 0O~ 01+02
M ultiply
by
Sin 18=0.3090 _ _
?/'4
02
Pi
— W2
Pi
-0i
Sin 36=0.5878 .
103
W 1
Sin 54=0.8090 _ _
wz
01
-Pi
— M’4
-pz
-02
Sin 72=0.9511 _
W\
-Wz
Sin 90=1.00000 _ . .
wo
00
Po
wn
Po
00
Sum col. 1 . .
Sum col. 2 . . . . _
= 5C<
=SCie
=5C8
=5Ci2
Col. 1+col. 2
= 5 C6
Col. 1 —col. 2
=5C]8
=5 Ci 4
Check: Co+C2+C<+Ce+C8+C,o+C,2+Cn+Ci6+C,s+C2o=0.
220
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
!/i
PLATE III.— COMPUTING FORM
FOR EVALUATING ANGLE COEFFICIENTS, Bn
20 POINTS
f/t 1/3 Vt Vs Vi Vi Vi 1/9 l/io Vn V\i Vn Vu Vis Vie Vn Vit Vn
J/i+1/7— 2/9-2/is+2/i7=ri
yi+yt—yio-vu+yis^n
V3+ys-Vn—Via+vit=n
^4— 2/12+.H2/20 —t*
Multiply
Sin 4.5-0.0785
Vt
i/13
1/17
Sin 9.0-0. 1564
1/2
-1/H
-1/6
Sin 13.5-0. 2334 . . ..
Vi
1/1
-2/11
Sin 18 0—0. 3090
Vi
1/12
1/12
Sin 22.5 = 0.3827 _
Vi
-1/15
ri
i/5
Sin 27.0- 0, 4540 ..
Vi
1/2
-1/18
Sin 31 5— 0. 5225
y-
Vn
1/1
Sin 36 0 - 0. 5878
Vi
-1/16
1/16
Sin 40 5—0 6494
y >
1/3
-1/7
Sin 45.0=0. 7071 _
y 10
1/10
ri
-l/io
Sin 49.5-0. 7604 . ..
J/11
-1/17
V 13
Sin 54 0-0. 8090
1/12
2/4
Vi
Sin 58 5-0. 8526
Vn
1/9
— J/l«
Sin 63 0—0. 8910
Vu
-1/18
1/2
Sin 67.5=0. 9239 _
V\ s
1/5
n
1/15
1/16
1/3
-1/8
Sin 76 5-0. 9724
J/l7
— i/19
-1/9
Sin 81.0-0. 9877 .. .
1/13
1/8
1/14
Sin 85 5-0. 9969
1/19
1/7
2/3
Sin 90.0= 1.0000... _
Hl/20
— Hl/20
T\
-H1/20
Sum col. 1 -
Sum col. 2 _
Col. l+col. 2 _
10Bi
10B3
lOBs
10 Bt
Col. 1— col. 2 _
10 B39
IOB37
lOBss
10B33
by
1/9
-I/11
1/3
1/7
-1/19
2/18
1/18
-1/6
—Vu
Vi
1/13
-1/7
2/9
VU
VU
1/4
-Vi
— 1/12
-1/12
-Vi
-Vs
y 15
1/15
— n
1/5
— 1/15
-1/14
-1/14
—1/18
1/2
Vs
— !/ir
1/3
1/19
-1/9
V 13
-1/8
08
-Vis
Vis
-2/8
1/1
-2/19
y 13
. . —
-1/17
-Vn
1/10
2/10
-1/10
r-i
l/io
l/io
2/19
1/1
2/7
-Vs
2/9
1/12
— 1/12
-Vi
-Vi
— 2/12
2/3
0tr
1/1
Vn
-1/7
-Vs
-1/a
1/2
-2/18
1/14
-2/15
-Vs
-Vs
n
1/15
Vs
— 1/16
1/16
VS
-1/8
-Vie
-2/7
-2/13
-1/11
l/i
-1/3
1/2
1/2
2/14
Vs
2/18
2/u
2/9
-2/17
-Vn
!/i
Hl/20
—H1/20
H1/20
—rt
Hi/ 20
— H1/20
10B9
1023,1
1023,3
IOB15
lOBn
IOB19
10B3i
10 #29
10B27
IOB25
IOB23
10B21
Check: Bi — B3+B5— B7+B1— ... -f- ••• ^39= i/20.
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS 221
PLATE IV— COMPUTING FORM FOR EVALUATING PLAN FORM COEFFICIENTS, C2„
20 POINTS
'Avn'
Vi'
vW
Vi'
Vi s'
y/
Va'
Vi'
Via'
Vi'
yn'
Vi'
y\i'
v‘,
Vis
Vi'
Vis'
Vt'
Vu‘
Sum _
V\
Vi
Vz
V*
Vs
Vi
Vl
Vz
Vo
Difference _
.*--W0
w 1
Wi
IV 3
Wi
ws
Wt
wi
Wi
WO
Vo
Cl
Vi
Vi
Vi
Vs
Po
pi
Pi
»10
cs
Vi
Vi
Po
Pi
Pi
Sum. .
---Po
Pi
P2
Pi
Pi
Pi
ro
T\
T2
Difference _
---Qo
<1i
Q2
Qi
Qi
So
Si
S2
20 Co =P0+Pl+P2+P3+P<+P5
10 Cl0= W% — W5+WJ-|-W9)+M!0— W{-\-Wt
10 C20 = ?0— 92+?4
10 Cso=V2(— W1+W3+WS— Wi— Wi)+Wa— Wi+Ws
20 C4l) = Po-Pl+P2-P3+P4-P5
Multiply
by
Sin 9—0.1564... . .
wo
Wi
Wi
W 1
Sin 18=0.3090 _
Wi
ns
-Wi
-52
-Wi
tog
Si
ri
-Si
Ti
Sin 27 =0.4540 _
Wi
—Wi
W\
— Wz
Sin 36=0.5878 _ _
Wi
Qi
W2
Qi
—w 2
— We
Sin 45-0.7071 .
Wr>
— Ws
W 5
We
Sin 54=0.8090 _
W\
Qs
— Wi
-Qi
—w%
Wi
Si
—Ti
-Si
-Ti
Sin 63 =0.8910 .
vh
w 1
— Wo
— Wi
Sin 72 = 0.9511.. .
W2
Q 1
—we
-Qi
We
—W2
Sin 81=0.9877 .
Wi
—w 7
— Wz
Wo
Sin 90=1.0000 _ _
Wo
Qo
wo
Qo
Wo
WO
so
To
So
TO
Sum col. 1 - -
10C8
10C,6
10C24
IOC32
Sum col. 2 ..
Col 1-f-col. 2
10C2
10 Ci
lOCo
IOC12
10C14
lOCis
10C38
10 Cm
10C34
10C28
10C28
10C22
Check: Co+C2+C1....CM=0.
TABLE I.— VALUES OF La FOR TAPERED WINGS WITH ROUNDED TIPS
.4 = 6
.4 = 10
\ Vlb
Vlb /
2/
//x
V
\
0
0. 15
0.30
0.45
0.60
0.70
0.80
0.90
0.95
0. 975
0
0. 15
0.30
0. 45
0.60
0. 70
0.80
0.90
0. 95
0. 975
1.00
1. 164
1. 163
1. 144
1. 115
1.050
0. 987
0. 870
0.669
0. 485
0.358
1. 116
1.111
1. 106
1.090
1.052
1.011
0. 929
0. 757
0. 572
0. 433
1.00
. 75
1.217
1.204
1. 167
1. 112
1. 026
. 953
.840
.648
.468
.340
1. 194
1. 179
1. 140
1.089
1.020
.964
. 875
.710
. 536
.396
. 75
.50
1.291
1. 263
1. 191
1. 107
.995
.908
.789
.607
.447
.319
1.292
1.257
1. 184
1. 093
.982
.903
. 800
.648
.492
. 367
.50
.25
1.392
1.349
1.243
1. 118
.954
.841
.709
.521
.386
.286
1.424
1. 368
1.247
1. 104
.940
. 823
. 695
.528
.407
.308
.25
TABLE II.— VALUES OF Lb FOR TAPERED WINGS WITH ROUNDED TIPS
[Valves of Lb given for flaps at center. Reverse signs when using for flaps at tips]
REPORT NO. 585 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
TABLE III. — CALCULATION OF LIFT DISTRIBUTION
FOR ILLUSTRATIVE EXAMPLE
[A, 6; bflbu, 0.383; S, 266.7 sq. ft.; b, 40 ft.; X, 0.625; Cl, 1.72; Ac,, 0.60; q, 57.5]
1
2
3
4
5
6
7
8
9
Station
«/i
Chord
(ft.)
La
Lb
Cl .
ol
Cl
(l
c'b
Cl
l
(lb.)
0
8.500
1.254
0. 356
0.984
1.693
0. 168
1.861
91.0
.15
8.022
1. 233
.334
1. 025
1.762
. 167
1.929
89.0
.30
7. 544
1. 179
.232
1. 043
1.794
. 123
1.917
83.1
.45
7.066
i. no
-.118
1.047
1.801
-.067
1.734
70.5
.60
6.588
1.010
-.220
1.022
1. 758
-. 134
1.624
61.6
.70
6.269
. 930
-.232
.989
1.700
-. 148
1.552
56.0
.80
5. 820
.815
-. 220
.934
1.607
-. 151
1.456
48.7
.90
4.825
.628
-. 179
.868
1.492
-. 148
1.344
37.3
.95
3. 655
.457
-.134
.835
1.435
-.147
1.288
27. 1
.975
2. 635
.330
-.097
.835
1.435
-.147
1.288
19.5
TABLE IV.— CIRCULATION COEFFICIENTS
[A, 6; X, 1.0; b//bw, 0.649]
No flaps
Flaps at center
Coeffi¬
cient
4 har¬
monics
retained
6 har¬
monics
retained
10 har¬
monics
retained
Coeffi¬
cient
4 har¬
monics
retained
6 har¬
monics
retained
10 har¬
monics
retained
A,
A 3
As
A?
At
An
An
A\s
An
An
0. 9280
.1158
.0251
.0069
0. 9290
. 1160
.0251
.0072
. 0026
.0011
0. 9290
. 1161
.0251
.0073
.0026
.0011
. 0005
.0003
.0002
.0004
Ai
Ai
As
Ai
Ai
An
A\z
Ais
An
A 19
0. 6682
-. 1825
-.0298
.0588
0. 6684
-.1826
-.0301
.0585
.0017
-.0286
0. 6682
-. 1826
— . 0300
. 0586
.0019
-.0281
.0058
.0168
-.0083
-. 0104
TABLE V.— GEOMETRIC CHARACTERISTICS OF WING USED IN EXAMPLE
■
2
3
4
5
6
7
8
9
10
Fraction of
e
sin 6
a
mo for
771,
c.
A
semispau
(deg.)
(rad.)
a sin g
b= oo
771 o
c
- sin 6
m oc
20
0
90
1. 0000
1
1.0000
5. 67
1.0
1. 0000
1. 0000
19
.0785
85.5
.9969
i
. 9969
5. 67
1.0
1. 0400
1. 0370
18
. 1564
81
.9877
1
.9877
5.67
1.0
1. 0848
1.0717
17
. 2334
76.5
.9724
1
.9724
5. 67
1.0
1. 1295
1. 1030
16
.3090
72
.9511
1
.9511
5.67
1.0
1. 1827
1. 1252
15
.3827
67.5
.9239
1
.9239
5. 67
1.0
1. 2386
1. 1445
14
.4540
63
.8910
1
.8910
5.67
1.0
1. 2937
1. 1530
13
. 5225
58.5
.8526
0
0
5.67
1.0
1. 3555
1. 1560
12
.5878
54
.8090
0
0
5. 67
1.0
1.4162
1. 1455
11
.6494
49.5
.7604
0
0
5.67
1.0
1. 4785
1. 1245
10
.7071
45
.7071
0
0
5. 67
1.0
1. 5469
1. 0939
9
.7604
40.5
.6494
0
0
5. 67
1.0
1. 6100
1. 0458
8
.8090
36
. 5878
0
0
5. 67
1.0
1. 6793
.9869
i
.8526
31.5
.5225
0
0
5. 67
1.0
1.7415
.9100
6
.8910
27
.4540
0
0
5. 67
1.0
1. 8219
.8272
5
.9239
22.5
.3827
0
0
5. 67
1.0
1. 9605
.7500
4
.9511
18
.3090
0
0
5. 67
1.0
2.2504
.6953
3
.9724
13.5
.2334
0
0
5. 67
1.0
2. 8280
.6600
2
.9877
9
.1564
0
0
5.67
1.0
4. 0742
.6372
1
.9969
4.5
.0785
0
0
5. 67
1.0
7. 9740
.6260
0
1.0000
0
0
0
0
5. 67
1.0
224
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE VI.— COMPUTATION OF ANGLE COEFFICIENTS, Bn
Vi V2 V2 y< yi yt yi y» y 10 vn yn yn vn vn yn vn yn yn
0 0 0 0 0 0 0 0 0 0 0 0 0 0.8910 0.9239 0.9511 0.9724 0.9877 0.9969 0.5000
ri = 0+0— 0—0.9239+0.9724 = 0.0485
r2 = 0+0— 0—0.8910+0.9877= .0967
r3=0+0— 0— 0 +0.9969= .9969
r4=0— 0+0.5000 = .5000
Multiply
by
Sin 4.5=0.0785.
0
0
0.0763
0
0
0
0
-0.0783
Sin 9 = 0.1564.
0
-0.1394
0
0.1545
0.1545
0
-0.1394
0
Sin 13.5=0.2334.
0
0
0
0
0
0
0.2327
.2270
Sin 18 =0.3090.
0
0
0
0
0
0
0
0
Sin 22.5=0.3827.
0
-0.3536
0.0186
0
0
0.3536
0.3536
—0.3815
0
-.3536
Sin 27 =0.4540.
0
0
-0.4484
-.4045
-.4045
-0.4484
0
0
Sin 31.5=0.5225.
0
0
0
-0.5081
0
.5209
0
0
Sin 36 = 0.5878.
0
-.5591
.5591
0
0
-.5591
.5591
0
Sin 40.5=0.6494.
0
0
0
0
-.6474
0
-.6315
0
Sin 45 =0.7071.
0
0
0.0684
0
0
0
0
0.0684
0
0
Sin 49.5=0.7604.
0
-.7394
0
.7580
0
0
0
0
Sin 54 =0.8090
0
0
0
0
0
0
0
0
Sin 58.5 = 0.8526.
0
0
-.8500
0
.8291
0
0
0
Sin 63 = 0.8910.
.7939
-.8800
0
0
0
0
-.8800
0.7939
Sin 67.5=0.9239
.8536
0
.9210
.8536
-.8536
0
0
.0448
.8536
0
Sin 72 =0.9511.
.9046
0
0
-.9046
.9046
0
0
-.9046
Sin 76.5=0.9724
.9456
-.9694
0
0
0
0
0
0
Sin 81 =0.9877.
.9756
0
.8800
0
0
.8800
0
.9756
Sin 85.5=0.9969
.9938
0
0
0
0
-.9694
0
0
Sin 90 =1.0000.
.5000
-.5000
.5000
-.5000
.5000
-.5000
_
.5000
-.5000
.5000
-.5000
Sum col. 1 _
2.7930
-2.0624
0.9396
0.0799
-0.6037
0.5353
-0.0949
-0.3367
0 4548
-0.2049
Sum col. 2 _
3.1741
-2.0785
.5684
.4907
-.6546
.1546
.3725
-.4316
.0397
.3649
Col. 1+col. 2 _
5.9671 = 105,
1
4-
£
O
O
II
O
1. 5080 = 10 Bs
0.5706 = 1057
-1.2583 = 10B9
0.6899 = 10Bn
0.2776 = 105,3
-0.7683 = 105,5
0.4945 = 105,7
0.1600 = 105,9
Col. 1— col. 2 _
— .3811 = 10+?38
.0161 = 10B37
.3712=10B35
-.4108 = 10533
.0509=10531
.3807 = 10529
-.4674 = 10527
.0949=10525
.4151 = 10523
-.5698 = 1052,
Cheek:
5, — Ih + Bi — Bi + Bn — Bn + Bn — 5,5 + Bn — Bn + Bn — B23 + B25 — B2? + Bw — Bn + Bn — Bn + By, — Bn = ','20.
0.5967+0.4141+0.1508-0.0571-0.1258-0.0690+0.0278+0.0768+0.0495-0.0160-0.0570-0.0415+0.0095+0.0467+0.0381-0.0051-0.0411-0.0371+0.0016+0.0381 = 1.0000.
COMPUTATION OF PLAN-FORM COEFFICIENTS, Cin
0. 5000
0. 6260
1.0370
0. 6372
1.0717
0. 0600
1. 1030
0. 6953
1. 1252
0. 7500
1. 1445
0. 8272
1. 1530
0. 9100
1. 1560
0. 9869
1. 1455
1. 0458
1. 1245
1. 0939
Sum _
Difference _
0. 5000
-.5000
1.6630
-.4110
1. 7089
-. 4345
1. 7630
-.4430
1.8205
-.4299
1. 8945
-. 3945
1. 9802
-. 3258
2. 0660
-.2460
2. 1324
-.1586
2. 1703
-.0787
1. 0939
1. 0939
0. 5000
1. 0939
1.6630
2. 1703
1. 7089
2. 1324
1. 7630
2. 0660
1. 8205
1. 9802
1. 8945
1. 5939
1. 8945
3. 8333
3. 8007
3. 8413
3. 8290
Sum . .
Difference _
1. 5939
-. 5939
3. 8333
-.5073
3. 8413
-. 4235
3. 8290
-.3030
3. 8007
-. 1597
1.8945
3. 4884
-.3006
7. 6340
.0326
7. 6703
.0123
20Co =1.5939+3.8333+3.8413+3.8290+3.8007+1.8945 = 18.7927
10C,io=1.4142( -0.4110+0.4430+0.3945-0.2460-0.0787) -0.5000+0.4299- 0.1586= -0.0847
10C2o= -0.5939+0.4235- 0.1597= -0.3301
10C3o=1.4142(0.4110— 0.4430 — 0.3945+0.2460+0.0787)— 0.5000+0.4299 — 0.1586= —0.3727
20C«=1. 5939—3.8333+3.8413—3.8290+3.8007—1.8945= —0.3209
Multiply
by
Sin 9=0.156+
-0.0123
-0. 0693
-0. 0385
-0. 0643
Sin 18 =0.3090-
-0. 0490
-0. 0493
0. 1328
0. 1309
0. 1328
-0. 0490
0. 0038
2. 3589
-0.0101
2. 3701
Sin 27=0.4540,
—.1117
.0357
-. 1866
.2011
Sin 36=0.5878.
-. 1915
-0. 1781
-.2554
-0. 2982
.2554
.1915
Sin 45=0.7071.
-.2790
.2790
-.2790
-. 2790
Sin 54 =0.8090.
-.3478
-. 3426
. 1283
.1292
. 1283
-.3478
. 0264
-6. 2053
-.0100
-6. 1759
Sin 63=0.8910.
-.3947
-. 3662
.0701
.2192
Sin 72=0.951+
-.4133
-.4825
.3099
.2882
-.3099
.4133
Sin 81=0.9877.
-.4059
.2430
.4376
-. 0777
Sin 90=1.0000.
-. 5000
-. 5939
-. 5000
-. 5939
-. 5000
-. 5000
-.3006
3. 4884
-. 3006
3. 4884
Sum col. 1 _
-1. 5016
-. 9858
-. 1844
-.3338
-. 2934
-.2920
-.2704
-.3580
-.3207
-.3174
Sum col. 2-
-1.2036
-. 6606
. 1222
-. 0100
.0036
-. 0007
10 Ct
10 C,6
10 C24
10 C32
Col. 1+col. 2 _
-2. 7052=10 C2
-1.6464 = 10 C,
-.0622=10 C6
-.3438=10 C12
— .2898=10 Cn
-. 2927=10 5,8
Col. 1— col. 2_.
-.2980=10 C3s
-.3252=10 C36
-.3066=10 C34
-.3238=10 C28
-. 2970=10 C26
-.2913=10 C22
Check: 0.9390 - 0.2705- 0.1646 -0.0002- 0.0270- 0.0085 - 0.0344- 0.0290-0.0358 - 0.0293 - 0.0330- 0.0291-0.0321-0.0297 - 0.0324 - 0.0373 - 0.0317 - 0.0307 - 0.0325 - 0.0298 - 0.0160 = 0.
SPAN LOAD DISTRIBUTION FOR TAPERED WINGS WITH PARTIAL-SPAN FLAPS
225
TABLE VII.— SOLUTION OF An COEFFICIENTS
1
2
3(a) I
3(b)
3 (C)
4 (a)
4 (b)
4 (C)
(T'i— Ci)^4a
-0. 1059
-0. 2563
-0. 2487
0. 0271
0. 0263]
(G— GsMs -
-.1584
.0824
.0823
-.0131
- 0130>
1
/'(7ft— .
.0208
.0182
.0169
. 0004
. 0004 1
/
-.0185
-.0411
-.0400
. 0008
.0007
V
/
.0259
.0190
.0189
. 0005
. 0005
k
—.0054
.0092
.0087
0
0
/
.0068
-. 0201
-.0197
-.0001
-.0001
-.0065
.0117
.0118
-.0001
-.0001
V
.0037
. 0032
.0032
0
0
0
. 0155
.0147)
2/2_ . -
0
.0077
. 0073
Pj S/2
. 5967
.5967
. 5890
. 5894)
(Pi —2/2)
/l. 2667
. 4711
. 4650
. 4653
yl‘ -
((Ca— Ci)A\ _
-0. 1059
0. 4711
0. 4650
0. 4653
-0. 0499
-0. 0492
-0. 0493)
) (Ci—CtiAb _
-. 2435
. 0824
.0823
-. 0201
-.0200-
\(C!a (7i
-. 1561
.0182
.0169
-.0028
-.00261
(Cl Ct o') A 0
.0282
-.0411
-.0400
-. 0012
-.0011
. 0020
.0190
. 0189
0
0
. 0273
.0092
.0087
.0002
. 0002
( c, o (7,jA/4h
-. 0051
-.0201
-.0197
.0001
. 0001
( C ,4 (7oaMi?
.0040
.0117
.0118
.0001
.0001
-. 0067
.0032
.0032
0
0
|S _
-.0499
-.0730
-.07261
| yJ?. _
-.0249
-.0365
-.0363
< Ri — S/2 .
-.4141
-.3892
-.3776
— . 3778 [
(Pa-2/2)
/ 1. 5185
-. 2563
-.2487
-. 2488)
1 Ai Pa -
( ( C4 — C6)-4 1 _ . . -
-0. 1584
0. 4711
0. 4650
0. 4653
-0. 0746
-0. 0736
0— . 0737)
(C.-CsMs .
-.2435
-.2563
-. 2487
-.2488
. 0024
.0606
. 0606}
|(C2-Cl2)A7 -
-.2361
_
.0182
.0169
-.0043
—,004l|
<r, (?,,'! /In
- 1356
-. 0411
-. 0400
. 0056
. 0054
irv (7.ftWtn
. 0296
. 0190
.0189
. 0006
. 0006
rr'o (7. a) /1 1
. 0023
.0092
.0087
0
0
. 0245
-.0201
-.0197
-.0005
-.0005
-. 0053
.0117
.0118
-.0001
-.0001
. 0031
.0032
.0032
0
0
s _
-.0122
-.0117
-.01181
S/2
-.0061
-.0059
-.0059
p5— S/2
. 1508
. 1569
. 1567
. 1567?
(P5— 2/2)
/ 1. 9035
.0824
.0823
. 0823 j
"la p5 —
0. 0280
0.4711
0. 4650
0. 4653
0.0098
0. 0097
0. 0097)
• (G-G0M3 _
-. 1561
-. 2563
-. 2487
-.2488
.0400
.0388
. 0388?
1(C2-CuMs _
-.2361
. 0824
.0823
.0823
-.0195
-.0194
-.0194)
-.2347
-.0411
-. 0401
. 0091
.0094
(7.o ) An
-. 1353
.0190
.0189
-. 0026
-. 0026
.0268
.0092
.0087
.0002
. 0002
.0021
-.0201
-.0197
0
0
.0236
.0117
.0118
.0003
.0003
-.0047
.0032
.0032
0
0
lY
.0303
. 036C
. 0364)
[s/2
. 0152
.0183
.0182
< P7 — S/2
. 0571
.0419
.0388
.0389?
(Pj-2/2)
/2. 2977
.0182
. 0169
. 0169 )
1 P; .
-0. 0185
0.4711
0. 4650
0. 4653
-0. 0087
-0. 008f
-0.0086
(C6-C12M3 _
.0282
-. 2563
-.2487
-.2483
-.0072
-.0071
0070
(C4-C1OA5 _
-. 1356
.0824
. 0823
. 0823
-.0111
-.0112
-.0112
(C2-C16M7 _
-. 2347
.0182
. 0161
. 0169
-.0041
-.0041
-.0040
-.2375
.0190
. 0181
_
-. 004f
-.0045
— . 1355
.0092
.0087
-.0012
-.0012
. 025S
-.0201
-. 0197
-.0001
-. 0005
.0027
.0117
.0113
0
0
. 023S
.0031
.0031
.0001
.0001
S .
-.0314
-.0369
-.0369
S/2
-.015"
-. 0184
-. 0184
Ho S/2
-. 1255
-. 110
-. 1074
-.1074
(69— 2/2)
/2. 6817
.
-.041
-. 0401
-.0400
P8 -
1
1
2
3 (a)
3 (b)
3(c)
4(a)
4 (b)
4 (c)
0. 0259
0. 4711
0. 4650
0. 4653
0.0122
0.0120
0. 0120
.0020
-. 2563
-.2487
-. 2488
-. 0005
-.0005
-.0005
.0296
. 0824
.0823
.0823
. 0024
.0024
. 0024
(G-GsM? _
-. 1353
. 0182
.0169
. 0169
-.0025
-. 0023
-.0023
-.2375
-.0411
-.0400
-.0400
.0098
. 0095
. 0095
-.2384
. 0092
.0087
-.0022
-.0021
-. 1349
-.0201
-.0197
.0027
.0027
. 0262
.0117
.0118
.0003
.0003
.0103
.0032
.0032
0
0
V
.0214
.0219
. 0220
2/2 .
.0107
.0110
.0110
Bn— 2/2 . .
. 0690
.0583
.0580
.0580
„ (Pn— 2/2)
/3. 0654
.0190
. 0189
.0189
P11 .
_
-0. 0054
0. 4711
0. 4650
0. 4653
-0. 0025
-0. 0025
-0. 0025
(Go— C\%)Ai .
.0273
-.2563
-.2487
-.2488
-.0070
-.0068
-. 0068
(G— Cn)As - -
. 0023
.0824
. 0823
.0823
. 0002
. 0002
.0002
(G— 020)^7 _
.0268
.0182
.0169
.0169
. 0005
.0004
. 0004
(C4-C22M9-- .
-. 1355
-.0411
-.0400
-.0400
. 0056
.0054
.0054
(C 2— Cu) An . .
-.2384
. 0190
.0189
.0189
-.0045
-.0045
-.0045
-. 2381
-.0201
-.0197
. 0048
.0047
— . 1273
.0117
.0118
—.0015
-.0015
.0255
. 0032
.0032
. 0001
.0001
2
-.0077
-.0044
-.0045
2/2 __
-. 0039
-. 0022
-. 0022
P13-2/2 ..
. 0278
.0317
. 0300
.0300
Att (Bl3-2/2)
/3. 4496
.0092
.0087
.0087
‘ P ]3 . .
(G4— Ge)-4i -
0. 0068
0.4711
0. 4650
0. 4653
0. 0032
0. 0032
0. 0032
-.0051
-.2563
-.2487
-. 2488
.0013
.0013
.0013
(Go— (720)^5 -
. 0245
.0824
. 0823
.0823
.0020
. 0020
. 0020
. 0021
.0182
.0169
.0169
0
0
0
. 0259
-.0411
-. 0400
— . 0400
-.0011
-.0010
-.0010
-. 1349
. 0190
. 0189
.0189
-.0026
-. 0020
-.0026
(C2—C2s)A\3--~ -
-. 2381
.0092
. 0087
.0087
-. 0022
-. 0021
-.0021
-. 2388
.0117
.0118
-.0028
-, 0028
-. 1339
.0032
. 0032
-.0004
-. 0004
■y
.0006
-.0024
-.0024
2/2
. 0003
-.0012
-.0012
Pi5— 2/2
-. 0768
-.0771
-.0756
-. 0756
a15-(b,5-s/2).„.
/3. 8373
-.0201
-.0197
-.0197
-r 15
-0. 0065
0 4711
0. 4650
0. 4653
-0. 0031
(). 0030
-0. 0030
(G4-G0M3 _
.0040
-. 2563
-. 2487
-. 2488
-.0010
-.0010
-.0010
(G2-G22M5 _
-.0053
.0824
.0823
. 0823
-.0004
— . 0004
-.0004
.0236
.0182
.0169
.0169
. 0004
. 0004
. 0004
. 0027
-.0411
-.040(1
-. 0400
-.0001
-. 0001
-.0001
(C6— C28UI11 -
.0262
.0190
. 0189
.0189
.0005
.0005
. 0005
(G— C3(Uli3- .
~. 1273
.0092
.0087
. 0087
-.0012
-.0011
-. 001 1
(C2— C32).4i5 .
-. 2388
-.0201
-.0197
-.0197
.0048
.0047
.0047
-.2380
.0032
.0032
-.0008
-. 0008
V
-.0001
-.0008
-.0008
2/2 .
0
-. 0004
-. 0004
Pi:— 2/2
.0494
.0494
.0498
.0498
. (Pi:-2/2)
14. 2180
.0117
.0118
.0118
P17
0. 0037
0. 4711
0. 4650
0. 4653
0.0017
0. 0017
0.0017
(Cl6— G22)^43 -
-. 0067
-. 2563
-.2487
-. 2488
.0017
.0017
.0017
(Cu-Cn)As . -
.0031
. 082'
. 082c
. 0823
. 000c
. 000c
. 0003
(G2-G0M7--- .
-.0047
. 0182
.0169
.0169
-.0001
-.0001
-.0001
.0239
-.0411
-.0400
-. 0400
-. 0010
-.0010
-.0010
.0103
. 019C
.0189
.0189
.0002
.0002
. 0002
.0255
. 0099
. 0087
. 0087
.0002
.0002
.0002
(G— Cm) An -
-. 1339
-.0201
-.0197
-.0197
.0027
.0026
. 0026
238C
.Oil?
.0118
.011?
-. 0028
-.0028
-.0028
.0021
.0028
.0028
2/2 .
.0015
.0014
.0014
Pis— 2/2
.oik
.0145
.0141
.0146
, (Pio-2/2)
14. 6014
.
.003?
. 003?
.0032
P is .
.
226
REPORT NO. 585— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE VIII.— COMPUTATION OF LOAD DISTRIBUTIONS
i
20
18
16
14
12
10
8
6
4
2
90
81
72
(53
54
45
36
27
18
9
*
(Sin 0 . . - . .
1. 0000
0. 9877
0. 9511
0. 8910
0. 8090
0. 7071
0. 5878
0. 4540
0. 3090
0. 15641
J Sin 30 . . . . -
-1.0000
-.8910
-. 5873
-. 1564
. 3090
.7071
.9511
.9877
. 8090
,4540l
1 Sin 50 . - . .
1.0000
.7071
0
-.7071
- 1. 0000
-.7071
0
.7071
1. 0000
.70711
(siu Id _ _
-1.0000
-. 4540
. 5878
. 9877
. 3090
-.7071
-.9511
-. 1564
. 8090
. 8910J
"Sin90 . .
1. 0000
. 1564
-.9511
-. 4540
. 8090
.7071
-. 5878
-.8910
.3090
.9877
Sin 110 _ _ _
-1.0000
. 1564
.9511
-. 4540
-. 8090
.7071
. 5878
-.8910
-. 3090
. 9877
Sin 130 . . .
1.0000 .
-. 4540
-. 5878
.9877
3090
-. 7071
.9511.
-. 1564
-. 8090
.8910
Sin 150 _ _
-1.0000
.7071
0
-. 7071
1. 0000
-. 7071
0
.7071
-1. 0000
.7071
1.0000
-.8910
.5878
— . 1564
-. 3090
.7071
-.9511
. 9877
-. 8090
. 4540
Sin 190 . — .
-1.0000
.9877
-.9511
.8910
-. 8090
.7071
-. 5878
.4540
-. 3090
. 1564
<Ai sin 0 _ _
. 4653
.4596
. 4425
.4146
. 3764
. 3290
.2735
. 2112
. 1438
. 0728)
U, sin 30 _ _ _ _ -
.2488
. 2217
. 1462
.0389
-.0769
-. 1759
-. 2360
-. 2457
-.2013
-. 1 129 1
1 As sin 50 _
. 0823
.0582
0
-. 0582
-. 0823
-. 0582
0
. 0582
. 0823
. 0582 f
[A; sin 70 - _
-. 0169
-. 0077
.0099
.0167
.0052
-. 0120
-.0161
-. 0026
.0137
. 0151 J
.•Is sin 90 . . _ _ _
-. 0400
-. 0063
.0381
. 0182
-.0324
-.0283
. 0235
.0357
-. 0124
-. 0396
.Au sin 110. _
-.0189
. 0030
. 0180
-.0086
-.0153
. 0131
.0111
-. 0168
-. 0058
.0187
A is sin 130 _
.0087
- 0039
-.0051
. 00S6
-. 0027
-.0061
.0083
-. 0014
-. 0070
.0077
Ansin 150 . . .
.0197
-. 0139
0
.0139
-.0197
. 0139
0
-.0139
.0197
-. 0139
A 17 sin 170... _ .. _
.0118
-.0105
. 0069
-.0018
-. 0037
. 0084
-.0112
.0117
-. 0096
. 0054
A 19 sin 190 _ _
-. 0032
.0031
-. 0030
.0028
-. 0026
. 0022
-.0019
.0014
-. 0010
.0005
1 2/1 n Sill 7l0 _ _ _
.7576
.7033
. 6535
.4451
. 1460
. 0861
.0506
.0378
. 0224
.0120)
\m,c,/c _ _
5.670
6. 152
6. 708
7. 337
8. 029
8. 772
9.520
10.331
12. 760
23. 100 1
lci=m,c,/cXS() . .
4.296
4. 327
4.384
3.266
1. 172
.7579
.4817
.3905
.2858
. 2772)
[Ai sin 0 _ _ _
.4653
. 4596
.4425
.4146
.3764
. 3290
.2735
.2112
. 1438
. 0728)
I3A3 sin 30 _
. 7463
. 6650
.4387
. 1167
-.2306
-. 5277
-. 7098
-.7371
-. 6038
-. 33881
I5A5 sin 50 _
.4115
.2910
0
-. 2910
-.4115
-.2910
0
.2910
.4115
. 2910 1
I.7A7 sin 70 _ _
-. 1184
-. 0538
. 0696
. 1170
. 0366
-. 0837
-.1126
-.0185
. 0958
. 1055)
9A9 sin 90 _ _
-. 3604
-. 0564
. 3428
. 1636
-. 2916
-. 2549
.2119
.3212
-. 1114
-. 3560
11 An sin 110 . . . . .
-. 2078
. 0325
. 1976
-. 0943
-. 1681
. 1469
. 1221
-. 1851
-. 0642
. 2052
13Ai3 sin 130 _ _
. 1130
-. 0513
-. 0664
. 1116
-. 0349
1 -. 0799
. 1074
-.0177
-.0914
. 1007
15Ai5 sin 150 _ _
.2957
-.2091
0
. 2091
-. 2957
. 2091
0
-. 2091
. 2957
-.2091
17/1 17 sin 170 . . _ . .
.2009
-. 1790
. 1181
-. 0314
-.0621
. 1421
-. 1911
. 1985
-. 1626
. 0912
19/1 19 sin 19# . . . . .
-. 0602
. 0595
-. 0573
.0537
-.0487
. 0426
-. 0354
. 0273
-. 0186
. 0091
[SnAn sin n0 . _ _ _
1. 4859
. 9580
1. 4856
. 7696
-1. 1302
-. 3675
-.3340
-. 1183
-. 1052
-. 0281
J m.c, /46X2()/sin 0 . .
.2852
. 1839
.2851
. 1477
-. 2169
-. 0705
-.0641
-.0227
-. 0202
-.00541
L.=c 1
1.2252
.7957
1.2499
.4824
-. 2542
-. 0534
-. 0309
-. 0089
-.0058
-. OOlsJ
1 * L 46 sin 0J
REPORT No. 586
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE
REYNOLDS NUMBER
By Eastman N. Jacobs and Albert Sherman
SUMMARY
An investigation of a systematically chosen representa¬
tive group of related airfoils was made in the N. A. C. A.
variable-density wind tunnel over a wide range of the
Reynolds Number extending well into the flight range.
The tests were made to provide information from which the
variations of airfoil section characteristics with changes in
the Reynolds Number could be inferred and methods of
allowing for these variations in practice could be deter¬
mined. This work is one phase of an extensive and general
airfoil investigation being conducted in the variable-density
tunnel and extends the previously published researches
concerning airfoil characteristics as affected by variations
in airfoil profile determined at a single value of the
Reynolds Number.
The object of this report is to provide means for making
available as section characteristics at any free-air value
of the Reynolds Number the variable-density-tunnel airfoil
data previously published. Accordingly , the various cor¬
rections involved in deriving more accurate airfoil section
characteristics than those heretofore employed are first
considered at length and the corrections for turbulence are
explained. An appendix is included that covers the
results of an investigation of certain consistent errors
present in test results from the variable-density tunnel.
The origin and nature of scale effects are discussed and
the airfoil scale-effect data are analyzed. Finally, meth¬
ods are given of allowing for scale effects on airfoil section
characteristics in practice within ordinary limits of accu¬
racy for the application of variable-density-tunnel airfoil
data to flight problems.
INTRODUCTION
When data from a model test are applied to a flight
problem, the condition that should be satisfied is that
the flows for the two cases be similar. The Reynolds
Number, which indicates the ratio of the mass forces to
the viscous forces in aerodynamic applications, is ordi¬
narily used as the criterion of similarity. The practical
necessity for having the flow about the model aerody-
namically similar to the flow about the full-scale object
in flight becomes apparent from the fact that aero¬
dynamic coefficients, as a rule, vary with changes in the
Reynolds Number. This phenomenon is referred to as
“scale effect.”
Early investigations of scale effect were made in
small atmospheric tunnels at comparatively low values
of the Reynolds Number and, for airfoils, covered a
range of the Reynolds Number too limited and too
remote from the full-scale range to permit reliable
extrapolations to flight conditions. Attempts were
made to bridge the gap between the two Reynolds
Number ranges by making full-scale flight tests for
comparison with model tests. These investigations of
scale effect, however, proved disappointing owing
partly to the difficulty of obtaining good flight tests
and to the difficulty of reproducing flight conditions
in the model tests and partly to the large unexplored
Reynolds Number range between the model and flight
tests with consequent uncertainties regarding the
continuity of the characteristics over this range.
Furthermore, the flight tests could not ordinarily
include a sufficiently large range of the Reynolds
Number to establish the character of the scale effects
for certain of the airfoil characteristics over the full-
scale range of the Reynolds Number, which may extend
from values as low as a few hundred thousand to thirty
million or more.
These limitations of the early investigations were
first overcome by the N. A. C. A. through the use of
the variable-density tunnel, which was designed to
facilitate aerodynamic investigations over the entire
range of Reynolds Numbers between the wind tunnel
and flight values. Several miscellaneous and com-
monly used airfoils were investigated for scale effect
in the variable-density tunnel during the first years of
its operation. The results indicated that important
scale effects for some airfoils may be expected above
the usual wind-tunnel range and even within the flight
range of values of the Reynolds Number. Later,
when the N. A. C. A. full-scale tunnel was constructed,
airfoil tests therein served to confirm the importance
of scale effects occurring in the full-scale range and also
provided valuable data for the interpretation of the
variable-density-tunnel results, particularly in con¬
nection with the effects of the turbulence present in the
227
228
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
variable-density tunnel. The interpretation of the
variable-density-tunnel results has consequently been
modified to allow for the turbulence on the basis of an
“effective Reynolds Number” higher than the test
Reynolds Number.
In the meantime, the investigations of airfoils in
the variable-density tunnel had been turned to an
extensive study of airfoil characteristics as affected
by airfoil shape. This phase, which resulted in the
development of the well-known N. A. C. A. airfoils,
involved the testing of a large number of related
airfoils, but these tests were largely confined to one
value of the Reynolds Number within the full-scale
range. Such a procedure expedited the investigation
and provided comparable data for the various airfoils
within the full-scale range of the Reynolds Number
but, of course, gave no information about scale effects.
As previously stated, the full-scale-tunnel results had
provided information regarding the application of the
variable-density-tunnel data to flight. Methods were
accordingly developed for correcting the data and for
presenting them in forms that would facilitate their
use as applied to flight problems. Flight problems,
however, require airfoil data at various values of the
Reynolds Number between values as low as a few
hundred thousand in some cases to thirty million or
more in others. Obviously the results available from
the tests of related airfoils at one value of the Reynolds
Number (effective Reynolds Number= 8,000,000) are
inadequate for the purpose unless they can be corrected
to other values of the Reynolds Number. The present
investigation was therefore undertaken to study the
scale effects for the related airfoil sections primarily
with a view to the formulation of general methods for
determining scale-effect corrections for any normal
airfoil section so that the standard test results from
the variable-density tunnel coidd be applied to flight
at any Reynolds Number. For most practical uses it
is considered desirable and sufficient to present airfoil
test results in the form of tabular values giving certain
important aerodynamic characteristics for each airfoil
section. The primary object of this investigation,
therefore, is to give information about the variation of
these important airfoil section characteristics with
Reynolds Number.
In regard to the scope of the experimental investiga¬
tion, the Reynolds Number range was chosen as the
largest possible in t lie variable-density tunnel and the
airfoil sections were chosen to cover as far as possible
the range of shapes commonly employed. Accord¬
ingly, groups of related airfoils (fig. 1) were tested to
investigate the following variables related to the
airfoil-section shape:
Thickness.
Camber.
Thickness and camber.
Thickness shape.
Camber shape.
Sections with high-lift devices.
The testing program was begun in May 1934 and
extended several times as it became apparent that
additional tests would be desirable. The final tests
in the variable-density tunnel were made in September
1935.
TESTS AND MODELS
Descriptions of the variable-density wind tunnel
and of the methods of testing are given in reference 1.
The tests herein reported were made for the most
part for each airfoil at tank pressures of 1/4, 1/2, 1, 2,
4, 8, 15, and 20 atmospheres, covering a range of test
Reynolds Numbers from 40,000 to 3,100,000. The
1/4- and 1 /2-atmosphere runs were omitted for many
of the airfoils and, in several cases, only the lift-curve
peaks were obtained at the lower Reynolds Numbers.
Runs at reduced speeds (1/5 and 1/2 the standard value
of the dynamic pressure q) at 20 atmospheres were
sometimes substituted for the tests at 8 and 15 atmos¬
pheres. Several check tests at 8 and 15 atmospheres
and results from some earlier investigations have shown
that the specific manner of varying the Reynolds
Number with respect to speed or density is unimportant
when the effects of compressibility are negligible. For
all the airfoils, the air in the tunnel was decompressed
and the airfoil 'repolished before running the higher
Reynolds Number tests. Tares obtained at corre¬
sponding Reynolds Numbers were used in working up
the results.
The airfoil models are of metal, usually of duralumin
and of standard 5- by 30-inch plan form; the sections
employed (see fig. 1), except for the slotted Clark Y,
are members of N. A. C. A. airfoil families (references
2 and 3). The slotted Clark Y model is of 36-inch span
and 6-inch chord (with the slot closed) and was made
to the ordinates given in reference 4. For this airfoil,
the coefficients are given as based on the chord and area
corresponding to the slot-closed condition. The slat
was made of stainless steel and fastened to the main
wing in the position reported (reference 4) to result in
the highest value of maximum lift coefficient. This
model was tested at a much earlier date than the others,
and the test data are somewhat less accurate. The
main wing of the N. A. C. A. 23012 airfoil with external-
airfoil flap is of 30-inch span and 4.167-inch chord.
The flap is of stainless steel and is also of N. A. C. A.
23012 section having a chord of 20 percent that of the
main airfoil. It was fastened to the main wing m the
optimum hinge position reported in reference 5. Data
for this airfoil combination are given herein for two
angular flap settings: —3°, which corresponds to the
minimum-drag condition; and 30°, which corresponds
to the maximum-lift condition. The coefficients are
given as based on the sums of the main wing and flap
chords and areas.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 229
N.A.C.A
0003
Thickness
N.A.C.A.
0013 (
Comber shape
Thickness and camber
Figure l. — Airfoil sectiors employed for the scale-effect investigation.
High -lift devices
The sections, except for the slotted Clark Y. arc members of N. A. C. A. airfoil families
230
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ACCURACY
The accuracy of the experimental data of this investi¬
gation at the highest Reynolds Number is comparable
with that of the standard airfoil test data as discussed
in reference 2. The systematic errors of measurement
therein mentioned, however, have since been investi¬
gated and the results are presented in the appendix to
this report. The systematic errors of velocity measure¬
ment have hence been eliminated, the errors associated
with support deflection have been largely removed, and
the errors associated with model roughness have been
minimized by giving careful attention to the model
surfaces.
The remaining systematic errors are mainly those
associated with the interpretation of the wind-tunnel
results rather than the direct errors of measurement.
These errors are associated, first, with the calculation
of airfoil section characteristics from the tests of finite-
aspect-ratio airfoils and, second, with the correction
of the test results to zero turbulence or free-air condi¬
tions. Such errors will be more fully treated in the
discussion where the methods of correction, including
the interpretation of the results as involving the effec¬
tive Reynolds Number, are considered.
The magnitude of the direct experimental errors,
particularly of the accidental errors, increases as the
Reynolds Number is reduced. Any variation of the
support interference with the Reynolds Number was
not taken into account in spite of the fact that the test
results tend to indicate that the uncorrected part (see
appendix) of the support interference may cease to be
negligible at low test Reynolds Numbers. These errors
may be judged by a study of the dissymmetry of the
test results for positive and negative angles of attack
for the symmetrical airfoils and by the scattering of the
points representing the experimental data. (See figs.
2 to 24.) Such a study indicates that the results from
tests at tank pressures at and above 4 atmospheres
(effective Reynolds Numbers above 1,700,000) are of
the same order of accuracy as those from the highest
Reynolds Number tests. The drag and pitching-
moment results for effective Reynolds Numbers below
800,000, however, become relatively inaccurate owing
to limitations imposed by the sensitivity of the measur¬
ing equipment. In fact, it appears that the accuracy
becomes insufficient to define with certainty the shapes
of curves representing variations of these quantities
with angle of attack or lift coefficient. Hence airfoil
characteristics dependent on the shape of such curves,
e. g., the optimum lift coefficient and the aerodynamic-
center position, are considered unreliable and in most
cases are not presented below an effective Reynolds
Number of 800,000.
RESULTS
Figures 2 to 24 present the test results corrected after
the methods given in reference 1 for approximating
infinite-aspect-ratio characteristics. Curves are given
(for each airfoil for different test Reynolds Numbers) of
lift coefficient CL against effective angle of attack a0,
and of profile-drag coefficient CDq and of pitching-
moment coefficient about the aerodynamic center
Cnia c against lift coefficient CL. The x and y coordi¬
nates of the aerodynamic center from the airfoil quarter-
chord point are also given where the data permit.
Although not precisely section characteristics , character¬
istics so corrected have been used heretofore as section
characteristics because of the lack of anything more
exact.
Further corrections, however, to allow for the effects
of wind-tunnel turbulence, airfoil-tip shape, and some
of the limitations of the previous corrections based on
airfoil theory were developed during the course of this
investigation and, when applied, give results repre¬
senting the most reliable section data now available
from the variable-density wind tunnel. These addi¬
tional corrections and their derivation are fully dis¬
cussed later in this report. The more exact section
characteristics have been distinguished by lower-case
symbols, e. g., section lift coefficient cu section profile-
drag coefficient Cd0, section optimum lift coefficient
ciopt, and section pitching-moment coefficient about the
aerodynamic center cma c_. These values are then con¬
sidered applicable to flight at the effective Reynolds
Number, Re.
Table I presents, for various Reynolds Numbers, the
principal aerodynamic characteristics, in the form of
these fully corrected section characteristics, of the air¬
foils tested. Cross plots of certain of these section
characteristics against Revnolds Number are also given
for use with the discussion. (See fig. 28 and figs. 32
to 43.)
DISCUSSION
Scale effects, or the variations of aerodynamic coef¬
ficients with Reynolds Number, have previously been
considered of primary importance only in relation to
the interpretation of low-scale test results from atmos¬
pheric wind tunnels. It now appears from variable-
density and full-scale-tunnel data that important
variations of the coefficients must be recognized within
the flight range of values of the Reynolds Number,
particularly in view of the fact that the flight range is
continually being increased.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 231
S/o.
O
1.25
2.5
5.0
7.5
/O 3.5/2
Up'r.
L'w'r.
0 0
/ .420 \- 1 .420
1.961 \- 1.96/
2.666-2. 666
3. 150-3.150
-3.5/2
4.009 -4.009
4 303 -4.303
4.456 -4.456
4.50/ '-4.50/
4.352 - 4.352
3 97/ -3.9 7/
3.423 3. 423
2. 748 -2. 7 48
/ .96 7
7.086
.605
I. 967
- 1.066
.605
(.095- (.095)
20 40 60 80
Percent of chord
100
■p
b
.8^
QJ
0
O
.6
.4
•47
Airfoil: N. A. C. A. 0009
Size: 5"x30" Vei(ft./sec.):68.
Pres. (sthd. aim.) : 1/4 to 20
Test: V. D. T. 1 134, 1 136
Where tested : L.M.A.L.
-.4
-8 -4 0 4 8 12 16 20 24 28
Angle of attack for infinite aspect ratio, cx0
.10
.09
i
c
QJ
i.8
o .07
$
i.6
o -06
o
i. 4
drag
o
on
t-z G*
^■04
'47
t-o |
£.03
.O
G
.02
.01
0
. -. I
57
<U
O
U
-.2
c: _ q
• a
$
o
7
Tl
Test
I
1;
Hey no ids
It
j|
n
Number |
3,/40,000~~
1,3/0,000 ~
’,290,000 ~
665,000 -
334,000 -
-169.000 _
]J
n o - -
l
—
111
fx- -
J
I ~r
f V
Ji n
—
! ^ - 84,400
V
- 42
,300
II
1 a i j
|
_
•I i j
r
/
7/ '
i
i
i
-
~A
; /
X
\
i
td.
' ■"
X
r <
/
/
J-
eJ
fJZ
F'
/ ,
A
A >
5^*
r
k'-
5W-1 25
ji
d
Airfoil: N.A.C.A. 0009
Date: 5-34 Test: V.D.T. H34, t/36
Hesu/ts corrected to infinite aspect ratio
-.4 ~.2 0
32
(degrees)
Figure 2.— N. A. C. A. 0009.
.4 .6 .8 1.0
L iff coefficient, CL
1.2 L4 i.6 i.8
S/o.
0
!2S
2.5
5.0
7.5
10
IS
Up'r.
O
1.894
2.6/5
3.555
4.200
4.683
Liw'r.
0
- 1.894
-2.6/5
-3.555
-4.200
-4.683
5.3451- 5.345
x 7}
o o
Hi o
U •£
0 0i
SJ X
*1. o
"nl
!0\
at
-/o
a
c
-V-
X 1/
d
1
1
c/4
20 40 60 80 100
Percent of chord 2.0
25
3C
4G
50
60
70
8C
90
95
!OC
/Of
5.941-5.94/
6.002.-6.002
5.803 -5.803
5234 \- 5.294
A SP ? - A RP 1
3.66<
2.62.
1.44
.80'
(. / 26
O
-3.664
-2.623
- 1.448
7 - .807
) (-J26)
O
X
A
I
1
f
u
*
L.
E.Pac
i.: 1.58
/
t
'h
V
//
X
X
V
-I'x
'
"s
- *
= i '
X
"
Li
^2
r
/
if
7*
A
irfni
/: N. A
.C.A. 00 U
p
. Size : 5"x 30 " Vet (ft. / sec.):68_
Pres.(stnd. atm.) : i to 20
j
©
7
? si: V.D.T. 1237-8 Date: 3- 35
’here tested : L.M.A.L.
_ l - 1 - J — — 1 - 1 - *-
15
i.8
1.6
1.4
1.2
i.O
.8
.6
G?
c
.'ll
.G
$
<u
0
0
.2
0
-.2
-.4
-8 -4 0 4 8 !2 !6 20 24 28 32
Angle of attack for infinite aspect ratio, cc0 (degrees)
Lift coefficient, CL
Figure 3.— N. A. C. A. 0012.
232
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Sto.
Up'r.
0
7.25 2.367
2.5 [3.268
5.0 4.323
7.5,5. 2SO\-5. 250
70\5.853\ -5.853
L'w r.
0
■2.367\
3.268
4.43 3\
o
<j -c
F 4
ib V
A. O
-20
70\
ot,
-!0\ i
X
a
c.
Cj
1 4 i_ .
*
tf-fFr
_
-C/
’4
/5
6.68 7 \ -6.68/
0 20 40
60 80
O f chord
700
2.0
2.
37
41
51
61
5 742
1 7.50
5 7.25
7 6.6/1
1 5. 70‘
7-7.427
9-7.502
4 - 7.254
■i - 6.618
4 -5. 104
70! 4. 58t
8013.27
90\ / .an
95 ' 7 00
100. (.758
700:0
7 -4.5
9 -3.2
7 - 7.8
80
79
10
\
5 ~ 7.008
) h.758)
0
_
/>
1
_
jf
Sc l
N
NS
L.E. Rod.: 2.48
/l
4 i 7X
if
\
XT
N
N
< \
\
k
bn
V
KJ
/
l :
/}
• C ! IUI J
L
* i y
t.2-4
/■ /— [ J
1.2 -
2.4 _U
1.5 0
C'rta.c.
7
.002
.00/
.001
yj
u -
l
x- -
H -
V -
■1
-
Airfoil: N.A.C. A. 00/5
Size ; 5"x30" Vel. (ft./sec.):69 .
Pres. (sfnd. a/m.) : //4 to 20
Test: V.D.T. 1 1 35 Da/e: 5 -34
Where tes ted: L.M.A.L.
/.8
/.6
1.4
1.2
.0
<0
o
.6 u
.4
-4
.2
0
-.2
-.4
. to
.09
^■08
c:
<b
.0.07
$
o -06
o
0- 05
jo -04
P.03
.02
.01
0
H-./
v;
<d
8~-2
-n
C: _ o
|-4
-8 -4 0 4 8 72 76 20 24 28 32 -.4
Angle of attach for infinite aspect ratio , cca ( degrees )
Figure 4.— X. A. C.
rr
Test
i
Hey no ids Number
o
A
1260,000
?, 270,000
/, 270,000
655,000
3 9 / nnn
A'
+
57-
.□ -
- /
66,000
84,000
S] -
—
[/ - 42,900
<
r
i
\
"
U
n
i
\
f i
V
x
i
i
j
-
i
k ,
/ !
/ ;
i
/
u-£
.
L
T7
/
j
T
4
'
JX
7MPT/
/ 1
r
j.. .
X
%3.
— -
^2?
r
My.,
Lr-
i
1
m
rv
5^
* c -
,7
K
%
r
Airfoil: TV. A.C.A. 00/5
Date: 5-34 Test: V.D.T. 1/35
Results corrected to infinite aspect ratio
-.2 0 .2 .4 .6 .8 1.0 1.2 1.4 76 1.8
Lift coefficient, CL
A. 0015.
Sto I Up
r. Lw'r
O 0 ■
7.25,2.84 7
2.5\3.922\
5.0\5.332\
7.5 6.300\
10 7.024 \
75 8.0/8
20 8.606
25 8.9 7 2\
30 9.003 '
40 8. 705
50 7.941
60 6.845
5.496
0
2.847
3.922
-5.332
- 6.300
7.024
- 8.0/8
8.606
8.9/2
y
1 42
s-]cl.C
■j
r'
-
_ _
"1
c/4
-2.2
' 2.0
1.8
0.07
1.6
s
8-06
o
1.4
o'. 05
/,2 t-A
■ 04
>s.*
s;
1-0 5
Z-03
’
.8$
.02
<u
0
.6 °
.0/
.Jfc
.4^
„■ o
.2
0
I
Airfoil: N.A.C. A. 00/8
..Size: 5"x30" Vel. (ft./sec.):69 J_ p
Pres. (sfnd. atm.) : 1/4 to 20
Test: V.D.T. 1161 Date: 8-34
Where tested : L.M.A.L.
-.4
-8 -4 0 4 8 /2 16 20 24 28 32
Angle of attach for infinite aspect ratio, cta ( degrees )
Airfoil: N.A.C. A. 00/8
Date: 8-34 Test : V.D.T. / 161
Results corrected to infinite aspect ratio
-.4 -.2 0 .2 .4 .6 .8 1.0 7.2 f.4 1.6 7.8
Lift coefficient , CL
Figure 5. — N. A. C. A. 0018.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 233
Figure 6.— N". A. C. A. 2412.
5 to.
Up’r.
L'w 'r.
0
—
0
125
2.44
-t.43
2.5
3.39
— / .95
5.0
4.73
-2.49
1.5
5.76
-2.74
to
6.59
-2.86
1 5
7.89
-2.88
20
8.80
-2. 74
25
9.4/
-2.50
30
9.76
- 2.26
40
9.80
- t.QO
50
939
-1.40
60
8. !4
-LOO
70
6.69
- .65
80
4.89
- .39.
90
2.7/
- .22
95
/ .47
- 36
too
(33)
(-3 3)
too
~
0
L.E Rad
: 1.58
- 20
u/o
S-8 0
i V-/0
'A o
i
t
3C
ir
a
c.
_
1
r
r
-
T
—
-
-1
c/4
0 20 40 60 80
Percent of chord
too
jj-04
V
tol
£.03
.o
.02
1)
o
.6 °
.01
Airfoil: N.A.C.A. 441 2
Size: 5"x30" Ve!(ft./seci):69 2
Pres. (sthd. aim.) : 1/4 fo 20
Test: 1/. D. T. 1/59 ' Date : 7 -34 _ ^
Where tested : L.M.A.L.
J _ I -
w _ „ , „ _ .w „ _ . __ 32
Angle of a Hack for infinite aspect ratio, a0 (degrees)
Figure 7.— N. A. C. A. 4412.
Airfoil: N.A.C.A. 4412
Date: 7-34 Test : V.D.T. / 159
Results corrected to infinite aspect ratio
.2 .4 .6 .8 tO i.2 L4 1.6 1.8
Lift coefficient, CL
234
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Angle of attach, for infinite aspect ratio, a0 ( degrees ) Lift coefficient, CL
Figure 8.— N. A. C. A. 6412.
Figure 9.— N. A. C. A. 4409.
AIRFOTL SECTION CHARACTERISTICS AS AFFECTED
BY VARIATIONS OF THE REYNOLDS NUMBER
23
Figure 10.— N. A. C. A. 4415.
Angle of attach for infinite aspect ratio, a0 ( degrees ) Lift coefficient, CL
Figure 11.— N. A. C. A. 8318.
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 12— N. A. C. A. 23012.
St a.
Up'r.
L’w 'r.
O
—
O
1.25
1.90
- .77
2.5
2.89
— 135
5.0
4.34
-1.70
7.5
5.38
-238
to
6.15
-2.62
15
7.08
-3.40
20
7.49
-3.98
25
760
-4 30
30
7.55
-4.46
40
73/
-4.4 6
50
6.5?
-4.30
60
5.6/
-3.83
70
4.48
-334
80
3.16
-2.26
90
/. 70
-7.25
95
.93
- .70
too
(32)
(-3 2)
too
—
O
L . E. Pod.
: 0.40
Slope of radius
through end of
chord : 0.305
20 40 60 80
Percent of chord
100
2.0
Airfoil: N.A.C.A. 23012-33
Size: 5"x30" Vet (ft./sec.):68.
Pres, (sf'nd. aim.) : / to 20
Test: V.D.T./240 Date: 3-35
Where tested : L. M. A. L.
-8-4 04
Angie of attack
II
!0
.09-
,<o
.0
$
0)
o ■
u
D '
A.
08
0 7-
06:
'■2
^■04
-vT
P
t.O §
p .03
.73
<£
.02
o
.01
.4^
0
tj
.2
A -. /
O
O
^ - 2
<0 c
o
o
-.2
^ -.3
c
-.4
1 4
8 12 16 20 24 28 32
for infinite aspect ratio, ct0 (degrees)
I
1
:s
' -
i Te
1 1
1
Reynolds A/umbt
?r
c
5 -
3,030,000
2,420, OOO
A -
x- -
/, tzou,uuu
Ace: nnn
r~
341,000
/ 72,000
| |
—
r
1
1
I"
| |
nr
J
A
i
1
I
r
J
I
J
1
H
f
J
1
1
_
U
li
1
1
J
fj.r
Aa
A
_
J —
-**■
Hr-
-4
■
/h
b
j
(?
Air
foil:
N.A.C
.A. 230/2-^
33
D
ate: 3 -35 Test: V.D. T. 1240 _
esuits corrected to infinite aspect ratio
i i i J - 1 - 1 - 1 — - * - — 1
R
-.4 -.2 0 .2
.4 .6 .8 i.O t.2
L ift coefficient, CL
i.4 i.G
Figure 13— N. A. C. A. 23012-33.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 237
Sto.
Up’r.
L'w’r. 1
0
—
0
/.25
2.30
-1.52
2.5
3.16
-2.10
5.0
4.38
-2.76
7.5
5.29
-3.17
W
5.98
-3.42
!5
6.97
-3. 74
20
1.58
- 3.90
25
7.9 /
-3.9 7
30
8.00
-4.00
40
763
-3.98
50
6.73
-3.87
60
5.49
- 3.66
70
4.06
-3.27
SO
2.61
-2.64
SO
1.26
- / .63
95
.66
- .95
IOO
(.13)
(-.13)
100
0
-
L.E
Pad.
/ .58
y
. .
J
r»
Ac
—
L -j-
i r
15
'c/f
~c
c:
.jj
.o ,
$
CD
O ■
u
Ch
0
s:
o
£
C
si
<v
0
o
s*.
c
6
I
.11
. 10
.09
.08
.07
.06
.05
.04
.03
.02
01
0
-.1
-.2
- 3
-.4
1 —
1
test
Reynolds Number
o - 3, / 70, 000
A - 2,390,000
X - 1,340,000
. & ~ir non
V7 -- --
n - up. non
! 1 i | M 1
1
d
1
I
*
t
n
b
IT 1
I
1
L
t
1
1
1
1
0,
i.
I | ! I
J
1
f
h
F
7
/
i
7
/[
7
7-
A
n
.
\x/ 7
/
h
/
□,
ikt
T"
~
<
T5
4
| 1 1 |
.
dt
| | V
II
4-
J
_
Airfoil: N.A.C.A. 2R?
12
Dote: 3 ~35
Test
: V.D.T. 1233
L
Results corrected to Infinite aspect ratio
-.4-2 0
-8 -4 0 4 8 12 16 20 24 28 32
Angle of attack for infinite aspect ratio, cc0 (degrees)
Figure 14— N. A. C. A. 2R212.
.2 .4 .6 .8 i.O 12 1.4 1.6 18
L iff coefficient , CL
Sto.
Up'r.
L'w’r.
0
—
0
1.25
2.36
-1.50
2.5
3.28
-2.03
5.0
4.60
-2.59
7.5
5.6/
-2.89
10
6.44
-3.02
15
7. 75
-3.0/
20
8. 75
-2.80
25
9.5/
-2.43
30
10.0 7
- 1.99
40
10.70
- .92
50
10. 60
.19
60
10.44
1.3/
70
9.67
2.34
80
8.02
2. 73
90
4.88
088
95
2.7 /
/ .02
too
(.12)
(~./2)
100
—
0
L.E. Pad.
: 1.58
Slope of radius
throuqh end of
chord: 6/35
c/
a.
c.
20 . _
Percent of chord
%
Airfoil: N.A.C.A . 61 1 2
Size: 5"x30" Vei fff./sec.):68
Pres, (st 'nd. atm.) : t/4 to 20
Test: V.D.T.//66
Where tested : L.M.A.L.
.6
.2
-.2
--.4
-8 -4
4 8 /2 /6 20 24 28
.13
12
II
2.4
. 10
2.2
.09
2.0
i,s
1.8
o.O 7
£
1.6 ^
o .06
o
§\05
*
s;
.04
? .03
.02
.01
0
^ _ p
<U c
O
-v -.3
c:
<u
k-4
o-
Test
Reynolds Number
3, 080, 000 ^ <—
f
A - 2,330,000 '
X- - 1,280,000 '
■+ - 664,000 - •
-v - 338,000 --
□ - 170,000 A-X
n - 84,500
!■
t
\
1 1 1
4J
-4
— Y-
\
4i
44
I1
4
,
4
.to
'
T
r
/ !
i L*
L
l?
7
A 1
i
t
1
1
J
1
>
F 6
i
i.
1
J
V1
~ *“
-
y"
Ji
' -+
/
I
L
7
4
4
it
J
4
7
4
rr
Tf
...
4.
□f
t
F
A
/
/
y
N
N
— 3
r-
i
N,
H
4c.
CH
-r
r
&
•c
7
-
—5
7—
-v-
-.-H
. j
—
,
drr-
4
2^
s
P
'3*
■
^7
—
_
:4
Angle of attack for infinite aspect ratio, d0 (degrees)
-.4 -.2 O
Airfoil: N.A.C.A. 67/ 2
Date: 8 -34, 9~34 Test: V.D.T. 1/66.
Results corrected to infinite aspect ratio
~2 X .6 .6 tO 1.2 !4 1.6 1.8 2.0
L ift coefficient, CL
Figure 15. — N. A. C. A. 6712.
238
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 17.— N. A. C. A. 23012 with split flap deflected 60°.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER
Sto.
Up'r.
L'w'r.
0
~
0
t.25
2.67,
- / .23
2.5
3.6/
- /. 7/
5.0
4.9/
-2.26
7.5
5.80
-2.6/
to
6.43
-2.92
1 5
7. 19
-3.50
20
7.50
3.97
25
760
-4.28
30
7.55
- 4.46
40
7. / 4
-4.48
50
8.4/
-4./ 7
60
5.4 7
-3.6 7
70
4.36
-3.00
80
3.08
-2. !6
90
1.68
-1.23,
95
.92
- .70
too
(.131
(~./3)
too
—
0
L.E
Rod.
■ / .58
through end of
chord: 0.305
lit-
’ 2C
a.c. i
?/*
* ♦
n
i m
7
20
40
With
J
-4-
60 80 100
Percent of chord I
Without flop
'4
/
Airfoil: N.A.C.A. 23012 with
flop: Date: 8
Pres.(st'nd. atm.): I to 20
Size:5"x30" Vet. (ft. /sec.): 3/ to 70
Tested: L.M.A.L. , V.D.T. 1288
.8'
.4
0
-.2
—.4
-16 - 12 -6 -4 0 4 8 /2 16 20
Angle of at lack for infinite aspect ratio, ct0
24 28
( degrees )
Figure 18.— N. A. C
c
<L i
S.
.o .
$
13
o •
o
o
0 •
o
£ '
sc
1)
o
u
V
II .
13
I
r i i mi i i r t n
* a.c.pos t/on x=!.2-,y = 7
— ! - 1 - i
1 -
\ 1
1
,
’
m° c
—
w
iff
7M
1
D A
/
H
/ / n.iv.
With flop
3,070,0 OOf
2, 2 70, 000
1,440,000
X
—
+
- 660,000
1
V
- 336,000
□
—
- iby,uuu
i i i i i
i -
-) _
h non nnn-<
*
\
\
/
A
AT
r<
A-
Without
Jap
“23
zr=
ftzJ-
— .
—
—
P=
2J—
- .
-ZJ-
y
_ X
b-
w
ift
Jap,
—
c—
— c
—
o
-c
—
p-
j.
rt>
-* *
_ -
—
1 '
Airfoil: /
t.A.C.
A. 230/2 witiT split flap de
fleeted 75°
Test: V.D. T. 1288 Date: 8-35
Results corrected to infinite aspect ratio:
_ L . . • > ...... 1 ^ .1 ...... -1 . - F_ _1
-.2 0 .2 .4
.6 .8 t.O 1.2 1.4
L ift coefficient, CL
A. 23012 with split flap deflected 75°.
1.6 1.6 2.0 2.2 2.4
Sto.
Up'r.
L'w'r.
0
—
0
125
3.34
-/.54
2.5
4.44
-2.25
5.0
5.89
-3.04
7.5
6.9/
-3.6/
/O
7.64
-4.09
/5
8.52
-4.84
20
8.92
-5.4/
25
9.08
-5. 78
30
9.05
-5.96
40
8.59
-5.92
50
7.7 4
-5.50
60
6.6/
-4.81
70
5.25
-3.9/
80
3.73
-2.83
90
2.04
-1.59
95
/ ./ 2
- .90
100
(3 6)
(-36)
/OO
L_E
Rod.
: 2.48
-20
to
•s ~c>
P L-
o
o
ii y
t--
ft
3
%.c
— ]-
c
s:
-1
c/4,
\|
0 20 40 SO 80 /OO
Percent of chord
XDate:8-35,2-35j
| Size: 5"x J0"P~
~I6 -12 -8 ~4 0
Angle of attack for
Airfoil: N.A.C.A. 23015 with
split flap: Ve/.(ft./sec.):3t to70
Pres, (s t’nd. atm.): t to 20
4 8 /2 /6 20
infinite aspect ratio, a,
Figure 19
c:
.13
.u
03
0
o
Cl
*
sc
o
*
24
( degrees )
sc
0)
0
o
c
13
I
.24
.22
.20
. 1 8
.16
. 14
.12
JO
.08
.06
.04
.02
0
-./
-.2
-.3
-.4
* ~
'
. .
- 1 1 . 7
-/
■t
C L . L- . J 1 J O / t I t ' • / >
r
_
-n
DDR
-r>
-C\
(4
it
f/c
7P
y
j
X.
o
-ft
L
r
test R. A
With f/a
/.
\
p
1
o
—
2,2 70,00
t, 4 50, 00
680,00
350,00
H
\
A
0
\
°)
\
V
_ _
0 j
\
\
□
- 171,000
\
\
J 1 1
WITHOUT T lOD
-
V
V
4
- f /U.UUU-
\
\
h,
-- /
U,
\
\
a
J.
4"
S
A-
—
7
_
—
3 —
—
Wi
L
the
7U
t /■
tdf
0
— tL
”2)
_
■ - tL
Y
- ~L
—
“ -7
—
—
.ft -
- -
- T.
h -
• -
22
z
.
Vit
A
ft
op
-O
-
■K>
■ -
; "
Airfoil: N.A.C.A. 230/5
with split flap deflected 75°
Tested :L, M. A. L.,V.D.J 1289,1232 : Corrected to infinite A.R.
-.2 0 .2 .4 .6
.6 1.0 1.2 1.4 1.6
L ift coefficient, CL
1.8 2.0 2.2 2.4
-N. A. C. A. 23015 with split flap deflected 75°
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Sto.\ Up'r.
O
t.25\
2.5
5.0
7.5
m
15
4.87
6.14
7.93
9.13
10.03
I/./9
L'w’r.
0
-2.08
-3.14
-4.52
-5.55
-6.32
-7.5/
— 2tfT
C* >0
u ° Q\
u u
<b V •
^ O
./
a.c
£|
_
Sf
_
11
Kc/
'4
\
20
% of chord
25/2 05
30/2.06
40\ll.4S
50/0.46
rn a nr
-8. 76
- 8.95
\ -6.83
-8.14
- 7.07
-5.72
-4./ 3
-2.30
- / .30
-(■22)
0
iJ
« i
* • j»
*, |
.
\
7C
8C
9C
9i
/OC
/oc
? 7.05
1 5.05
2.76
/ .53
1 (.22,
1 -
. ■,
A1 L
/
■, \ \
\
/
/
\ |
\ ’
A
' » '
■ A '
L.E. Rad.: 4.65
Slope of radius
through end of
chord: 0.305
•
•ZA
/
\
6
Vi
)
/
'
K
/
1
r
L
L-With
flap
/
N
\
A
/
/
*
A
%
A
:
Is)
h
t
/
'
/
/.
it
t
f
? h
Hthout f/ap
1
/
7
(
/
J
f
r
A
/
r
f
\L
■4-
L
- I -
.6
.2
Size: 5"x30" Vel.(ft/sec.):3llo70_._
2.4
.18
2.2
-0-/6
2.0
.5
,u .14
t.e
$
<0 / p
o -12
t.6
u
&./0
/.4^
jv-08
(2 £
£.06
*
.0
.04
<u
o
.8 °
.02
1 Pres.fstnd. atm.): I to 20 Tested:L.M.A.L.,V.D.TI2Bl,l285\
-16 -12 -8 -4 0 4 6 /2 /6 20 24
Angle of attach, for infinite aspect ratio, of, ( degrees )
<D
o
u
c
5
I
a
.c.
pos/t/on
X
= C.J
>y=/_r\
X
- c
.O
;
Cm.
0
. uua
•
O
Witt
flap
cr
Tp. t R N.
A
With
flan a
b
.a
3,080,000 *
A
—
2,260,000 i
X
1,440,000
+
~ ~
b 50,00 U
2.
V
~ ~
333,000
165,000
1 l i
\
\
□
_
Without flar
>1
/J
.3.1 10.000'
b
N
-2,250,000
/\
<
—
...
-1,430,000
3
I>— ■
---
-65 J, DUO
338,000
in -7 nnn
A
<0—
—
%
r
'
■A-
-Z
A-
-A
—
Without flap
t
i.
=Zj
%
~z
i/i/;
f
<“C
-o
Air foil: N. A.C. A. 2302/ with split flap deflected 75°
8
Results corrected to infinite aspect ratio
Da te :
-35
-.2 0 .2 .4 .6
.8 /.0 /.2 1.4 /-6
Lift coefficient, CL
1.8 2.0 2.2 2.4 2.6
Figure 20.— N. A. C. A. 23021 with split flap deflected 75°.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 241
m
a.
_
JT
:
_
0
<
U
N -
0
_
Pivot oft
T.E.
L
to
P
IVO
c’’_
.03 Ci .025 c.
c/4
—
Pivot below Ci
.054 Ci .045 c.
Pivot aft L.E.
£
20 40
Percent
60 80
of chord
to
i
of flap
Pivot below c?
—
JOCt
.0/67 c.
r/op u/sp/ ele¬
ment ono/e
-3
o
\\
X
*
V
k
K
X
Jr
v.
r+
/
Sd1
=0
n
jL
Airf
o/7: A
KA.C.,
4. 23
0/2
with
exte
rnal-
J
airfoil flop.
Size:
5"x30"
»
Pres, (st'nd. a
tm): / to 20
Date :7 -35
Vet. (ft. /sec.): 69
Zested: L.M.A.L., V.U.i. 14/3,12/6
1_ 1 '■ 1_ 1 i_ l - 1
.12
.11
.10
.09
h.-. 08
o
<D
.0.071
$
1.6
o -06
1.4
o
o'. 05
*
<{,.04
S:
LOl
5-03
CL
.flS
.02
<u
0
.6 °
.01
.4Z
.2
0
3 ,
, S - /
-10 ~8 -4
8 12
o
0
<6
5 - 4
I
1
TT
1
Test
r
JTTTn '
T r 1 1
\
a. c. position
1 | Reynolds Numbe
r
X
y
c
a
c.
.
o -
3,1 10,000
3,330,000
/, 250,000
636,000
325,000
- 163.000
0
.5
0
/-
3
8
0.
00
00
ot
0/
9
A - c
X -
■
—
—
—
—
/
-/
-/
9
-//-
( /
9~
o-
!
—
_
n
-V
...
/
/
_
-
Coefficients based c
wing and flap chore
n
Is
th
at
e
id
su
Of
/77.
-e
3
as
1
if
th
e
mo
in
4
i
9
—
1
i
i
1
1
l
1
i
f
i
rr
4
T
i
1
1
4
I
i
/
/
\
7
/
r
•c
~D
X
A
N
1
P-
—
1
•r
-4
■fr-
^
l*V
— -
V-
f
V'
y
r
&
r
I
1
Y
Air foil: N.A.C.t
4. 23012 with e xternoi-oirfoil
l
t
/
7 ’op deflected - 3 ° Test: V.D. T. 1273-1276
zsults corrected to infinite aspect rotio :
. L .... i i 1 ; 1 1
i
i _ _
Rt
-.6 -.4 -.2 0
16 20 24 28 32
Angle of attack for infinite aspect ratio, c(0 ( degrees )
Figure 22.— N. A. C. A. 23012 with external-airfoil flap deflected— 3
Main wing section _ N. A. C. A. 23012 Main wing chord, c; - - -
Flap section _ N. A. C. A. 23012
.2 .4 .6 .8 t.O t.2
Lift coefficient, CL
1.4 1.6 1.8
.... . . . . 0.833c
Flap chord, C2=0.2ct _ .167c
Datum chord, c=ci+C2.
Pivot oft T. E.
of main wing
.03 Ci ,025 c.
Pivot below c,
. 054c i ,045c.
20
6. "*>
C u
<b O
u -L
U g
<b v. -10
‘L o
v f
(ai.c/
-ll
\
“Ff
fr
1
Pivot/
0
20 40 60 80
Percent of chord
too
of flap
.24 c2 ,040c.
Pivot below c2
JOce ,0167c.
Flap displace¬
ment angle
+ 30°.
\\
i
S
M
V,
/
1,
1
/
/
—
l
u
■>.
\
L^s
V.
t
V
\
'A
A
’
\
V
L
V
■
!
L
7
(S.
v
1;
\
//
v.
b
V7
/
>
ft
ft
jh
y
C f>
77/
/
Yl
c
it
J-
external-airfoil flap.
Pres.fst'nd. atm.): / to 20
Size: 5"x30" Date:7~35 ,8~35
Tested: L.M.A.L., V. D.T 1278
2.2
2.0
1.8
Of
.12
.//
. to
09
.08
c
.<o
0.07
$
t.6
q.06
0
t.4
0- os
O'
/,2v
A-04
c
.Qj
$
loA
5.03
T
.8 o
.02
o
.6-
.01
.4
.2
0
-.2
0
-. /
-.2
<n
0
u
^ -.3
0
5-4
I
n
I
1
Tes
nri it
t
[a. exposition*.
Reynolds Number\
•y y
c
5 -
3,080,001
2,350,00
0.5
8
A -
0
‘
x - /,
ryu.uu
545,00i
333,001
167 no
0
J
J
Lc
_
-II
4- - “
fic
1
Coef
ients based
on /
he
sun
IS
of
the m
ai
n
wing and flap chords and areas.
1
I *(for flap at -3°)
a
V
l
l
t]
J
r
i
/
7,
a
A
V\
Y
-
\
!
7
k
/
-
L/
V
L^v
s
£27
-K
r '
V
-
n
X
l7
L
~
a-
—
03
f=
—
—
£
k.
— —
—
-tfc
-n
n
AL
Airfoil: N.A.C.A. 2301c
deflected 30° ] Date 7-35,8-35-, Test:V.D. T. 1278
Results corrected to infinite aspect ratio :
0 .2 .4
6 .8 1.0 1.2 L4
Lift coefficient, CL
-16 -12 -8 -4 0 4 8 /2 /6 20 24
Angle of attack for infinite aspect ratio, c(0 (degrees)
Figure 23.— N. A. C. A. 23012 with external-airfoil flap deflected 30°.
Main wing chord, Ci . . . 0.833c
1.6 18 2.0 2.2 2.4
Main wing section.
N. A. C. A. 23012
Datum chord, c=Ci-f-C2.
Flap section _ N. A. C. A. 23012
Flap chord, C2=0.2ci.
,167c
242
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 24.— Clark Y with Handley Page slot.
As an example of scale effects within the flight range,
figure 25 has been prepared to show how the choice of
an airfoil section for maximum aerodynamic efficiency
may depend on the flight Reynolds Number at which
the airfoil is to be employed. The efficiency is judged
by the speed-range index CimaJcd0. Values of ctmax were
determined for the airfoil sections (N. A. C. A. 230
series) with a deflected 20 percent chord split flap
and at a Reynolds Number as indicated on each curve
corresponding to the landing condition. The cor¬
responding values of cd0 were taken as the actual profile-
drag coefficients associated with a high-speed lift
coefficient suitable to an actual speed range of 3.5,
but corrected by the methods of this report to the high¬
speed Reynolds Number (indicated landing Reynolds
Number R times 3.5). Four curves were thus derived
indicating the variation of speed-range index with
section thickness for four values of the landing Reynolds
Number: 1 , 2, 4, and 8 million, the extremes correspond¬
ing to a small airplane and to a conventional transport
airplane. The highest value shown, 414, of the speed-
range index may appear surprisingly high, but it should
be remembered that the corrections to section character¬
istics and for Reynolds Number, as well as the use of
flaps, are all favorable to high values. The important
point brought out by figure 25 is that the section thick¬
ness corresponding to the maximum aerodynamic
efficiency is dependent on the Reynolds Number.
The most efficient airfoil for a landing Reynolds
Number of 1,000,000, for example, is definitely not the
Figure 25. — Airfoil speed-range indexes for various Reynolds Numbers. N. A. C. A.
230 series sections; cimax taken for airfoil with 0.20c split flap deflected 75°; Cdo taken
for airfoil with flap retracted for a high-speed value of ci and at 3.5 times the R for
the Cj max-
most efficient for a larger airplane landing at a Reynolds
Number of 8,000,000. An analysis such as that of
the foregoing example or further analyses such as those
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED
discussed in reference 8 concerning the determination
of the characteristics of wings evidently require a
knowledge of the variation of airfoil section character¬
istics with profile shape over the practical range of
flight Reynolds Numbers.
determination of section characteristics applicable to
FLIGHT
The present analysis is intended primarily to supply
a means of arriving at airfoil section characteristics that
are applicable to flight at Reynolds Numbers within
the practical flight range. This object is best ac¬
complished by applying corrections to the standard
airfoil test results from the variable-density tunnel.
The standard airfoil characteristics at large Reynolds
Numbers are customarily defined in terms of a few
parameters or important airfoil section characteristics
that may be tabulated for each airfoil section. These
important characteristics are:
c, , the section maximum lift coefficient.
Lmax 7
a0, the section lift-curve slope.
aq , the angle of zero lift.
c(ll, . , the minimum profile-drag coefficient.
c. , the optimum lift coefficient, or section lift co-
1 op t
efficient corresponding to cdn . .
cm<i . , the pitching-moment coefficient about the sec¬
tion aerodynamic center.
a. c., the aerodynamic center, or point with respect to
the airfoil section about which the pitching-
moment coefficient tends to remain constant
over the range of lift coefficients between zero
lift and maximum lift.
Essentially, the general analysis therefore reduces to an
analysis of the variation of each of these important
section characteristics with Reynolds Number. Before
this analysis is begun, however, it will be necessary to
consider how values of these section characteristics
applicable to flight are deduced from the wind-tunnel
tests of finite-aspect-ratio airfoils in the comparatively
turbulent air stream of the tunnel. The variation of the
important section characteristics with Reynolds Number
will then be considered. Finally, consideration will be
given to methods of arriving at complete airfoil charac¬
teristics after the important section characteristics have
been predicted for flight at the desired value of the
Reynolds Number.
Correction to infinite aspect ratio. — The derivation
of the section characteristics from the test results un¬
corrected for turbulence will be discussed first; the
turbulence effects will be considered later. The reduc¬
tion to section characteristics is actually made in three
successive approximations. First, the measured charac¬
teristics for the rectangular airfoil of aspect ratio 6 are
corrected for the usual downflow and induced drag,
using appropriate factors that allow at the same time
BY VARIATIONS OF THE REYNOLDS NUMBER 243
for tunnel-wall interference. These induction factors
are based on the usual wing theory as applied to rec¬
tangular airfoils. The methods of calculation are
presented in reference 1 . (Second-order influences have
also been investigated; that is, refinement of the tunnel-
wall correction to take into account such factors as the
load grading and the influence of the tunnel interference
on the load grading. (See reference 6.) For the con¬
ditions of the standard tunnel test such refinements were
found to be unnecessary.) The results thus yield the
first approximation characteristics, e. g., the profile-drag
coefficient CD 0 that has been considered a section
characteristic in previous reports (reference 2).
These first-approximation section characteristics are
unsatisfactory, first, because the airfoil theory does not
represent with sufficient accuracy the flow about the
tip portions of rectangular airfoils and, second, because
the measured coefficients represent average values for
all the sections along the span whereas each section
actually operates at a section lift coefficient that may
differ markedly from the wing lift coefficient. The
second approximation attempts to correct for the
shortcomings of the wing theory as applied to rec¬
tangular airfoils.
It is well known that pressure-distribution measure¬
ments on wings having rectangular tips show humps in
the load-distribution curve near the wing tips. These
distortions of the load-distribution curve are not rep¬
resented by the usual wing theory. The failure of the
theory is undoubtedly associated with the assumption of
plane or two-dimensional flow over the airfoil sections
whereas the actual flow near the tips is definitely three-
dimensional, there being a marked inflow from the tips
on the upper surface and outflow toward the tips on the
lower surface. This influence not only affects the
induction factors and hence the over-all characteristics
of the rectangular wing but also produces local dis¬
turbances near the tips that may be expected to affect
the average values of the section profile-drag coefficients.
Theoretical load distributions for wings with well-
rounded (elliptical) tips agree much more closely with
experiment than do the distributions for rectangular-
tip wings. Local disturbances near the tips should also
be much less pronounced. Test results for rounded-tip
wings were therefore employed to evaluate the rectangu¬
lar-tip effects and hence to arrive at the second approx¬
imations. Four wings, having N. A. C. A. 0009, 0012,
0018, and 4412 sections, were employed for the purpose.
The normal-wing airfoil sections were employed
throughout the rounded-tip portion of the wing but the
plan area was reduced elliptically toward each tip
beginning at a distance of one chord length from the
tip. Section characteristics were derived from tests
of these wings in the usual way but using theoretical
induction factors appropriate to the modified plan
form. These section characteristics when compared
244
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
with the first approximation ones from tests of wings
with rectangular tips served to determine the second
approximations. These values indicated by double
primes were given from this analysis in terms of the
first approximation values indicated by single primes
as follows:
a0" = 0.96rto/
a0/, = a0/T 0.390// (degrees)
CD„" = CD„’ +0.00 16 a/2- 1 (f - 6)0.0002 (t 5 6)
where t is the maximum section thickness in percent
chord. In some recent reports on airfoil characteris¬
tics (references 3, 5, and 7) these values have been
presented as section characteristics except that a small
correction has in some cases been applied to the aero¬
dynamic-center positions. This correction is no longer
considered justifiable.
These corrections are, of course, entirely empirical.
They must be considered as only approximately correct
and as being independent of the Reynolds Number.
The corrections themselves, however, are small so that
they need not be accurately known. All things con¬
sidered, it is believed that through their use the reliabil¬
ity of the section data is definitely improved, at least
within the lower part of the range of lift coefficients.
For lift coefficients much greater than 1, however, the
profile-drag coefficients from the rounded tip and rec¬
tangular airfoil tests show discrepancies that increase
progressively with lift coefficient and, of course, become
very large near the maximum lift coefficient owing to
the different maximum-lift values. This difference
brings up the necessity for the third approximation.
The second approximation values may, however, be
considered sufficiently accurate to determine the section
profile-drag coefficient cf,n over the lower lift range and
also the following important section parameters that
are determined largely from the characteristics in the
low lift range:
a0
Cx ,
lopt
/i
min
^ ma.c.
a. c.
In this range of the lift coefficient the deviations from
the mean of the Ci values along the span have been
adequately taken into account. The mean values of cx
and cdo represent true values as long as the deviations
along the span are within a limited range over which
the quantities may be considered to vary lineally. Near
the maximum lift, however, the deviations become
larger and the rates of deviation increase so that the
profile drag of the rounded -tip airfoil, for example, is
predominantly influenced by the high cd() values of the
central sections which, according to the theory, are
operating at cx values as much as 9 percent higher than
the mean value indicated by the wing lift coefficient CL.
Moreover, the actual lift coefficient corresponding to
the section stall (in this case the center section) might
thus, in accordance with the theory, be taken as 9 per¬
cent higher than the measured wing lift coefficient
corresponding to the stall.
Several considerations, however, indicate that this
9 percent increase indicated by the simple theory is too
large. The simple theory assumes a uniform section
lift-curve slope in arriving at the span loading and
hence the distribution of the section lift coefficients
along the span. Actually on approaching the maximum
lift the more heavily loaded sections do not gain lift as
fast as the more lightly loaded ones owing to the bend¬
ing over of the section lift curves near the stall. This
effect has also been investigated approximately. The
results showed that for commonly used airfoil sections
the center lift drops from 9 percent to 5 or 6 percent
higher than the mean at the stall of rectangular airfoils
with rounded tips. For some unusual sections that
have very gradually rounding lift-curve peaks and with
little loss of lift beyond the stall, this correction may
practically disappear either because the lift virtually
equalizes along the span before the stall or because the
maximum lift is not reached until most of the sections
are actually stalled. Omitting from consideration these
sections to which no correction will be applied, the
question as to whether or not such a correction should
be applied to usual sections was decided by considering
how it would affect predictions based on the cx „
1 ''max
values.
Maximum-lift measurements had been made for a
number of tapered airfoils of various taper ratios and
aspect ratios. The same airfoil section data presented
in this report were applied (taking into account the re¬
duced Reynolds Number of the sections near the tips
of highly tapered wings) by the method indicated in
reference 8 to predict the maximum lift coefficients of
the tapered wings. These predictions appeared some¬
what better when the section data were obtained on
the assumption that the center-section lift coefficient
at the stall of the rectangular airfoil with rounded tips
is 4 percent higher than the wing lift coefficient. Hence
the third approximation as regards the section maximum
lift coefficients was obtained by increasing the maximum
lift coefficients by 4 percent, although the value of the
correction could not be definitely established because
it appeared to he of the same order as possible errors
in maximum lift measurements and predictions for
tapered airfoils. The correction has been applied,
however, except in the unusual cases previously men¬
tioned where it obviously was not applicable, by in¬
creasing the maximum lift coefficients for the sections
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 245
by 4 percent. With the rounded-tip correction this
increase makes the total maximum lift coefficient for
the section 7 percent higher than the measured maximum
lift coefficient for the rectangular airfoil of aspect ratio 6.
The correction of the important airfoil section para¬
meters has thus been completed, but the curve of pro¬
file-drag coefficient against lift coefficient should now
be modified at high lift coefficients owing to the change
in chnax and the variation of cd{) along the span. Com¬
pletely corrected cd0 curves are not presented for the
various airfoils in this report. The change resulting
from the variation of cd0 along the span has been ap-
influenced by the variation of cdu along the span. A
reference to figure 26 will show the relation of these
successive approximations to the original measurements
and to the final results.
Turbulence. — The correction for turbulence is made
as in reference 9 by use of the concept of an effective
Reynolds Number. Marked scale effects that have been
experimentally observed are usually associated with a
transition from laminar to turbulent flow in the boundary
layer. As examples, consider the more or less sudden
increase in the drag coefficient for skin-friction plates
and airship models and the drop of the drag coefficient
plied only in a general way in the construction of a
generalized cdQ curve. From this curve, values of
cdo at any ct may be derived in terms of the presented
airfoil section parameters. This “generalized section
polar” (see fig. 45) was derived from tests of rounded-
tip N. A. C. A. 0012 and 4412 airfoils, taking into
account the variation of cd0 along the span. For con¬
ventional airfoils of medium thickness, cd0 values from
this generalized section polar should be more nearly
true section characteristics than the CDo values obtained
directly from the test data. This conclusion is particu¬
larly important for lift coefficients above 1 where the
second approximation correction becomes definitely
unreliable and near Cimax where the CDo values are
for spheres and cylinders with increasing Reynolds
Numbers in the critical range. The latter scale effects
are associated with the greater resistance to separation
of the turbulent layer. The increase of maximum lift
coefficient with Reynolds Number shown by most com¬
monly used airfoils is a similar phenomenon. The drag
scale effect for most airfoils, moreover, is at least com¬
parable with the corresponding scale effect for the skin-
friction plate.
This transition from laminar to turbulent flow in the
boundary layer, as in Reynolds’ classic experiments, is
primarily a function of the Reynolds Number but, as he
showed, the transition is hastened by the presence of
unsteadiness or turbulence in the general air stream.
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
246
Likewise, the transition in the boundary layer is
hastened by the turbulence in the air stream of a wind
tunnel so that transition occurs at a given point on the
model at a lower Reynolds Number in the tunnel than
it would in free air. Likewise the associated scale
effects that appear in the tunnel tend to correspond
with those that would appear in flight at a higher
Reynolds Number. This Reynolds Number may there¬
fore be referred to as the “effective Reynolds Number”
and is, of course, higher than the actual Reynolds
Number of the test.
It appears that the effective Reynolds Number for
practical purposes may be obtained by multiplying the
in passing from the test to the effective Reynolds
Number, moreover, is approximately allowed for by
deducting a small correction increment from the
measured airfoil profile-drag coefficients.
This correction increment was originally employed
for tests at high values of the Reynolds Number when
the boundary layer on an airfoil is largely turbulent.
The correction was therefore estimated as the amount
by which the drag coefficient representing the turbulent
skin friction on a flat plate would decrease in passing
from the test Reynolds Number to the effective
Reynolds Number. The values of the increment thus
deduced from Prandtl’s analysis of the turbulent
test Reynolds Number by a factor referred to as the
“turbulence factor.” This factor was determined
(reference 9) for the variable-density tunnel by a com¬
parison of airfoil tests with tests in the N. A. C. A.
full-scale tunnel and hence indirectly with flight. The
value 2.04, which was thus obtained after a considera¬
tion of sphere tests in the full-scale tunnel and in flight,
agrees with a subsequent determination (reference 10)
by sphere tests in the variable-density tunnel that were
compared directly with corresponding tests in flight.
An effective Reynolds Number is thus determined at
which the tunnel results should, in general, be applied to
flight. Flight conditions as regards the effects of the
transition may then be considered as being approxi¬
mately reproduced, but it should be remembered that
the flow at the lower Reynolds Number cannot exactly
reproduce the corresponding flow in flight. Both the
laminar and turbulent boundary layers are relatively
thicker than those truly corresponding to flight and
both boundary layers have higher skin-friction coeffi¬
cients at the lower Reynolds Number. Nevertheless
the most important source of scale effects is taken
into account, at least approximately, when the tunnel
results are applied to flight at the effective Reynolds
Number. The change in skin-friction drag coefficients
friction layer, which is substantially in agreement with
von Karman’s original derivation, are as follows:
Test Reynolds
Number
Effective Rey¬
nolds Number
300, 000
792, 000
0. 0020
500, 000
1, 320, 000
. 0017
1, 000, 000
2, 640, 000
.0014
2, 000, 000
5, 280, 000
.0012
3, 000, 000
7, 920, 000
.0011
The objection might be raised that the increments
A cd are based entirely on a turbulent skin-friction layer
whereas the boundary layers on airfoils are actually
laminar over a considerable part of the forward portion,
particularly for the lower values of the Reynolds
Number. The A cd correction was nevertheless em¬
ployed over the complete range of Reynolds Numbers
for several reasons: primarily for simplicity and con¬
sistency, because in the practical flight range the
turbulent layer predominates; and secondarily because
on most airfoils the boundary layer must be turbulent
over a considerable part of the surface at any Reynolds
Number sufficiently high to avoid separation. Refer¬
ence to the corrected minimum-drag results for the
N. A. C. A. 0012 section shown in figure 27 may
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 247
clarify these statements. Included in the figure are
curves representing the variations with Eeynolds
Number of fiat-plate drag coefficients for laminar and
turbulent boundary layers and the Prandtl-Gebers
transition curve, which represents a computed variation
substantially in agreement with Gebers’ measurements
of the actual variation in drag coefficient for a flat plate
towed in water at various Eeynolds Numbers. The
computed curve is the result of a calculation of the
average drag coefficient for the plate when the forward
part of the boundary layer is laminar and the after
part turbulent and the transition is assumed to take
place at a fixed value of the surface-distance Eeynolds
Number Rx. It is apparent that the airfoil curve tends
to parallel the actual flat-plate curve throughout the
flight range of values of the Eeynolds Number.
In references 11 and 12 corresponding curves were
presented for a very thin airfoil section. These results
were uncorrected for the turbulence in the tunnel anti
hence, although they appear to parallel a transition
curve like the present corrected results, the transition
curve does not correspond to zero turbulence, or flight,
but is displaced to the left. The correction increment
could have been based on the difference between these
two transition curves for flat plates, the one calculated
for the tunnel and the other calculated for flight con¬
ditions. Such a correction increment would have
been slightly different from the one actually employed,
particularly in the range of the Eeynolds Number
below the flight range, owing to larger drag reductions
in the laminar part of the boundary layer in passing
to the higher Eeynolds Number. Both the test
results for the N. A. C. A. 0012 (fig. 27) and theoretical
calculations for the same airfoil by the method of
reference 13 indicate, however, that separation must
occur as the Eeynolds Number is reduced even in the
case of this excellently streamlined form at zero lift.
The separation is indicated by the abnormal increase
of the drag coefficient shown by the experimental
results below a Eeynolds Number of 800,000. This
separation may at first be a local phenomenon, the
flow subsequently changing to turbulent and closing
in again downstream from the separation point. In
any case it is apparent that the flow will either be to
a considerable extent turbulent or will separate so
that a correction increment based mainly on a laminar
layer would have little significance.
The applied correction increment based on the
turbulent layer is thus justifiable as being conserva¬
tive over the flight range of the Eeynolds Number
and the influences not considered in its derivation
will henceforth be considered as sources of error in
the experimental results. Admittedly it would be of
interest to give further consideration to the results in
the range of Eeynolds Number below the usual flight
range where the influences of extensive laminar bound¬
ary layers and separation are of primary importance,
38548—38 - 4 7
but the relatively poor experimental accuracy of the
test data for these low Reynolds Numbers and the
lack of practical applications tend to discourage an
extensive analysis of the low-scale data.
The accuracy of the final results as applied to flight
is best judged from a comparison of the results with
those from the N. A. C. A. full-scale tunnel. Such
comparisons have been made in references 9 and 10.
The agreement for both the maximum lift and minimum
drag for the Clark Y is easily within the accuracy of the
experiments. For the other airfoil for which a compari¬
son is possible, the N. A. C. A. 23012, the results show
similar satisfactory agreement for maximum lift, within
4 percent, and for the drag coefficient at zero lift,
within 5 percent. The polar curve of the profile-drag
coefficients from the full-scale tunnel, however, tended
to show a marked drop for a small range of lift coeffi¬
cients near that for minimum profile drag. Although
the same phenomenon was apparent from the variable-
density-tunnel tests, it was less marked. The fact that
the minimum drag shown by the full-scale-tunnel test
was 17 percent lower than shown by the variable-
density-tunnel test thus appears less significant than it
otherwise would. Furthermore, it might be expected
that this localized dip in the profile-drag curve would
tend to disappear at the higher Eeynolds Numbers
common to flight at low lift coflieients. In spite of the
fact that the above-mentioned difference between the
results is but slightly outside the limit of possible
experimental errors, the difference does tend to show
how much the turbulence corrections applied to the
variable-density-tunnel data may be in error, particu¬
larly for a condition like the one considered for which
rather extensive laminar boundary layers may be
present. Comparatively high velocities over the lift¬
ing airfoil as contrasted with the flat plate may also
tend to increase the value of the correction increment
so that all these considerations are in agreement in
indicating that the correction increment applied may be
considerably too conservative in some instances, par¬
ticularly for the lower range of flight Eeynolds Num¬
bers.1 The greatest uncertainty, however, in regard to
the application of the drag data to flight is due to the
possibility that under certain favorable conditions in
flight, corresponding to very smooth surfaces and to
practically zero turbulence, the transition may be
i Since the writing of this report, the results of comparative experiments made in
the less turbulent British C. A. T. on the N. A. C. A. 0012 airfoil have come to the
attention of the authors. For the model with the most carefully finished surface,
the results do show lower drags over the lower range of flight Reynolds Numbers
than the data in this report.
Still more recently the results of tests from England and Germany at moderately
large Reynolds Numbers have added further support to the conclusion that the
correction increments applied herein are too small. Furthermore, as indicated
by the foregoing discussion, the increments should probably increase with the airfoil
thickness or drag. For example, better agreement is obtained if, instead of the
increment 0.0011 subtracted from the usual large-scale profile-drag results, a cor¬
rection as a factor applied t.o the measured profile drag is employed. This factor
is 0.85, as similarly determined from the flat plate with completely turbulent bound¬
ary layer. Final conclusions, however, must await further information on the tran¬
sition as it actually occurs in flight.
248
REPORT NO. 58G— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
abnormally delayed. For example, Dryden (reference
14) found very large values of Rx corresponding to
transition on a flat plate. The conditions are remi¬
niscent. of those of supersaturation in solutions. Fol¬
lowing this analogy, it may be impossible to set an
upper limit of R above which transition must occur.
Unusually low drags would, of course, be associated
with the presence of this type of abnormally extensive
laminar boundary layer; but, while this possibility
should be recognized, it is probable that in most prac¬
tical applications, conditions such as slight surface
irregularities, vibration, or self-induced flow fluctuations
will operate against it. The present results may there¬
fore be used in flight calculations as conservative for
wings that are not aerodynamically rough.
VARIATION OF IMPORTANT SECTION CHARACTERISTICS WITH
REYNOLDS NUMBER
Maximum lift coefficient Cimax.- — The maximum lift
coefficient is one of the most important properties of the
airfoil section. It largely determines not only the max¬
imum lift coefficient of wings and hence the stalling
speed of airplanes but also, for example, influences how
and where tapered wings stall and hence the character
of the stall in relation to lateral stability and damping
in roll. The maximum lift coefficient, moreover, in¬
dicates the useful lift range of the section and tends to
define the nature of the variation of profile drag with
lift. Finally, the maximum lift coefficient is the im¬
portant aerodynamic characteristic that usually shows
the largest scale effects.
It is not surprising to find large variations of Cimax
with Reynolds Number because Cimax is dependent en¬
tirely on the boundary-layer behavior, which in turn is
directly a function of viscosity as indicated by the
value of the Reynolds Number. In other words, po¬
tential-flow theory alone is totally incapable of any pre¬
dictions concerning the value of Cimax.
The following discussion traces the mechanism of the
stall with a view to reaching an understanding of how
the stall, and consequently the maximum lift, is affected
bv variations of the Reynolds Number. Basicallv, the
discussion is concerned mainly with air-flow separation.
The pressure distribution over the upper surface of the
conventional airfoil section at lift coefficients in the
neighborhood of the maximum is characterized by a
low-pressure point at a small distance behind the leading
edge and by increasing pressures from this point in the
direction of flow to the trailing edge. Under these
conditions the reduced-energy air in the boundary layer
may fail to progress against the pressure gradient.
When this air fails to progress along the surface, it
accumulates. The accumulating air thereby produces
separation of the main flow. The separation, of course,
reduces the lift.
Whether or not separation will develop is dependent
on the resistance to separation of the boundary layer.
The turbulent layer displays much more resistance to
separation than the laminar boundary layer. This
dependence of separation on the character of the bound¬
ary-layer flow was first observed in sphere-drag tests.
At low Reynolds Numbers separation of the boundary
layer develops near the equator of the sphere. When
the boundary layer on the sphere is made turbulent, how¬
ever, as it is when the Reynolds Number is sufficiently
increased, the separation shifts to a position considerably
aft.
The occurrence of separation for airfoils, as affected
by the transition from laminar to turbulent flow in the
boundary layer, is indicated by the scale effects on
Cimax (fig. 28) for symmetrical sections of varying thick¬
ness. For these airfoils at any considerable lift coeffi¬
cient the low-pressure point on the upper surface tends
to occur just behind the nose, on the leading-edge-radius
portion of the airfoil. When the boundary layer is
laminar behind this point, separation may be expected
Effective Reynolds Number
Figure 28.— Section maximum lift coefficient. cimaz. Symmetrical airfoils of varying
thickness.
to occur very quickly behind or almost at the low-
pressure point owing to the presence of large adverse
pressure gradients. In fact, the von Karman-Millikan
method of calculating the incipient separation point
for laminar boundary layers (reference 13) has been
applied by Millikan to estimate the position of the
separation point and also its relation to the tran¬
sition point as it is assumed to influence the scale effect
on the maximum lift coefficient. The number and char¬
acter of the assumptions involved in such an analysis,
however, are such that the results may be expected to
yield only qualitative predictions. Elaborate calcula¬
tions in such cases are of doubtful necessity as indicated
by the fact that qualitative predictions, perhaps more
reliable, had previously been reached without them.
(See references 12, 15, and 16.) Exact methods of
calculation are unquestionably desirable but are defi¬
nitely not a matter for the present but for a time when
much more experimental data concerning both separa¬
tion and transition shall have been secured.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER. 249
For the present discussion it is sufficient to consider
that, if the boundary layer remains laminar, separation
will occur very close behind the low-pressure point on
the upper surface. Incidentally, the actual separation
point is expected, in general, to be forward of the calcu- !
lated incipient separation point; that is, nearer the
low-pressure point. It should not, however, be assumed
that the occurrence of separation defines the maxi¬
mum lift coefficient. For example, at very low Rey¬
nolds Numbers, separation on the N. A. C. A. 0012
airfoil occurs even at zero lift, which on this assumption
would define zero as the maximum lift. Motion
pictures have been made showing the air flow and
separation for airfoils at low values of the Reynolds
Number. Three photographs from the smoke tunnel
are included as figures 29, 30, and 31 to indicate the
position and character of the laminar separation for a
cambered airfoil. The first two pictures show well-
developed separation even at zero angle of attack; the
third shows how laminar separation occurs just behind
the nose at higher angles of attack.
Figure 29. — Separation occurring on an airfoil at a low angle of attack.
It is thus apparent that separation of the laminar
boundary layer will always be present at a point near
the nose at any moderately high lift coefficient if the
Reynolds Number is not sufficiently high to make the
flow turbulent at that point. This condition certainly
exists for the results in figure 28 over the lower range
of the Reynolds Number; that is, separation near the
nose must have occurred at angles of attack well below
that of Ci owing to the very small Reynolds Number
associated with the short distance from the nose to the
laminar separation point. In this range of R the Cimgx
values are of the order of 0.8 and change little with
either R or the section thickness. (See fig. 28.) This
value of cl/nax corresponds approximately to that for a
flat plate.
Now consider the character of the flow as the Rey¬
nolds Number is increased. The effects are shown very
clearly by a comparison of figure 29 and figure 30.
Figure 30 corresponds to a higher Reynolds Number and
shows turbulence forming at a “transition point” along
the separated boundary layer behind the laminar sepa¬
ration point. Incidentally, it should be remembered
that the transition point is not really a point but is a
more or less extended and fluctuating region in which
the laminar layer is progressively changing to the fully
Figure 30. — Separation occurring on an airfoil at a low angle of attack (fig. 29) but
at an increased Reynolds Number.
developed turbulent layer. This transition region now
moves forward toward the separation point as the
Reynolds Number is further increased. The formation
of turbulence results in a thickening of the boundary
layer between the dead air and the overrunning How
until the turbulent mixing extends practically to the
airfoil surface. The separated flow may then be con¬
sidered reestablished. This process would leave a bubble
of “dead air” between the separation point and the
transition region, the existence of which was predicted
several years ago. Subsequently Jones and Farren
(reference 17) have actually observed this phenomenon.
As the Reynolds Number is further increased, the
transition region progresses toward the leading edge,
approaching the region of the laminar separation point.
Consider now, for example, the flow about the N. A.
C. A. 0012 at a value of R in the neighborhood of Rc,
the critical Reynolds Number, where the maximum lift
Figure 31.— Separation occurring on an airfoil at a high angle of attack.
increases rapidly with R. As shown in figure 28, Cjmax
for the N. A. C. A. 0012 begins to increase rapidly with
R at approximately Re= 1,000,000. Consider therefore
two flows, one at Re= 1,000,000 just at the attitude of
Ci , and the other at the same attitude but at a higher
hnax* °
250
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
effective Reynolds Number, say 1,750,000. For the
former, separation is probably occurring near the low-
pressure point, but the turbulence is forming closely
enough behind the separation point so that the flow
over the upper surface is partly reestablished. An
increase o-f angle of attack fails to increase the lift,
however, because the turbulence is forming so late that
the local separation and its resulting adverse effect on
the thickening or separation of the turbulent layer
farther aft prevent a further gain of lift. Now as the
Reynolds Number is increased the transition region
moves to a position nearer the separation point, the
extent of the separated region is reduced and, as shown
by reference to figure 3, CL at the same angle of attack
is increased from 0.85 to 1.05 (for the approximately
corresponding test Reynolds Numbers of 330,000 and
660,000). Furthermore, the angle of attack may now
be increased until Cl reaches 1.1 before the flow follow¬
ing the upper surface fails. The failure now occurs
suddenly, causing a break in the lift curve, but again
may be delayed by a further increase of the Reynolds
N umber.
In such cases the scale effect evidently varies with
the shape of the nose of the airfoil. If the leading-edge
radius is reduced by making the airfoil thinner, the
local Reynolds Number for the separation point or the
transition region, either II a based on boundary-layer
thickness or Rx based on the distance along the surface,
is reduced with respect to R because the local dimen¬
sions near the nose are reduced with respect to the air¬
foil chord. Higher values of R are therefore required
to reach the critical Rx or R5 values in the neighborhood
of the nose. This result is indicated by the higher
critical Reynolds Number Iic for the N. A. C. A. 0009
than for the N. A. C. A. 0012, as shown in figure 28.
Likewise, the 15 and 18 percent thick airfoils show
progressively lower values of Rc than the N. A. ( . A.
0012, but the critical range tends to disappear as the
thickness is increased.
The range of R is limited by the wind tunnel so that
in most instances the scale effect above the critical
range could not be determined. It is probable, how¬
ever, that the highest maximum lift coefficients are
reached when the Reynolds Number corresponds to
the occurrence of fully developed turbulence practically
at the laminar separation point but that this condition
occurs above the highest Reynolds Numbers reached
except possibly for the thickest airfoil, N . A. C. A. 0018.
High local Reynolds Numbers at the laminar separa¬
tion point could, however, be reached by employing a
thick, highly cambered airfoil. The N. A. C. A. 8318
airfoil was included for this reason. The results (see
fig. 32) indicate, as expected, a very low critical Rey¬
nolds Number. With increasing Reynolds Number,
Ci rises to a maximum at 7^—900,000 and then falls
off slowly. In this instance, at the highest Reynolds
Numbers transition probably occurs ahead of any point
at which laminar separation could occur. The maxi-
Figurk 33. — Section maximum lift coefficient, cimal. Camber series.
mum lift coefficient must therefore be determined by
the behavior of the turbulent layer. The significant
conclusion is that c,max then decreases with increasing
R. Another significant observation is that under these
conditions stalling is progressive as indicated by the
rounded lift-curve peaks in figure 11. This type of
stalling corresponds to a progressive separation or
thickening of the turbulent layer in the region of the
trailing edge.
The process of stalling in general is more complex
than either of the two distinct processes just discussed.
It has been compared by Jones (reference 17) to a
contest between laminar separation near the nose and
turbulent separation near the trailing edge, one or the
other winning and thus producing the stall. Actually
it appears from these scale-effect data that, for com¬
monly used airfoils at a high Reynolds Number, the
forward separation usually wins but that it is largely
conditioned and brought about by the thickening or
separation of the turbulent boundary layer near the
AIRFOIL SECTION
CHARACTERISTICS AS AFFECTED
BY
VARIATIONS OF THE REYNOLDS NUMBER
25 1
trailing edge, which, in turn, may be largely influenced
by the local separation near the leading edge. The
reasons for these statements will become clear from the
consideration of the scale effects for the different types
of aii foil.
Consider first the maximum lift of the conventional
type of cambered airfoil. Where stalling is determined
largely by separation near the leading edge, the maxi¬
mum lift would be expected to be a function of the
curvature near the leading edge and also a function of
the mean camber because the effect of the camber is to
add a more or less uniformly distributed load along
the chord. At some angle of attack above that of zero
lift the flow over the nose part of the cambered airfoil
approximates that over the nose of the corresponding
symmetrical airfoil at zero lift. This correspondence
of flows at the leading edges between the symmetrical
and cambered airfoils continues as the angles of attack
of both are increased. If the stalling were determined
largely by the flow near the nose, the two airfoils would
stall at the same time, but the lift of the cambered
airfoil would be higher than that of the symmetrical
airfoil by the amount of the initial lift increment.
Reference to figure 33 shows that this expected change
of Cimax with camber is approximately that shown by
the results from tests in the lower range of the Reynolds
Number. At high Reynolds Numbers, however, the
change of c , with camber is much smaller than would
be expected if the stall were controlled only by condi¬
tions near the leading edge. On the other hand, some
of the cambered airfoils show a sudden loss in lift at
the maximum indicating that separation is occurring
near the leading edge but, as the camber is increased,
the lift curves become rounded. (See figs. 6, 7, and 8.)
For the N. A. C. A. 2412, which shows a sharp break
in lift at the maximum but a small gain in Cimaz due to
camber at the high Reynolds Numbers, the boundary-
layer thickening or turbulent separation must become
pronounced near the trailing edge at the higher Rey¬
nolds Numbers before the flow breakdown occurs near
the leading edge. This alteration of the flow results
in higher angles of attack for a given lift and con¬
sequently more severe flow conditions over the nose of
the airfoil. These flow conditions, which really origi¬
nate near the trailing edge, thus bring about the flow
breakdown near the leading edge that finally produces
the actual stall. It must not, however, be concluded
that more gradually rounding lift-curve peaks with in¬
creasing R should be the result; actually, the opposite
is usually true (e. g., figs. 6, 7, and 8). The explana¬
tion is probably that increasing the Reynolds Number
reduces the extent of the local separation near the
leading edge, which influences the boundary-layer
thickening near the trailing edge, at least until the
transition region reaches the separation point. That
Clmax continues to be influenced by the flow conditions
near the leading edge, even for highly cambered sec¬
tions, is shown by the fact that the critical Reynolds
Number is little affected by increasing the camber to
that of the N. A. C. A. 6412 in spite of the fact that
the actual gain in c , throughout the critical range
becomes less for the more highly cambered airfoils.
This conclusion is an important one because it can be
extended to predict that the critical Reynolds Number
will not be affected by flaps and other high-lift devices
placed near the trailing edge, which act much like a
camber increase.
2.8
1
n —
>
J
2.6
2.4
g
1 V.Ai. O.A1. C-^JUOt H
- split flop
//tn
O 'VN
Ach
A
''
A
N.A.
C.A. 230/2
A
A
V 2.0
C LQ
dj
O 1.6
0
L 1.4
V-
S 1.0
Is
c;
.0
$
,0)
1/1 A
.2
0
with split -
flap de-
— -
A
/
fleeted 60
°
to
H
N.A
n
/y
->or
£
&
T
J
- -
V
_
N.A
C.A
om
p
Wj
th ■
/
/
r
8a
4
split flap |
deflected 60
Cr
J _
o
2
o or
2
/
U
LiJ
/ rv.r\.K*.+
4.-L-l.J-
u
h
o
a -
-A-i
■-
• At
r
A. _ A
/ a n a
1
n n /
A
r
JU /
d
-
8
. 6
8
100,000 2 3 4 5 6/, 000,000 2 3 4 5 10,000,000
Effective Reyno Ids Number
Figure 34.— Section maximum lift coefficient, cimax. Airfoils with and without flaps.
Reference to figure 34 shows the correctness of this
conclusion. It will be noted, moreover, that each scale-
effect curve representing an airfoil with a split flap tends
to parallel the corresponding curve for the same airfoil
without a flap. The split flap thus simply adds an in¬
crement to the maximum lift without otherwise chang¬
ing the character of the scale effect. In this respect the
behavior with the flap differs from the behavior with
increasing camber. With the split flap, the distribution
of pressures over the upper surface is apparently not
affected in such a way as to increase the tendency
toward trading-edge stalling, otherwise the scale-effect
variations would not he similar with and without the
flaps. Incidentally, it is of interest to note that the
maximum lift increment due to the split flap is not
independent of the airfoil section shape but, for ex¬
ample, increases with the section thickness, (('f. the
N. A. C. A. 230 series, with and without split flaps,
table I.)
As regards flaps other than split flaps, recent tests
have shown that the maximum lifts attainable arc ap¬
proximately equal for either the ordinary or the split
flap. This result might have been expected because the
252
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
results of references 18 and 19 had indicated that the
How does not follow the upper surface of an ordinary
flap except for small angles of flap deflection. It should
therefore make little difference whether or not the upper
surface of the flap is deflected with the lower. Further¬
more, the same reasoning might be applied to predict
the effects of camber, when the mean line is of such a
shape that the maximum camber occurs near the trail¬
ing edge so that the separation associated with increas¬
ing camber is localized in this region. Thus it might
have been predicted that the scale effect as shown in
figure 35 for the N. A. C. A. 0712 airfoil would be more
like that of an airfoil with a split flap than like that of
the usual type of cambered airfoil.
Another important conclusion can be deduced from
the results in figure 35 showing the scale effects for air¬
foils having various mean-line shapes. When a mean-
line shape like that of the N. A. C. A. 23012 is em-
Fioure 35. — Section maximum lift coefficient, Airfoils with various mean-
line shapes.
ployed — that is, one having marked curvature near the
nose and a forward camber position — the effect is to
alter the conditions of the leading-edge stall. The critical
Reynolds Number is thus shifted to the left and the
general character of the scale effect becomes more like
that of the usual airfoil of 15 instead of 12 percent
thickness.
The opposite effect on the nose stall is shown in figure
36 where the critical Reynolds Number is shifted to the
right by decreasing the leading-edge radius, that is, by
changing from the N. A. C. A. 23012 section to the
23012-33. Thus it appears, in general, that the charac¬
ter of the Ci„ scale effect, particularly in relation to
the value of the critical Reynolds Number, depends
mainly on the shape of the airfoil near the leading edge.
The two remaining airfoils not covered by the previ¬
ous discussion (fig. 37) have slotted high-lift devices.
Both the Clark Y airfoil with Handley Page slot and
the airfoil with external-airfoil flap show unusual scale
effects. The airfoil with Handley Page slot shows an
increasing clmax throughout the Reynolds Number
range but shows a peculiar change in the character of
the stall in the full-scale range near 2^=3,000,000.
(See also fig. 24.) The airfoil with the external-airfoil
flap shows a break in the scale-effect curve. Two
values of Cimax were measured for the condition corre¬
sponding to Re= 1,700,000 (fig. 23, test I? — 645,000),
one lift curve having a sharp break at the maximum
and the other being rounded. It is believed that the
change is associated with the action of the slot at the
nose of the external-airfoil flap. It is particularly
interesting because it represents one of the cases men¬
tioned under the interpretation of the wind-tunnel
data for which the failure of the tunnel flow to repro¬
duce exactly at the effective Reynolds Number the
corresponding flow in flight becomes of practical im¬
portance. A comparison of these tests with tests in
the 7- by 10-foot tunnel (reference 5) indicated that
such scale effects may be due primarily to the action
Figure 30. — Section maximum lift coefficient, Cimax. Thickness-shape variation.
of the slot as affected by the boundary-layer thickness
relative to the slot width, which is a function of both
the test and the effective Reynolds Number, rather
than to the transition from laminar to turbulent flow.
When interpreted on the basis of the test rather than
the effective Reynolds Number as regards the occur¬
rence of the break in the low Reynolds Number range,
better agreement with the results from the variable-
density tunnel was obtained. On this basis the dis¬
continuity shown in figure 37 as occurring at Re=
1,700,000 would be expected to occur in flight at a con¬
siderably lower Reynolds Number outside the usual
flight range.
With regard to c, scale effects for conventional
0 lmax
types of airfoils, it now appears in the light of the
preceding discussion that a position has been reached
from which the scale effects appear rational and suf¬
ficiently regular and systematic so that general scale-
effect corrections may be given for such airfoils. This
position represents a marked advance. In a later
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 253
section of this report such generalized scale-effect cor¬
rections for Cimax are presented for engineering uses.
Lift variation near clmaxm — The variation of the lift
near the maximum as indicated by the shape of the
lift curve is of some importance because it often affects
the character of the stall and the corresponding lateral
control and stability of the airplane in flight. The
character of the stall for the airfoils may be inferred
approximately from the preceding discussion of c,mnx
and is indicated by the lift curves in figures 2 to 24.
The moderately thick symmetrical airfoils in the critical
or flight range of R show sudden losses of lift beyond
the maximum. Efficient airfoils of moderate thickness
and camber, for example, N. A. C. A. 2412 and 23012,
likewise usually show sudden breaks in the lift curve
at the maximum for the higher Reynolds Numbers.
When the influence of trailing-edge stalling becomes
sufficiently marked as it does with airfoils N. A. C. A.
4412 and 6412, the breaks in the lift curves disappear
and the lift curve becomes rounded at the maximum.
It is interesting to note that breaks occur at compara¬
tively low values of the Reynolds Number for the
N. A. C. A. 8318. In this case the breaks appear in
the critical range of R, where critical leading-edge
stalling occurs, and disappear at higher and lower Rey¬
nolds Numbers. (See figs. 11 and 32.)
Lift-curve slope u0. — The scale effects for a0 are
represented in figure 38. It will be noted that, within
the full-scale range, the airfoils show little variation of
a0 with either airfoil shape or with R. In this range
most of the airfoils show a slight tendency toward
increasing a0 with R but, for engineering purposes, the
variation of a0 may usually be considered negligible
within the flight range. The lift-curve slope, like
several of the other section characteristics, begins to
display abnormal variations below a Reynolds Number
of approximately 800,000. For the lowest values of R
the lift curves often became so distorted that lift-curve
slopes were not determined. (See figs. 2 to 24.)
Angle of zero lift a,0- — Scale-effect variations of
<u0 are represented in figure 39. The conclusions with
respect to this characteristic are almost the same as
for the lift-curve slope a0. Symmetrical airfoils, of
course, give <u0 = 0 at all values of R. The cambered
airfoils, in general, show a small decrease in the absolute
value of the angle with increasing R above the value
at which the variations are abnormal.
Minimum profile-drag coefficient ca inm — The mini¬
mum profile-drag coefficient is indicative of the wing
drag In high-speed flight and is the other important
section characteristic, aside from c, , that shows
marked scale-effect variations within the full-scale
range which must be taken into account in engineering
work.
Figure 37. — Section maximum lift coefficient, Ci
Airfoils with high-lift devices.
Figure 38.— Lift-curve slope, at.
Effective Reyno Ids Number
Figure 39.— Angle of zero lift, aio-
254
(c) Thickness and camber.
Figure 40. — Minimum profile-drag coefficient, cd0 mi„.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED
BY VARIATIONS OF THE REYNOLDS NUMBER
255
(f) Camber shape.
38i)48 — as - 18 Figure 40 (continued.)— Minimum profile-drag coefficient, Cdo min.
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The experimental drag results are presented by means
of logarithmic plots with the well-known laminar and
turbulent skin-friction curves and the Prandtl-Gebers
transition curve shown for comparison. (See figs.
40 (a) to 40 (f).) At the higher Reynolds Numbers a
striking similarity exists between the minimum profile-
drag coefficients for the airfoils and the transition curve
representing the drag coefficient variation with R for a
flat plate towed in water. The other striking feature of
the drag curves is their departure from regularity at
Reynolds Numbers below a certain critical value. This
critical value of the Reynolds Number usually lies in
the range between 400,000 and 800,000, but a study of
the experimental results will show that the critical
value itself is irregular, that is, it does not vary system¬
atically with the airfoil shape. The results appear as
though two or more drag values were possible within
this Reynolds Number range and accidental disturb¬
ances determined whether a high or a low value of the
drag was measured at a given value of R within this
range. One is reminded of Baker’s experiments towing
airship models in water in a towing basin where meas¬
urements could not be repeated until transition was
definitely brought about by the use of a cord passing
around the model near the nose.
The shape of the scale-effect curve for the N. A. C. A.
0012 airfoil at zero angle of attack (fig. 40 (a)) was
studied in the light of boundary-layer calculations.
The results indicated that the computed skin-friction
drag coefficients to give scale-effect variations in agree¬
ment with the measured ones required the presence of
rather extensive laminar boundary layers in this
critical range of the Reynolds Number. In fact, for
the N. A. C. A. 0012 airfoil, the laminar boundary layer
was found to have become so extensive when R was
reduced to the experimentally determined critical value
that a further reduction of R would have required the
laminar boundary layer to extend behind the computed
laminar separation point, which would have involved
at least local separation. It seems evident, therefore,
that the increased drag coefficients below the critical
range are the result of this condition, which is probably
associated with laminar separation and a resulting
increase of the pressure or form drag of the section.
Fortunately, however, this phenomenon seems to
appear below the usual flight range of R.
When designers are concerned with the minimum
drag of an airfoil section, it is usually for high-speed or
cruising flight, which for modern transport airplanes may
correspond to a Reynolds Number of 20,000,000 or more
for some of the wing sections. The drag coefficients for
the Reynolds Number range above the highest reached
in the tunnel are therefore of more interest than those
well within the experimental range. Unfortunately,
the precision of the measurements permits only an
approximate determination of the shape of these scale-
effect curves even in the higher experimental range of
R so that extrapolations into the higher flight range will
necessarily be unreliable. Nevertheless, much en¬
gineering work requires a knowledge of airfoil drag
coefficients within this range so that the engineer must
resort to extrapolation. For this purpose the data may
be studied in relation to the slopes of the curves for the
various airfoils (fig. 40) in the highest range of R
reached in the experiments. Such a study indicates
that the airfoils, excluding the unusual airfoils N. A.
C. A. 8318, N. A. C. A. G712, and the Clark Y with
Handley Page slot, show a decreasing cd{) m in with R
that seems, in general, to parallel approximately the
corresponding curve for the flat plate. Thus, in
general, the slope of the cdomin scale-effect curves in
the neighborhood of a Reynolds Number of 8,000,000
may be taken as approximately —0.11, which leads to
the following extrapolation formula:
where the subscript std refers to the standard airfoil-
test results from the variable-density tunnel corres¬
ponding to an effective Reynolds Number of approx¬
imately 8,000,000. In such extrapolation formulas,
values of the exponent have been used between 1/5,
taken from Prandtl’s original analysis of the completely
turbulent skin-friction layer, and 0.15, which agreed
better with experiments with pipes and flat plates at
very high values of R and agrees better with von Kar-
man’s recent analysis of the completely turbulent layer
in this range of R. It should be emphasized, however,
that these comparatively large exponents are not
conservative and would be expected to lead to pre¬
dictions of large-scale drag values much too low, partic¬
ularly when the extrapolation is made from measure¬
ments made in the transition region; for example, in
figure 40 (a) measurements in the range between
1,000,000 and 2,000,000 should not be extrapolated by
such methods to 20,000,000. Extrapolations from
if = 8,000,000 using the comparatively low' exponent 0.11
are, however, considered reasonably conservative for
aero dynamically smooth airfoils.
In regard to profile-drag coefficients at lift coefficients
other than the optimum, figure 41 (a) shows the scale
effects for cdQ at C/=0.8 for the symmetrical series of
airfoils. The drop in the scale-effect curves in the
transition region has disappeared and the two thinner
airfoils show evidences of the approaching stall. Curves
for members of the camber series of airfoils, N. A. C. A.
0012, 2412, 4412, and 6412 at zero lift are shown in
figure 41 (b). Here the symmetrical airfoil is operating
at its optimum lift and the departure from the optimum
for the other airfoils increases with camber. A pro¬
gressive transition from the cdomin type of scale effect
to that of figure 41 (a) is apparent. Results (reference
10) from other wind tunnels for the Clark Y airfoil,
which is in a sense similar to the N. A. C. A. 4412 but
has slightly less camber, are also indicated in figure
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 257
41 (b) for comparison. The comparison of the results
from the various tunnels should serve to indicate the
limitations of accuracy that must be accepted when any
of the data are extrapolated to the higher full-scale
Reynolds Numbers.
Optimum lift coefficient Ci . — The optimum lift
coefficients are presented in figure 42. This character¬
istic is of importance mainly in relation to cdQ values at
other values of ch It is not possible, nor essential for
this purpose, to evaluate Ci very accurately. In fact,
Figuke 41. — Profile-drag coefficient.
The determination of cd() values at various lift co¬
efficients in engineering work is best accomplished by
a consideration of increments from cdomin. The
method of a “generalized polar” discussed in a later
section of this report gives such increments in terms of
the departure of ct from clgpt as compared with the
departure of c, from c, ,
1 max 1 opt-
the accuracy of the experimental data is not sufficient
to establish Ihc scale-effect variations with certainty.
Nevertheless, the results show a definite tendency
toward a decreasing c, , with increasing R. Thus
values measured in small atmospheric tunnels may be
expected to be too high. Values from the standard
airfoil tests in the variable-density tunnel may usually
258
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
he taken as approximately correct within the usual full-
scale range but may be somewhat too high for the
higher flight range of It.
Pitching-moment coefficient cm<i c ana aerodynamic-
center position a. c. — The values of the pitching-
Figure 42. — Optimum lift coefficient, ciopl.
moment coefficient and the aerodynamic-center position
establish the pitching-moment characteristics of the
airfoil section in the normal operating range between
zero lift and the stall. In this range the pitching
moment about the aerodynamic-center point may be
considered constant for conventional airfoils. The
accuracy of the low-scale data did not permit the
evaluation of aerodynamic-center positions for values
of It much below the flight range, and the variations
found in the higher range showed little consistency.
Values are indicated in figures 2 to 24 and in table I,
but it is not considered advisable in practice to allow
for a variation of aerodynamic center with It. The
cni(i c values corresponding to these aerodynamic-center
positions are plotted in figure 43. The values are
nearly independent of It at high values of It but usually
show a tendency to increase numerically as It is reduced
toward the lower extremity of the flight range. Thus
low-scale tunnel tests may be expected to give pitching
moments that are numerically too large.
PREDICTION OF AIRFOIL CHARACTERISTICS AT ANY
REYNOLDS NUMBER FOR ENGINEERING USE
In the consideration of methods of predicting wing
characteristics, it should be remembered that the scope
of this report is confined to the prediction of the airfoil
section characteristics. Actual wing characteristics are
obtained from these section characteristics by integra¬
tions along the span with suitable allowances for the
induced downflow and the corresponding induced drag.
Such calculations as applied to tapered wings are fully
discussed in reference 8. It remains therefore to pre¬
dict the airfoil section characteristics at any value of
the flight Reynolds Number. The preceding discussion
has shown that for engineering purposes many of the
important airfoil section characteristics may be con¬
sidered independent of It within the flight range, so
that for application to flight at any value of It these
characteristics may be taken directly from the tabu¬
lated values from the standard airfoil tests in the
variable-density tunnel. There remain then the two
important section characteristics ct and cdn which in
general will require correction to the design Reynolds
Number before they are employed.
Section maximum lift. — For the prediction of the
section maximum lift coefficient c, at values of It
other than the Ite value for which they are commonly
tabulated, the correction-increment curves of figure 44
have been prepared from the data in this report. In
this figure, curves giving the corrections A Cimax are
grouped in families corresponding to the measured scale-
effect variations for various types of airfoils. In gen¬
eral, for normal airfoils the curves in figure 44 marked 0
for types B, C, D, and E correspond to the symmetrical
airfoil sections of different thickness and the curves
indicated by increasing numbers correspond to airfoil
sections of increasing camber.
In practice, the particular curve to be employed for a
given airfoil will be indicated in the standard tables of
airfoil characteristics such as table II of this report
(see also reference 3) under: “Classification, SET
c
<b
c
dl
U
u
^ 5
C 0
c >>
0'S
'
-C ^
O -K
o
-0
0
t;
o
.o
$
Qj
O
U
.02
O
-.02
-.04
-.06
-.08
-JO
-.12
-.14
-.16
-.16
-.20
-.22
/ 00.000
2.30/2 with 'exter
N.A.C. A.
'ho/ flap
P Q _ /P 3 d
sef3JJ>-
~ la— Ux-
4>
—
”T ITT
230/2-33-
- t-t
230/2'.
Jl -i
—
--
-J
>
►-r-
4-
^ A
f.A.C.
a)
OOi
00
09
!2
A/.,
1
4.C.
J
2±
/A
2
A
V
<
00/5
00/8
1
-c
r—
—
/ —
>
N
A.
c
A
. ^
t4L
is
N
A
C
/
1.
4
4/
5
"i;
i
--
&
r!
t
Jy-5
i
N
A
c
J
14)
2
—
\!
l
X
4
cv
1/P -
A
--
--
r
/
-
V.
A
.C.A
rr
13
18"
A
/
X
A
<\.c
4. 67
!2-
t-y
—
v-
8
2 3 4 5 61,000,000 2 3 4 5/0,000,000
Effect ive Reynolds Number
Figure 43.— Pitching-moment coefficient about the aerodynamic center, Cm„.c
From the curve thus designated, the correction incre¬
ment is read at the design Reynolds Number. The
required ct for the section at the particular Reynolds
Number is then obtained by adding this increment to
the tabulated c, value.
lmax
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED
BY VARIATIONS OF THE REYNOLDS NUMBER
259
Figure 44.— Scale-effect corrections for cimax. In order to obtain the section maximum lift coefficient at the desired Reynolds Number, apply to the standard-test value
the increment indicated by the curve that corresponds to the scale-effect designation of the airfoil.
Airfoil section drag. — In design work, values of
the section minimum drag coefficient <Y0 min for aerody-
0 ./ .2 .3 4 .5 .6 .7 .8 .9 1.0
I C ~ c i opt\ J c i max~ c i opt
Figure 45. — Generalized variation of Ac do.
The c<t0 values at other lift coefficients may now be
obtained from the generalized variation of A C/0 with
Q _ Q
- lo- presented in figure 45, where the standard
C l max C l opt
airfoil characteristic table is again employed to find
Ciopl. The Cimax value employed should, of course, cor¬
respond to the Reynolds Number of the Cf0 value being
calculated. This procedure may involve the use of
cimax values corresponding to very high Reynolds
Numbers. These values, however, may be estimated
by extrapolating the maximum-lift scale-effect curves,
little accuracy being required because ct will usually
be near cUvl and AQ0 therefore small. A series of
ACrf0 values may thus be derived for various lift coef¬
ficients and Reynolds Numbers. The corresponding
values of cdo are then obtained by adding these incre¬
ments to the Ca0 min value calculated from the preceding
extrapolation formula for the corresponding Reynolds
Number. In practice, a series of values of crfo may
thus be derived to form a curve of L/0 against ct along
which the Reynolds Number varies with lift coefficient
as in flight.
namically smooth airfoils are first obtained from the
tabulated data by means of the extrapolation formula
previously given,
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., June 24, 1986.
APPENDIX
INVESTIGATION OF CERTAIN CONSISTENT ERRORS PRESENT IN TEST RESULTS FROM THE
VARIABLE. DENSITY TUNNEL
By Ira H. Abbott
INTRODUCTION
An investigation lias been made to evaluate three
corrections that were not applied to the data, obtained
in the variable-density wind tunnel, and published in
reference 2 and earlier reports. The need for these cor¬
rections had been recognized, and possible errors in the
data resulting from the lack of these corrections have
been listed as consistent errors (reference 2) due to the
following elfects:
1. Aerodynamic interference of the model supports
on the model.
2. Effect of the compressed air on the effective weight
of manometer liquids used to measure the dynamic
pressure.
3. Combined effects on the measured dynamic pres¬
sure of blocking due to the model and to errors in pitot-
tube calibration arising from differences in dynamic
scale and turbulence between conditions of use in the
variable-density tunnel and conditions of calibration.
These effects result in errors in the calibration of the
static-pressure orifices used to determine the dynamic
pressure.
INTERFERENCE OF MODEL SUPPORTS
The model supports used in the variable-density tun¬
nel and the method of determining the tare forces are
described in reference 1. The usual tare tests deter¬
mine the tare forces on the supports including the inter¬
ference of the model on the supports. In addition,
the usual method of determining the balance alinement
with respect to the air-flow direction by testing an air¬
foil erect and inverted includes any interference of the
supports on the model that is equivalent to a change in
air-flow direction. Earlier attempts to determine any
additional interference of the supports on the model were
inconclusive except to show that such interference was
small.
Two airfoils of moderate thickness were chosen to be
used in the present investigation, one being a symmetri¬
cal airfoil (N. A. C. A. 0012) and the other an airfoil of
moderate camber (N. A. C. A. 4412). Tests were made
of each airfoil using three methods of supporting the
model. Besides the method using the usual support
struts, tests were made with the models mounted on the
usual supports with the addition of special wire sup¬
ports and with the models mounted only on the wire
supports. The wire supports consisted of three wires
attached to the quarter-chord point of the model at
260
each wing tip and of a sting and angle-of-attack strut
so located as to be free from aerodynamic interference
with the usual supports. The sting used was sym¬
metrical with respect to the airfoil and v'as attached near
the trailing edge instead of to the lower surface, as
is usual.
The tares due to the wire supports were determined
from the data obtained from the tests with the models
on the usual supports with and without the wire
supports. Some difficulty was experienced in obtaining
sufficiently accurate tares because of the relatively
large drag of the wires as compared with the drag of
the model. Sufficient accuracy was obtainable only at
the highest value of the test Reynolds Number ordinar¬
ily obtained (about 3,000,000). The profile-drag coeffi¬
cients obtained for the two airfoils are plotted as solid
lines in figures 46 and 47, together with data obtained
from several tests made with the usual supports over
a considerable period of time. The scattering of the
points obtained from the tests with the usual supports
about the solid line is within the limits of the accidental
errors listed in reference 2, showing that there is no
support interference within the accuracy of the results
at high values of the Reynolds Number.
It is evident that the data obtained can be analyzed
in different ways. For example, the data obtained
with the models mounted on both the usual supports
and the wire supports can be corrected for the usual sup¬
port tares and compared with the data from tests with
the models mounted only on the wire supports. The
comparison was made correcting the data for the change
in air-flow direction due to the usual supports and failed
to show any support interference within the test
accuracy.
Analysis of the data to determine the effects of the
support interference on the measured pitching-moment
coefficients was more difficult. The support wires
stretched under the lift and drag loads, necessitating
a correction to the measured pitching-moment coeffi¬
cients, and the method of supporting the model at the
wing tips allowed the model itself to deflect under the
lift loads much more than when mounted on the usual
supports. The correction due to the deflection of the
model is difficult to evaluate with certainty because it
involves integrations along the span after determination
of the span load distribution. Accordingly, the effect
of the support interference for the pitching moments
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 261
was determined only at zero lift where it was found
that the measured pitching-moment coefficient was too
large (algebraically) by 0.002. This same correction
had been found previously from tests with symmetrica]
Angles V.D.T.
Pos.Neg. Test
- 1080-6
A
.06
743
It 20
1233
Dote Condition Test R,
millions
IO-26~33 Wire support 3.07
I2~30~3l Usual « struts 3.24
4-17-34 " • * '3.20
2~ 6~35 * " " 3.17
c
,<U
V .04-
CD
o
u. 03\
%
k
.43
o
k-0/
O'-
c
4-
A
/
/
&
k —
- 4
to —
L_
0 ±.2 ±.4 ±.6 ±.8 ±1.0
Lift coefficient, CL
-.1.2 ±1.4
Figure 46— Lift and drag characteristics of the N. A. C. A. 0012 airfoil as determined
from tests with the model mounted on the usual support struts and on special wire
supports.
airfoils and had been applied so that no new corrections
were necessary.
EFFECTIVE WEIGHT OF MANOMETER LIQUIDS
The dynamic pressure is measured by two manome¬
ters connected to two sets of calibrated static-pressure
orifices as described in reference 1 . One manometer
is filled with grain alcohol and the other with distilled
water, the one filled with alcohol being ordinarily
used to hold the dynamic pressure constant through¬
out a test because it is more easily read than
the water manometer. Readings of the water
manometer taken during each test serve to check
the alcohol manometer and to indicate any
change in the specific gravity of the alcohol,
which is obtained from time to time by calibrating
the alcohol manometer at atmospheric pressure
against a head of distilled water.
It is apparent, as has been pointed out by
Relf, that when the tank is filled with compressed
air the increased density of the air reduces the
effective weight of the alcohol or water in the
manometers. This effect may be considered as a
buoyancy of the air on the liquid and may be
computed, but there is no assurance that the
effects of other factors such as the amount
of air dissolved in the liquid are negligible.
An experimental determination of the effect of the
compressed air was made by calibrating the alcohol
and water manometers at several tank pressures against
a third manometer filled with mercury. The compara¬
tively small buoyancy effect on the mercury was com¬
puted and applied to the results as a correction. The
effects of other factors on the mercury were considered
negligible. In addition to the correction determined
in this way, a further small correction was applied to
the specific gravity to compensate for the small change
in balance calibration with air density due to the buoy¬
ancy of the air on the balance counterweights. The
net correction at 20 atmospheres tank pressure was
found to be 2.0 percent for the alcohol and 1.7 percent
for the water, the dynamic pressure as measured being
too high. It is planned to replace the manometers by
a pressure balance in the near future. Measurements
of dynamic pressure will then be independent of specific
gravity.
CALIBRATION OF STATIC-PRESSURE ORIFICES
The static-pressure orifices used to measure the dy¬
namic pressure are calibrated by making a velocity
survey at the test section, using a calibrated pitot tube
(reference 1). The calibration may be in error partly
because of differences in dynamic scale and turbulence
between conditions of pitot-tube calibration and of use
in the variable-density tunnel and also because of pos¬
sible blocking effects of the model. It is evident that
a new method of calibration is necessary to eliminate
these uncertainties.
These uncertainties may be largely eliminated by
calibrating pitot tubes on an airplane in flight and by
calibrating similar pitot tubes, similarly mounted on a
model of the airplane in the tunnel. A detailed 1/20-
V.D.T.
Test
— / 090-2
o 1085-2
x / 159-8
+ 732
Dote
Condition
1 2- /9~33 Wire support
//- Q~33 Usual " struts
7-27-34
12-15-3/
Test R,
millions
3.1/
3. 05
3.00
3.21
Figure 47.— Lift and drag characteristics of theN. A.C. A. 4412 airfoil as determined from tests
with the model mounted on the usual support struts and on special wire supports.
scale model of the FC-2W2 airplane (reference 20) and
the airplane itself were available. Three nonswiveling
pitot tubes were mounted on the airplane as shown in
figure 48. These pitot tubes were 2 inches in diameter
262
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
with two staggered rows of static-pressure holes. Each
row consisted of 12 equally spaced holes 0.22 inch in
diameter. The pitot tubes were calibrated in flight
against a previously calibrated trailing air-speed head.
Three geometrically similar pitot tubes 0.10 inch in
diameter were similarly mounted on the model and
calibrated in the variable-density tunnel. Great care
Figure 48.— Outline drawing showing location of pitot tubes on the FC-2W2 airplane.
was taken to make the small pitot tubes geometrically
similar to the large ones and to mount them in the
correct positions on the model.
The pitot tubes were calibrated in the tunnel over
an angle-of-attack range from — 8° to 14° and over a
range of the test Reynolds Number from 1,000,000 to
2,500,000. Tests were made with three tail settings.
All pressures were measured by a multiple-tube, photo¬
recording manometer using a mixture of alcohol and
water. Ratios of pressures were obtained directly
from ratios of measured deflections and are independent
of the specific gravity of the manometer liquid. A
test was made with the pitot tubes interchanged as to
position on the model to check the accuracy with which
they were made. The results checked satisfactorily.
Surveys were made upstream from the model with and
without the model in place using a bank of 21 small
pitot tubes mounted on a strut extending across the
tunnel, surveys being made on the vertical center line
and 6 and 12 inches to one side of the center line.
The data obtained from these surveys are used to check
the calibration of the static -pressure orifices from time
to time as required. Force tests were also made on the
model with and without the pitot tubes in place and
with several tail settings.
The results obtained from the calibration of the pitot
tubes are presented in figure 49. The data are pre¬
sented as ratios of the dynamic pressures measured by
the pitot tubes to the dynamic pressure as usually
obtained from the static-pressure orifices. A fairly
consistent variation of the results is shown with
changes in Reynolds Number and tail settings. The
results obtained from the calibration of the pitot tubes
in flight are shown by outlined areas indicating the
location of all points obtained.
Comparisons between the tunnel and flight results
have been made -on the basis of angles of attack, cor¬
rected in the case of the tunnel results for the tunnel-
Angle of attack, a, degrees
tu.uRE 49. C alibraticn of pitot tubes mounted on the FC-2V2 airplane in flight and on the FC-2W2 airplane model in the variable-density wind tunnel. Results
corrected for tunnel-wall effect.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 263
wall effect. Force tests made in the tunnel and in
flight show that this method of comparison is very
nearly equivalent to making the comparisons at equal
lift coefficients. A value of the ratio q/q0 was selected
from the tunnel data to correspond as well as possible
to flight conditions of trim and Reynolds Number for
each pitot-tube position at each angle of attack. The
values obtained were, in general, higher than the flight
values at small angles of attack. Accordingly, the
values obtained were reduced by increasing the value
of q0 by 1.5 percent, which is equivalent to a change
in the static-pressure-orifice calibration factor from
1.172 to 1.190. The values of the ratio so obtained
are plotted on the figure as solid lines, and the values
agree reasonably well with the flight data at small
Figure 50.— Comparison of data obtained in flight and in the variable-density wind
tunnel for the FC-2W2 airplane and model.
angles of attack. A comparison of the tunnel and
flight data indicates that a further correction, which
may be due to blocking effects, may be desirable at
high angles of attack. The airplane model, however,
had large drags at high angles of attack as compared
with models normally used in the tunnel, making the
application of this additional correction questionable
for the usual airfoil tests.
The results of the force tests of the model are shown
by means of composite curves drawn as solid lines in
figure 50. The curves were obtained from the test
results by selecting, at each angle of attack, test results
to correspond as well as possible with flight conditions
of trim and Reynolds Number. The tunnel results
have been fully corrected including corrections to the
effective Reynolds Number. Data obtained in flight
tests (reference 20) are shown on the figure.
Although the model was much more detailed and
accurate than is usual in wind-tunnel models, it was
not considered before the tests to represent the air¬
plane with sufficient accuracy and detail to give
reliable drag results. Therefore too much emphasis
should not be given to the good agreement of drag
coefficients obtained in flight and in the tunnel. At
lift coefficients less than 1.0 the agreement between
flight and tunnel data is considered satisfactory. At
higher lift coefficients some divergence of the tunnel
and flight data is indicated. As previously stated,
the results obtained from the pitot-tube calibration
showed that an additional correction to the calibration
factor of the static-pressure orifice might be desirable
at high angles of attack. Such a correction has been
determined from figure 49 and applied to the data.
The results are plotted as dotted lines in figure 50 and
show an improved agreement of the lift coefficients
obtained in flight and in the tunnel at high angles of
attack.
This additional correction is not ordinarily applied to
the data obtained in the variable-density tunnel be¬
cause it is doubtful whether the correction in most cases
would give a better approximation to the actual condi¬
tions than no correction. The pitot-tube calibration
tests were less accurate at high angles of attack than at
low ones and, as previously stated, the drag of the
model was larger than is the case for the models usually
tested. Another fact indicating that this correction is
small is that, up to the point of maximum lift, the lift
curves obtained in the tunnel for some airfoils are very
nearly straight. Any appreciable correction of this
type would result in such lift curves being concave
upward.
CONCLUSIONS
1. The results of the investigation show no inter¬
ference of the model supports on the model for which
corrections had not previously been made.
2. The investigation of the effects of compressed air
on the effective weight of the manometer liquid showed a
2.0 percent error in the measured dynamic pressure; the
dynamic pressure as previously measured was too large.
3. The investigation of the calibration of the static
pressure orifices showed an error of 1.5 percent in this
calibration; the dynamic pressure as previously meas¬
ured was too small.
4. The total effect of the investigation is a change in
the measured dynamic pressure of 0.5 percent; the
dynamic pressure as previously measured was too large.
Data previously published (reference 2 and earlier
reports) to which these corrections have not been
applied may be corrected by changing the coefficients
to correspond to a reduction of measured dynamic
pressure of 0.5 percent.
264
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
REFERENCES
1. Jacobs, Eastman N., and Abbott, Ira H.: The N. A. C. A.
Variable-Density Wind Tunnel. T. R. No. 416, N. A.
C. A. 1932.
2. Jacobs, Eastman N., Ward, Kenneth E., and Pinkerton,
Robert M.: The Characteristics of 78 Related Airfoil
Sections from Tests in the Variable-Density Wind Tun¬
nel. T. R. No. 460, N. A. C. A., 1933.
3. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests in
the Variable-Density Wind Tunnel of Related Airfoils
Having the Maximum Camber Unusually Far Forward.
T. R. No. 537, N. A. C. A., 1935.
4. Wenzinger, Carl J., and Shortal, Joseph A.: The Aero¬
dynamic Characteristics of a Slotted Clark Y Wing as
Affected by the Auxiliary Airfoil Position. T. R. No.
400, N. A. C. A., 1931.
5. Platt, Robert C., and Abbott, Ira H.: Aerodynamic Char¬
acteristics of N. A. C. A. 23012 and 23021 Airfoils with
20-Percent-Chord External-Airfoil Flaps of N. A. C. A.
23012 Section. T. R. No. 573, N. A. C. A., 1936.
6. Millikan, Clark B.: On the Lift Distribution for a Wing of
Arbitrary Plan Form in a Circular Wind Tunnel. Pub¬
lication No. 22, C. I. T., 1932.
7. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests of
N. A. C. A. Airfoils in the Variable-Density Wind Tun¬
nel. Series 230. T. N. No. 567, N. A. C. A., 1936.
8. Anderson, R. F.: Determination of the Characteristics of
Tapered Wings. T. R. No. 572, N. A. C. A., 1936.
9. Jacobs, Eastman N., and Clay, William C.: Characteristics
of the N. A. C. A. 23012 Airfoil from Tests in the Full-
Scale and Variable-Density Tunnels. T. R. No. 530,
N. A. C. A., 1935.
10. Platt, Robert C.: Turbulence Factors of N. A. C. A. Wind
Tunnels as Determined by Sphere Tests. T. R. No. 558,
N. A. C. A., 1936.
11. Stack, John: Tests in the Variable-Density Wind Tunnel to
Investigate the Effects of Scale and Turbulence on Air¬
foil Characteristics. T. N. No. 364, N. A. C. A., 1931.
12. Toussaint, A., and Jacobs, E.: Experimental Methods-
Wind Tunnels. Vol. Ill, div. I of Aerodynamic Theory,
W. F. Durand, editor, Julius Springer (Berlin), 1935, p.
332.
13. von Ivdrmdn, Th., and Millikan, C. B.: On the Theory of
Laminary Boundary Layers Involving Separation. T.
R. No. 504, N. A. C. A., 1934.
14. Dry den, H. L.: Air Flow in the Boundary Layer Near a
Plate. T. R. No. 562, N. A. C. A., 1936.
15. Dryden, Id. L., and Kuetlie, A. M.: Effect of Turbulence
in Wind Tunnel Measurements. T. R. No. 342, N. A.
C. A., 1930.
16. Jacobs, Eastman N.: The Aerodynamic Characteristics of
Eight Very Thick Airfoils from Tests in the Variable-
Density Wind Tunnel. T. R. No. 391, N. A. C. A., 1931.
17. Jones, B. Melvill: Stalling. R. A. S. Jour., vol. XXXVIII.
No. 285, Sept. 1934, pp. 753-769.
18. Higgins, George J., and Jacobs, Eastman N.: The Effect
of a Flap and Ailerons on the N. A. C. A. -M6 Airfoil
Section. T. R. No. 260, N. A. C. A., 1927.
19. Jacobs, Eastman N., and Pinkerton, Robert M.: Pressure
Distribution over a Symmetrical Airfoil Section with
Trailing Edge Flap. T. R. No. 360, N. A. C. A., 1930.
20. Thompson, F. L., and Keister, P. H.: Lift and Drag Char¬
acteristics of a Cabin Monoplane Determined in Flight.
T. N. No. 362, N. A. C. A., 1931.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED
BY VARIATIONS OF THE REYNOLDS NUMBER
TABLE I
IMPORTANT AIRFOIL SECTION CHARACTERISTICS
N. A. C. A. airfoil
R,
(millions)
a*o
(deg.)
«o
C! 1
m ax
' opt
Cd0min
Cma.c.
a.
c.
X
(percent c)
V
(percent c)
0009 _ _
8.470
2 0. 0061
8.290
0
0. 098
Al. 39
0
. 0064
0
1.0
5
6. 100
0
.097
Al. 28
0
. 0064
0
1.0
4
3.410
0
.097
D. 94
0
.0062
0
1.8
8
1. 760
0
. 096
D. 88
0
.0060
0
1.7
13
.882
0
. 096
D. 86
0
.0049
0
.446
0
. 105
D.85
0
. 0065
0
.223
0
. 117
o. 83
0
.0131
0
. 112
0
.104
D. 78
0
.0135
0
0012 _ _
8. 370
0
.099
Al. 66
0
.0069
0
.6
3
8. 450
0
. 100
Al. 65
0
. 0069
0
.6
3
6. 280
0
.097
A 1.62
0
.0073
0
.8
3
3.540
0
.097
Al. 49
0
. 0077
0
1.0
4
1.740
0
.096
Al. 18
0
. 0075
0
1. 1
3
.871
0
.094
D. 91
0
. 0065
.449
0
.098
D. 89
0
. 0105
0015 _ _
8.610
0
.097
Al. 66
0
.0077
0
1.2
4
5. 990
0
.096
Al. 60
0
.0082
0
1. 1
3
3. 350
0
.094
Cl. 48
0
. 0086
0
1.2
1
1. 730
0
.093
Cl. 28
0
.0088
0
2.4
1
.874
0
.092
Cl. 09
0
. 0084
0
1. 5
0
.438
0
.091
D. 98
0
.0079
.222
0
. 101
D. 89
.0149
.113
0
. 134
D. 90
.0158
0018 _
7. 840
0
.096
Al. 53
0
.0088
0
1.7
4
6. 240
0
. 096
Al. 53
0
. 0092
0
1.6
3
3. 300
0
.096
ci. 42
0
. 0098
0
2.2
3
1.730
0
.095
“1. 26
0
. 0100
0
2.2
0
.866
0
.090
ci. 15
0
.0102
0
2.4
0
. 430
0
.086
Al. 03
0
.0127
0
1.8
0
.214
0
. 092
D. 96
0
. 0179
. 109
0
. 114
D. 86
0
. 0297
2412...
8. 240
-2.0
.098
Al. 72
. 14
.0071
-.043
.5
3
6. 100
-2.1
.097
Al. 68
. 14
. 0080
-.043
1. 1
3
3.420
-2.0
.098
ci. 53
. 15
. 0079
-.045
1. 1
1
1.730
-2. 1
.096
Dl. 33
.30
. 0089
-.045
.9
_2
.879
-2.1
.096
Dl. 16
.22
. 0085
-.054
1.8
0
438
—2. 0
.098
Dl. 08
.42
. 0067
218
—2. 2
. 102
Dl. 08
.26
. 0159
no
-1.3
Dl. 03
.0227
23012
8. 370
2. 0071
8. 160
-1.2
. 100
*1,72
.08
. 0070
-.008
1.2
7
6. 070
-1.2
.098
Al. 67
.08
. 0079
-.007
1.3
7
3.400
-1.2
.098
A 1 . 53
.05
.0080
-.007
1.3
5
1.760
-1.2
. 097
Dl. 41
. 16
. 0090
-.012
1.4
5
.884
-1.2
. 096
Dl. 28
.28
.0084
-.010
2.0
7
44Q
— 1. 3
. 096
D1 19
. 12
. 0098
221
— 1. 6
. 109
Dl. 15
. 37
. 0179
1 12
— 1. 4
Dl. 00
. 20
. 0182
23012-33. . .
8. 000
-1.2
.097
Bl. 49
.20
.0071
-.010
.6
5
6. 390
-1.2
.098
Al. 42
. 10
.0075
-.010
.8
5
3.380
-1.2
.096
Dl. 26
.23
. 0076
-.011
1.0
6
1.760
-1.2
. 096
Dl. 12
.28
.0071
-.014
.9
3
. 900
-1.2
. 094
Dl. 07
. 10
. 0084
-.011
.9
0
.454
-1.4
. 096
Dl. 01
.40
. 0096
-.014
.4
-1
2Rjl2. . . .
8.370
-.6
.098
Al. 61
. 10
. 0073
.005
1.0
7
6. 310
— . 7
.097
nl. 55
.02
. 0078
. 006
1. 1
6
3. 540
— . 7
.097
Dl. 44
.11
. 0077
. 005
1.0
4
1.770
-.8
.095
°1. 28
.23
. 0077
. 002
.8
0
.884
-.8
.096
Dl. 14
.28
. 0073
-.001
1. 1
0
4^4.
— 9
100
D1 08
. 35
. 0118
4409 _ _
8. 080
-3.9
.096
*1. 77
.26
.0073
-.088
.6
2
5. 970
-3.9
. 096
Dl.70
. 26
.0080
-.088
.7
t
3.340
-4.0
.095
ci. 50
.34
.0077
-. 090
1.0
-1
1.700
-4.0
.098
Dl. 29
.41
.0084
-. 092
1. 1
-1
.869
-4. 1
.096
Dl. 26
.40
. 0080
-. 098
1.4
-4
438
— 4 i
007
D] 23
. 55
. 0097
3 7
105
Dl 21
. 57
. 0096
tin
0. 1
— 9 5
116
Di no
. 0189
4412 _ _
7. 920
-4.0
.098
Dl. 74
.32
.0082
-.088
.8
2
6. 100
-4. 1
. 096
Dl.70
.22
. 0085
-.088
.9
1
3. 270
-4. 1
.098
Dl. 61
.30
.0087
-.091
1.0
-1
1. 680
-4.2
.097
01.46
.37
. 0095
-.095
1.2
-5
.874
-4.3
. 096
01.36
.36
.0091
-. 097
1. 1
-8
4 3
094
Dl 31
51
. 0109
4 3
100
I ' 1 32
. 57
. 0194
9 O
2. J
1 13
Dl 20
. 0276
4415 _
7. 920
-4.0
.097
Cl. 72
.22
.0090
-.085
1.0
1
6. 280
-4.0
. 095
01.66
.20
. 0093
—.086
1.4
1
3. 340
-4. 1
. 096
Dl. 56
.23
. 0094
— . 085
1.4
-2
1. 730
-4.2
. 095
Dl. 48
.31
. 0099
-.090
1.7
-4
.882
-4.3
.094
01.41
.34
. 0103
-.092
1.4
-8
4 4
OXQ
Dl 35
39
. 0123
4 4
1 089
Dl 31
! 46
. 0198
3 1
Dl 34
. 68
. 0269
6412 . . . . . .
8.210
-5.9
.098
01.82
.37
.0091
-. 133
.9
1
6.020
-5.9
.096
D1.75
. 25
. 0096
-. 130
1. 1
1
3. 350
-6. 1
.097
01.64
.38
. 0099
-. 131
.8
— 3
1.700
-6.2
.097
01.54
.52
.0104
-. 135
1.0
-2
O 3
OQ7
Dl 4K
60
. 0096
6 2
097
D1 47
. 0129
5 9
il06
Dl 46
.70
.0205
.110
-5.4
01.45
.0160
‘Type lift-curve peak:
1 From reference 2.
s From reference 7
A
B
C
a
REPORT NO. 586— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
266
TABLE I — Continued
IMPORTANT AIRFOIL SECTION CHARACTERISTICS— Continued
N. A. C. A. airfoil
R «
(millions)
"'0
(deg.)
a 0
C, 1
max
lopt
* ^0 min
a
c.
X
(percent c)
V
(percent c)
6712 . .
8. 100
-7.3
0.096
D2. 05
0. 35
0.0115
-0. 199
1.2
_ 2
6. 120
-7.4
.095
Dl. 99
.32
.0119
-. 197
1. 1
-4
3. 380
-7.4
.098
D 1.8.3
.33
.0120
-. 198
1. 1
-8
1.750
-7.6
. 103
ul. 65
.45
.0124
-. 210
1.6
-12
.892
-7.8
. 103
Dl. 52
.82
.0138
.449
-5.7
Dl. 45
.88
.0228
.222
-4.6
Dl. 50
1.01
.0283
. 112
-3.9
Dl. 41
-.02
.0411
8318 _
8. 450
-7.2
.095
D1.59
. 24
.0127
~. 132
1. 5
2
6. 420
-7.3
.092
. 10
.0128
-. 132
1.8
2
3. 460
-7.4
. 093
Dl, 67
.31
. 0128
-. 135
1.8
2
1. 790
— 7. 6
. 093
Dl. 76
. 36
. 0140
-. 137
2. 1
3
. 911
-8. 7
. 088
Dl. 80
. 43
.0173
.449
-9.0
. 085
D1.78
.0215
. 224
-9.2
. 080
n1.40
.58
. 0259
. 112
-8.0
.077
Dl. 02
.0332
0012 .
8. 110
4 -13. 1
5. 091
A2. 35
167
s— . 220
. 6
3
(With split flap at 60°. )
5.910
A2. 35
3. 770
A2. 30
3. 430
A2. 21
1. 740
A 1. 84
.919
nl. 67
. 449
Dl. 63
23012 _
8. 180
4 -14.3
5. 088
A2. 48
7. 166
s -. 236
1. 2
(With split flap at 60°.)
5.970
A2. 51
3. 620
A2. 39
(Average)
1 . 740
A2. 24
.882
A2. 07
. 444
D1.92
23012 ...
8. 100
4 -15. 6
5. 085
A2. 54
7. 201
8 -. 228
1. 2
rj
(With split flap at 75°. )
5. 990
a 2 52
3. 800
A2. 41
1. 740
A2. 21
.887
A2. 01
.446
A 1.90
23015 _
8. 370
-1. 1
. 098
Al. 73
. 10
.0081
-.008
1. 1
6
3. 880
--- _
Cl. 60
23015 _
8. 210
4 -16. 2
5. 086
A2. 70
7. 198
8 -. 245
1. 1
6
(With split flap at 75°.)
5. 990
A2. 09
3. 830
A2. 59
1.800
A2. 45
.924
A2. 32
. 450
A2. 11
23021 _
8. 210
-1.2
.092
»1. 50
.07
.0101
-.005
2.3
7
5, 940
Al. 54
3. 770
Al. 47
1. 720
Dl. 32
. 892
Dl. 26
. 441
Al. 20
23021 _
8. 130
4 -16. 5
5. 094
A2. 74
7. 191
8 -.300
2. 3
(With split flap at 75 °.)
5. 960
A2. 81
3. 800
A2. 79
1. 720
A2. 58
.879
A2. 46
. 435
A2. 28
43012 _
8. 390
-2.3
. 100
Al. 84
.26
.0079
-.019
1.0
7
3. 890
Al. 71
. 449
Al. 44
43012 _
8. 240
4 -17.3
X
o
A2. 65
7. 200
6 — . 225
1. 0
(With split flap at 75°.)
6.040
A2. 60
3. 830
A2. 47
1. 740
A2. 39
.887
A2. 29
. 449
A2. 18
23012 _
8.210
-.9
. 101
Al. 68
.07
. 0069
. 009
.5
8
(With 23012 flap 3° up.)
6. 150
-.8
. 100
A 1 . 62
. 15
.0074
.009
1.0
9
3. 300
-.8
. 100
A 1 . 54
. 19
.0078
.010
1. 1
11
1.680
-.8
. 097
A 1 . 39
. 13
.0068
.011
1. 2
11
.858
-.8
. 096
Dl. 24
.08
. 0093
.430
-1.2
.096
D], 12
.08
.0119
23012 _
8. 140
4 -13.8
5. 102
A2. 46
.45
.0161
9 -. 260
.5
8
(With 23012 flap set 30°. )
6. 200
A2. 40
3.410
A2. 32
1. 700
4 -12.5
3. 103
« c2. 13
. 70
.0184
9 -.260
1. 2
11
1. 700
6 D1.95
.879
4 -11.9
5. 102
D 1 . 75
.60
.0218
. 441
D], 66
Clark Y 10. _ ...
9. 900
-4.2
5.099
D2. 12
. 76
.0242
(With Handley Page slot.)
8.080
-4.3
3. 099
D2. 06
. 76
.0248
4. 990
-4. 2
5. 098
D2. 02
. 69
. 0260
3.090
-4.2
5.097
nl. 96
.62
. 0260
2. 040
-4. 1
5. 096
Dl. 98
.65
. 0264
1.290
—4 1
5. 092
Dl. 92
.63
.0272
. 784
—4 1
Dl. 82
.64
.0301
. 520
-4. 1
Dl. 75
63
.0291
. 261
-4. 1
Dl. 60
.64
. 0322
. 135
-4 3
Dl.41
.63
.0431
1 See footnote 1, p. 39.
4 Angle of zero lift determined from linear lift curve approximating experimental
lift curve.
5 Slope of lift curve determined from linear lift curve approximating experimental
lift curve.
6 Discontinuity present in the scale effect.
7 Value of the drag that applies approximately over the entire useful range of lift
coefficients.
C”>a.c. is taken about the aerodynamic center of the plain wing and is fairly con¬
stant at high lift coefficients.
5 cma.e. is taken about the aerodynamic center of the wing with flap neutral and is
fairly constant at high lift coefficients.
Not N. A. C. A.
AIRFOIL SECTION CHARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLDS NUMBER 267
TABLE II
AIRFOIL SECTION CHARACTERISTICS
Classification
R, <
(millions)
Fundamental section characteristics
N. A. C. A. airfoil
Chord i
SE2
Cl 3
max
L
m ax
a‘o
(deg.)
«o, per
degree
cl
opt
c
d0 min
c
m a . e.
o. c. (percent
c from c/4)
Ahead
A bove
0009 _ _
A
B
A
8.29
1.39
0
0. 098
0
0. 0064
0
1.0
5
0012 _
A
CO
A
8.37
1.66
0
.099
0
. 0069
0
.6
3
0015 _ _ _
A
DO
A
8.61
1.66
0
.097
0
. 0077
0
1.2
4
0018 _ _ _ - - -
A
E0
A
7.84
1.53
0
.096
0
. 0088
0
1. 7
4
2412 _ _ _
A
C2
A
8. 24
1.72
-2.0
. 098
. 14
. 0071
-.043
. 5
3
23012 _
A
D2
A
8. 16
1.72
-1.2
. 100
.08
. 0070
-.008
1.2
i
23012-33 _ _ _
A
B6
B
8.00
1.49
-1.2
. 097
.20
. 007 1
-.010
.6
5
2KZ12 _ _
A
C3
A
8. 37
1.61
-.6
.098
. 10
.0073
.005
1.0
7
4409 _ _ _
A
B4
A
8. 08
1.77
-3.9
.096
.26
. 0073
-.088
. 6
2
4412 _ _ _
A
C4
1)
7. 92
1.74
-4.0
. 098
.32
. 0082
-.088
.8
2
4415 _ _ _
A
D4
C
7. 92
1.72
-4.0
.097
.22
. 0090
-.085
1.0
i
6412 _
A
C6
D
8.21
1.82
-5.9
.098
. 37
.0091
-. 133
.9
i
6712- _
A
C2
D
8. 10
2.05
-7.3
.096
.35
.0115
-. 199
1.2
8318 _
A
E8
D
8. 45
1.59
-7.2
.095
.24
.0127
-. 132
1.5
2
0012 with split flap at 60° - - —
A
CO
A
8. 11
2. 35
5 -13. 1
6 .091
_ _ _
7 . 167
8 -. 220
. 6
3
A
U2
A
8. 18
2. 48
5 -14.3
6 . 088
1 . 106
s -. 236
1.2
7
23012 with split flan at 75° __
A
D2
A
8. 10
2. 54
5 -15.6
6 . 085
7 .201
s -.228
1.2
7
23015 _ * _ _ _
A
D2
A
8. 37
1.73
-1. 1
. 098
.10
.0081
-.008
1. 1
6
23015 with split flap at 75° _ - ----
A
D2
A
8.21
2.70
5 -16.2
« .086
_ - ..
7 . 198
s -.245
1. 1
6
23021 _
A
E2
B
8.21
1.50
-1. 2
. 092
.07
.0101
-. 005
2.3
7
A
E2
A
8. 13
2. 74
5 -16. 5
« . 094
7 . 191
s -. 300
2.3
7
43012 _
A
D4
A
8.39
1.84
-2.3
. 100
.26
.0079
-.019
1.0
7
43012 with split flap at 75° _ . -
A
D4
A
8.24
2. 65
s -17.3
6 .082
_
7 . 200
s -.225
1.0
7
23012 with 23012 flap 3° up.. _ _
A
D2
A
8.21
1.68
-.9
. 101
.07
. 0069
. 009
. 5
8
23012 with 23012 flap set 30°-
A
A
8. 14
2. 46
5 -13.8
e . 102
.45
.0161
9 -.260
. 5
8
B
])
8. 08
2. 06
-4 3
« . 099
.76
.0248
_
1 Type of chord. A refers to a chord defined as a line joining the extremities of the
•mean line.
2 Type of scale effect on maximum lift.
s Type of lift-curve peak as shown in the sketches below.
* Turbulence factor is 2.64.
s Angle of zero lift determined from linear lift curve approximating experimental
lift curve.
« Slope of lift curve determined from linear lift curve approximating experimental
lift curve.
T Value of the drag that applies approximately over the entire useful range of lift
coefficients.
s c m is taken about the aerodynamic center of the plain wing and is fairly con-
a.c,
stant at high lift coefficients.
« cm r is taken about the aerodynamic center of the wing with flap neutral (-3°)
and is fairly constant at high lift coefficients.
io Not N. A. C. A.
.
REPORT No. 587
BLOWER COOLING OF FINNED CYLINDERS
By Oscar W. Schey and Herman H. Ellerbrock, Jr.
SUMMARY
Several electrically heated finned steel cylinders enclosed
in jackets were cooled by air from a blower. The effect of
the air conditions and fin dimensions on the average surface
heat-transfer coefficient q and the power required to force
the air around the cylinders were determined. Tests were
conducted at air velocities between the fins from 10 to 130
miles per hour and at specific weights of the air varying
from 0.0 46 to 0.074 pound per cubic foot. The fin
dimensions of the cylinders covered a range of fin pitch es
from 0.057 to 0.25 inch, average fin thicknesses from 0.035
to 0.04 inch, and fin widths from 0.67 to 1.22 inches.
The value of q, based on the difference between the cylin¬
der temperature and the inlet-air temperature, varied as
the 0.667 power of the weight velocity of the cooling air for
cylinders having spaces from 0.077 to 0.21 inch between
fins. Below 0.077-inch space the exponent of the curves
increased for each successive decrease in space. The value
of q was independent of fin width for the range of widths
tested and decreased as the space between the fins decreased.
The power required for cooling, neglecting the kinetic
energy lost from the exit of the jacket, varied as the 2.69
power of the weight velocity for a given specific weight and
inversely as the square of the specific weight for a given
weight velocity of the cooling air. For a given weight
velocity of the cooling air or a given power and for a fin
width of 1 .22 inches, the fin space giving the maximum
heat transfer ivas approximately 0.045 inch.
INTRODUCTION
A general investigation is being conducted by the
Committee to determine the comparative cooling of
cylinders having fins of varying pitch, thickness, and
width when tested in a free air stream and when tested
with blower cooling. For the conditions in a free air
stream the cylinders are tested with and without
baffles and, for the conditions in which the blower is
used, the cylinders are enclosed in a jacket.
The first report published on the investigation (refer¬
ence 1) presents the results of extensive tests to deter¬
mine the heat-transfer coefficients of finned cylinders
m a free air stream and a method for calculating the
heat dissipated, utilizing these coefficients. The second
report (reference 2) includes results showing how the
heat-transfer coefficient may be increased by using
baffles to direct the air toward the rear of the cylinder.
Tests on nine steel cylinders, herein reported, were
conducted to investigate blower cooling. Tests were
made on all of the cylinders to determine the effect of
velocity and specific weight of the cooling air on the
heat transfer and on five of the cylinders to determine
the effect of the same factors on power required. The
cylinders had fins of varying width and pitch; the
range of fin width investigated varied from 0.C7 inch
to 1.22 inches, the pitch from 0.057 inch to 0.25 inch,
and the thickness from 0.035 inch to 0.040 inch.
APPARATUS
TEST CYLINDER
The construction of the test unit is shown in figure 1 .
This unit, which has been described in detail in pre¬
ceding reports (references 1 and 3), consists essentially
Figure 1.— Construction of test unit.
of three electrically heated finned cylinders, the central
one forming the test section and the ones on each end
serving as guard rings to prevent heat losses through
the ends. The guard rings are of practically the same
construction as the test section except that each ring
is only one-half as long as the test section. The heat
input to each guard ring and test specimen can be
separately controlled by oil-cooled rheostats. A com¬
plete wiring diagram of the test set-up is shown in
reference 1.
Four of the cylinders were machined from a steel
billet so that the fins were integral with the cylinder
wall. The other five cylinders were built up of indi-
269
270
REPORT NO. 587 -NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
vidually constructed fins (see fig. 1 (b)) held in place
by solder, a method that facilitated the making of
cylinders having closely spaced wide fins. With this
method of construction the same fins may be used on
several cylinders of different pitch by cutting down in
successive steps the thickness of the wall section and
thus reducing the space between the fins. As the
space is reduced, more fins are added so that the same
cylinder length is maintained and the same heating
unit can be used.
For convenience in referring to the finned cylinders,
the designations composed of the fin pitch, width, and
thickness adopted in reference 1 are also used in this
report. For example, the designation 0.25-0.67-0.04
AIR SYSTEM
The quantity of cooling air supplied was measured
by sharp-edge orifices placed at each end of a tank.
The air system used in testing the 0.25-1.22-0.04, 0.25-
0.97-0.04, 0.25-0.67-0.04, and 0.15-0.97-0.04 cylinders,
hereinafter designated “series A” tests, is shown
diagrammatically in figure 2 (a). A tank was placed
in the air duct on each side of the supercharger to reduce
the pressure pulsations created by the Roots blower.
At the entrance of the jacket there was another tank
equipped with a valve for throttling the air when the
specific weight was varied.
The cooling air was directed around the cylinder by a
jacket placed approximately Y& inch from the fin tips,
Orifice tanh
Se/ec tor
switch
6
a
j\-f
ll c
d
/
Surge
Ih
e
f
a Thermometer
b Manome ter
c Orifice
Pyrome ter
Cold junction
Am flow
Flow -
regulating
valve
Hoots
bio wer
Elec trie
mo tor
(b) Equipment used to test the 0.160-1. 22-0. 035, 0.137-1.22-0.035, 0.112-1.22-0.035, 0.083-1.22-0.035, and 0.057-1. 22-0 035 cylinders.
Figure 2. — Diagrammatic sketch of equipment.
indicates a finned cylinder having a fin pitch of 0.25
inch, a fin width of 0.67 inch, and an average fm thick¬
ness of 0.04 inch. The fm proportions for each of the
nine cylinders tested are shown in the following table
and in figure 8.
Fin pitch
(inch)
Fin width
(inches)
Fin thick¬
ness
(inch)
Fin space
(inch)
0. 25
1. 22
0. 04
0. 21
. 25
.97
.04
. 21
. 25
. (>7
.04
. 21
. 15
.97
.04
. 11
. 166
1. 22
. 035
. 131
. 137
1. 22
.035
. 102
. 112
1.22
. 035
.077
.083
1.22
.035
. 048
.057
1.22
.035
.022
The diameter of the cylinders at the fin root was 4.66
inches, the length of the test sections 10 inches, and the
length of each guard ring 5 inches.
as shown in figure 3 (a). Whenever the outside diameter
(fin width) of the test cylinder was reduced, the l^-inch
clearance at the tips was maintained by using sleeves
inside the jacket. The inlet of the jacket was faired
and proportioned in such a manner as to reduce as
much as possible the breakaway of the air from the
walls.
The air system used to test the 0.166-1.22-0.035,
0.137-1.22-0.035, 0.112-1.22-0.035, 0.083-1.22-0.035,
and 0.057-1.22-0.035 cylinders, hereinafter desig¬
nated “series B” tests, is shown diagrammatically in
figure 2 (b). The jacket used on these five cylinders
was in contact with the fin tips (fig. 3 (b)).
INSTRUMENTS
The cylinder temperatures were measured with 24
iron-constantan thermocouples connected through a
selector switch to a portable pyrometer. The thermo-
BLOWER COOLING OF FINNED CYLINDERS
271
(b) Jacket used to test 0.166-1.22 0.035, 0.137-1.22-0.35, 0.112-1.22-0.035, 0.083-1.22-0.035, and i
0.057-1.22-0.035 cylinders.
Figure 3.— Sketches of jackets.
couples were made of 0.013-inch-diameter silk-
covered enameled wire and were welded to the
cooling surface at the points shown in figure 4.
Differential thermocouples, which were con¬
nected to sensitive galvanometers, were placed
on the adjacent surfaces between the guard
rings and the test cylinder to facilitate adjusting
the heat input to the guard rings so that there
would be no heat exchange between the test
section and the guard rings. Ammeters and
voltmeters were used to measure the electrical
power input to the test cylinder and guard rings.
The temperature of the air at the entrance
of the jacket was measured with an alcohol ther-
Front
Figure 4.— Location of thermocouples on test cylinder.
mometer and at the exit of the jacket with three
chromel - constant an thermocouples connected
through a selector switch to a low-resistance
portable pyrometer. In the series A tests the
pressures at the entrance and the exit of the
jacket and the pressure drop across the orifice
tank were measured with water manometers.
In the series B tests the pressure drop across the
orifice tank and the pressure in the depression
tank were measured with water manometers.
TESTS
Tests were conducted at air velocities from 10
to 130 miles per hour and at specific air weights
from 0.046 to 0.074 pound per cubic foot. The
recorded data were the electrical power input to
the guard rings and test cylinder, the tempera¬
ture of the air entering the orifice tank, the tem¬
perature of air entering and leaving the cool-
272
REPORT NO. 587 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ing jacket, the pressure drop across the orifice tank, the
pressure at the entrance and exit of the jacket in series
A tests, the pressure in the depression tank in series
B tests, and the temperatures at the various points
on the cooling surface.
The velocity was varied by changing the speed of the
blower. The specific air weight was varied in the series
A tests by throttling the air at the entrance of the de¬
pression tank. The specific weight of the air was not
varied in the series B tests.
The heat inputs varied from 83 to 97 B.t.u. per square
inch wall area per hour (0.0326 to 0.0381 horsepower
per square inch wall area) for the various cylinders;
the heat input was approximately constant, however,
for any one cylinder.
The series A tests were conducted principally to de¬
termine the effect of fin width on heat transfer; those
of series B were conducted to determine the effect of
fin spacing on heat transfer and power required.
CALCULATIONS
The results were obtained by the following formulas:
Specific weight of the air, pxg\
1.325X26
460 + 7\
(1)
Mean velocity of the air between the fins, Vm:
V
Wt 144
pig a
(2)
tr
(The method of calculating IT, is given in reference 4.)
Experimental and calculated heat-transfer coefficients,
U exp and l ca{.
JJ
L exp A ft
(3)
cal'
- JL 2
s + qrt
‘ 1
w
2 R>
tanli aw' +s
1
(4)
where
The value of k~2.17 for this report.
Equation (4) is derived as equation (13) in refer¬
ence 1.
Average outlet cooling-air temperature T2:
The outlet cooling-air temperature is an average of
the indicated temperatures of the three thermocouples
after corrections have been applied for instrument
calibration and cold-junction temperature.
Power required across the test cylinder, Pt:
2X=0.000893FmA,{pI-(p2+0.00022kVp,f7A//A12)} (5)
In this formula the specific weight of the air at the
inlet of the jacket was used instead of the specific
weights at the inlet and outlet as theoretically should
be done. The error introduced by this method is
small, however, and formula (5) is simpler than the
rigorously correct one. It was very difficult to meas¬
ure the static head at the entrance and exit of the
jacket so that in formula (5) 26 is the total head in
the orifice tank (see fig. 2 (a)) and p2 is the static head
in the depression tank. The use of these heads leads
to very little error unless there is a vena contracta in
the entrance and exit.
Power required to generate the outlet velocity, Pa:
Pa= 1 .965 X 1 CTTWP7 (6)
RESULTS AND DISCUSSION
The problem of blower cooling can be divided into
two parts, a study of the heat transfer obtained and
of the blower power required for various conditions of
operation. The heat transfer for a given case can be
calculated when the surface heat-transfer coefficient 2
of the fins is known, use being made of equation (4).
A study will now be made of the dependence of g and
the blower power on the fin dimensions, the physical
properties of the air, and the air speed. Because a
large number of variables are involved, dimensional
theory is used in clarifying and simplifying the analysis.
As q depends on the specific weight, viscosity, specific
heat, thermal conductivity, velocity of the air, and the
various dimensions of the finned cylinder, by dimen¬
sional analysis the following expression can be set up
(see equation (1), reference 1):
q — CpPig 1 mj
Plf/I mD pCp
- ; TT’
M Ka
t W s\
D’ V D)
(7)
With the exception of the specific heat and the
conductivity of the air, the blower power depends on
the same group of variables and the following relation
can be obtained:
P t= PigV JDj
fpxgVmD t w s\
\ M ’ D’ D’ d)
(8)
where P t is the power per unit length of cylinder. In
this analysis the flow is assumed as two-dimensional,
which condition the tests very closety simulated.
EFFECT OF VARIABLES ON q
Weight velocity of the air and fin dimension —
Equation (7) shows that, when all other quantities
remain constant, the value of q varies as the weight
velocity of the cooling air, VmPl g. Tests presented
herein were performed in which both the velocity and
specific weight were independently varied. The values
of q obtained from these tests are plotted against weight
velocity on logarithmic-coordinate paper in figures 5
and 6. For any one test cylinder a straight line fitted
the data fairly well.
The curves of figure 5 for the cylinders having pitches
from 0.112 to 0.25 inch, inclusive, have been drawn
parallel and have a slope of 0.667. For cylinders with
pitches less than 0.112 inch the slope becomes increas¬
ingly greater as the pitch is decreased. From the
BLOWER COOLING OF FINNED CYLINDERS
273
relation between q and weight velocity shown in figure
5 for cylinders having pitches of 0.112 inch or greater,
equation (7) can be modified as follows:
2=
./// Mfp
7 \ka
t w s\
’D’D’DJ
(9)
Below 0.112-inch pitch the exponent —0.333 decreases
as the pitch decreases.
Vm p,g , Ib./sec./sq. ft.
Figure 5. — Effect of weight velocity of the cooling air on the average surface heat-
transfer coefficients, based on the difference between the cylinder temperature and
the inlet-air temperature.
The curves of figure 5 in which the value of q is
based on the difference between the inlet-air tempera¬
ture and the average cylinder temperature show that,
when the pitch is decreased, the value of q will decrease
even though the weight velocity of the cooling air
remains constant. If the values of q are based on the
difference between the average cooling-air temperature
and the average cylinder temperature, the results will
be as shown in figure 6. The outlet-air temperature
was calculated from the weight of air flowing over the
test cylinder, the heat input to the test cylinder, the
specific heat of the air, and the inlet-air temperature.
It was found that more than three thermocouples in the
outlet of the jacket were necessary to give a correct
average temperature. Because the effect of the heating
of the air on the value of q is greater at low air speeds
than at high air speeds, the slope of the curves in figure
6 is much less than the slope of the curves in figure 5 ;
all the curves in figure 6 have the same slope.
Figure 7 was obtained by cross-plotting figure 5 at
a weight velocity of the air of 4 pounds per second per
square foot and shows the effect of fin space on q.
The surface heat-transfer coefficient varies as the 0.386
power of the fin space from 0.09- to 0. 21-inch space.
From 0.048- to 0.09-inch space the slope is a little
greater than 0.386, and below 0.048 inch q decreases
rapidly.
Vm P, g , Ib./sec./sq. ft.
Figure 6.— Effect of weight velocity of the cooling air on the average surface heat-
transfer coefficients, based on the difference between the cylinder temperature and
the average air temperature.
It is interesting to note that the value of q, even when
corrected for the heating of the air, is less for cylinders
with closely spaced fins than for cylinders with widely
.0/ .02 .03 .04 .06 .08 .10 .20
Average fin space , s , inch
Figure 7.— Effect of fin space on the average surface heat- transfer coefficient. Weight
velocity 4 pounds per second per square foot.
spaced fins although the average weight velocity be¬
tween the fins is the same. Recent tests (reference 5)
based on a study of air flow between fins indicated that
274
REPORT NO. 587 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the cooling was best with a 0.03 1-inch space between
the fins, the minimum used in the air-flow tests. The
cooling with closely spaced fins is greatly impaired
because the flow pattern between the fins is not so
conducive to a high over-all heat-transfer coefficient
as the flow pattern for more widely spaced fins.
The test results indicate that fin width had little effect
on q for two of the cylinders tested, the 0.25-0.97-0.04
and the 0.25-0.67-0.04. The values of q for the 0.25-
1.22-0.04 cylinders are, however, greater than for the
other two cylinders.
Previous tests conducted on finned cylinders having
pitches of 0.15 and 0.25 inch and mounted in a free air
stream indicated that, for fin widths greater than 0.4
inch, the value of q varied little with change in width
(reference 1). For the tests herein reported the air was
guided around the cylinder and the velocity distribution
along the fin width was more uniform than for the
cylinder in the free air stream (reference 5). The varia¬
tion in q with fin width for two cylinders, as expected,
was less than in tests on cylinders in a free air stream
(reference 1). Because of the unexpected increase in q
for the 0.25-1.22-0.04 cylinder, further tests are being
made to determine the effect of fin width on q.
The tests on the cylinders in a free air stream also
indicated that fin thickness had a minor effect on the
value of q and it is reasonable to expect that the same
would hold true for cylinders surrounded by a jacket.
Therefore, no tests were conducted to determine the
effect of fin thickness.
Air temperature. — Although no experiments were
made to determine the effect of temperature of the air
on q, some idea of the effect can be obtained from equa¬
tion (9). The quantities u, cp, ka, and pxg depend on the
temperature of the air. The effect of pxg on q has been
determined. For the range of temperatures encountered
in an ordinary altitude change, however, cp, ucpfka, and
u°-333 are practically constant. The heat-transfer coeffi¬
cient q is therefore affected by temperature of the air
only as the latter affects pxg.
EFFECT OF VARIABLES ON U
Weight velocity of the air and fin dimensions. — As
tlie amount of base surface available on a cylinder for
finning is limited, a fin design should be selected that
gives the maximum value of U — the heat carried away
per unit wall area per degree temperature difference
between the cylinder wall and the cooling air per hour.
Therefore, in the design of fins, the maximum cooling
surface consistent with a high value of q must be used
to obtain maximum cooling. The calculated values of
U shown in figure 8, except for the 0.25-1.22-0.04
cylinder, were determined from equation (4) and from
the values of q given in figure 5; the experimental values
were computed from test results. The calculated val¬
ues of U for the 0.25-1.22-0.04 cylinder shown in figure
8 were obtained from equation (4) and from the values
of q shown in figure 5 for the 0.25-0.97-0.04 and 0.25-
0.67-0.04 cylinders. Values of U calculated from the
values of q for the 0.25-1.22-0.04 cylinder in figure 5
did not check the experimental values of U. This
discrepancy is a further indication that the experi¬
mental values of q for the 0.25-1.22-0.04 cylinder are
questionable and that fin width has little effect on q.
These curves show that the agreement between the
calculated and the experimental values is sufficiently
good to justify the use of equation (4) in calculating the
heat dissipated by a cylinder enclosed by a jacket.
Figure 9 is a cross plot of the experimental values of
U in figure 8 and shows the effect of fin pitch on U at
several constant weight velocities of the air for the
cylinders with 1.22-inch fin width and 0.035-inch fin
thickness. The value of U for these curves is based on
the difference between the inlet-air temperature and
the average cylinder-wall temperature. The values
of C/for the 0.112-1.22-0.035 and the 0.137-1.22-0.035
cylinders did not fall on the faired curves as well as the
values of U for the other cylinders but were sufficiently
close to establish this part of the curve. The calcu¬
lated values of U for cylinders 0.112-1.22-0.035 and
0.137-1.22-0.035 were very close to the faired curves.
The results show that for all weight velocities of the
cooling air investigated the maximum heat transfer
falls between cylinders of 0.057-incli and 0.083-incli
pitch or 0.022-inch to 0.048-inch space. The curves
have been dotted between these two values as no data
were taken to establish definitely these portions of the
curves. The curves show that the heat-transfer
coefficient is not sensitive to the number of fins per inch
for values on either side of and near the maximum.
For example, with 11 or 16 fins per inch the lieat-trans-
fer coefficient U is 95 percent of the maximum value,
obtained with approximately 13 fins per inch of 0.035
thickness. The fin space giving the maximum value
of the heat-transfer coefficient U will vary as the fin
thickness is varied and the number of fins per inch will
increase as the fin thickness decreases.
The experimental values of U for the curves in figure
10 are based on the difference between the average
cylinder-wall temperature and the average air temper¬
ature. The difference between the values of U in
figures 9 and 10 is caused by the heating of the air.
With a fin pitch of 0.05 inch and with a weight velocity
of 3 pounds per square foot per second the heat-transfer
coefficient is approximately 55 percent higher when
based on the average cooling-air temperature; whereas,
with a weight velocity of 8 pounds, the coefficient
would be approximately 19 percent greater when based
on the average cooling-air temperature. Likewise with
a fin pitch of 0.15 inch and with a weight velocity of
3 pounds per square foot per second the heat-transfer
coefficient would be approximately 29.6 percent greater
when based on the average cooling-air temperature;
whereas, with a weight velocity of 8, the heat-transfer
U , B . t . u ,/s q. in./ °?./hr.
BLOWER COOLING OF FINNED CYLINDERS
275
Figi re 8.— Effect of weight velocity of the cooling air on the average experimental and calculated wail heat-transfer coefficients for the nine test cylinders.
REPORT NO. 587 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
276
coefficient would be approximately 17.6 percent greater.
The curves in figure 10, like those in figure 9, show that
the pitch for the maximum heat transfer lies between
0.057 and 0.083 inch.
EFFECT OF VARIABLES ON BLOWER POWER REQUIRED
The blower power required can be divided into two
main parts: that required across the cylinder and that
required to generate the outlet velocity. For a given
Figure !).— Effect of fin pitch on the average wall heat-transfer coefficient, based on
the difference between the cylinder-wall temperature and the inlet-air temperature.
Fin width, 1.22 inches; fin thickness, 0.035 inch.
test arrangement, the power required to generate the
outlet velocity may be reduced a small amount by a
properly expanding exit passage.
Weight velocity of the air and the fin dimensions. —
The effect of w'eight velocity of the cooling air on powrer
for five of the cylinders tested is shown in figure 11,
by plotting P<(pi0)2/w against VmP\g on logarithmic
paper. The jacket around these cylinders was in
contact with the fin tips, as shown in figure 3 (b).
From equation (8), P t{p\9)2 varies as a function of
Vmpig. The effect of a small variation in the specific
weight was eliminated by plotting the results in this
form. Also P((pi#)2 was divided by the fin width
before plotting as it seemed reasonable to expect the
pressure drop to change very little with fin width; the
power would therefore vary directly as the fin width.
The slope of the curves in figure 11 show's that
Pt(p\9)2/w varies as the 2.69 power of the w'eight
velocity of the air. The data seem to show that there
is a break in the curves at the low'er values of weight
velocity, probably caused by a change from turbulent
to laminar flow' but, as there are not enough points
definitely to establish this break, the curves have been
dotted at the lower values of weight velocity.
Dryden and Kuethe (reference 6) have shown that
for flat plates the friction drag is theoretically propor¬
tional to the 1.8 power of the velocity for turbulent
flow. Unpublished tests made at the Massachusetts
Institute of Technology by R. H. Smith and R. T.
Sauerwein show' that for various finned plates the drag
varied as the velocity to the 1.75 to 1.96 power, depend¬
ing on the pitch and width of the fins. As the drag is
directly proportional to the pressure drop in the present
tests and as the power is proportional to the product of
the pressure drop and the volume, the power required
for friction drag should theoretically vary as the
Figure I o.— Effect of fin pitch on the average wall heat-transfer coefficient, based
on the difference between the cylinder-wall temperature and the average air tem¬
perature. Fin width, 1.22 inches; fin thickness, 0.035 inch.
velocity to the 2.8 power, which is very close to what
wras obtained.
From these results in order to give the observed
variation of blow'er power with specific weight and
weight velocity of the air, equation (8) must take the
form
p ( Pi. *7 1 m) ~r)
(M)2
// 0,gVmD ^ °y
' s t w\
d’d’d)
(10)
Figure 11 shows that the power required for cooling
increases as the space between the fins decreases for the
BLOWER COOLING OF FINNED CYLINDERS
277
same weight velocity of the air except for the 0.166
cylinder. The data for the 0.166 cylinder fell on the
same curve as the data for the 0.137-incli pitch cylinder.
This result was surprising as it was expected that less
vm p, g . tb./sec./sq. fi.
Figure 11.— ElTeet of weight velocity of the cooling air on Pt(p\g)Vw.
power would be required to force air by more widely
spaced fins. An analysis of the pressure drops around
cylinders to be presented in a later report shows that
power increases as space decreases but for the 0.166-
and 0.137-incli pitch cylinders the difference is very
smali.
Curves of P^gY/w plotted against weight velocity
of the air are shown in figure 12 for the same cylinders
as are shown in figure 11, where Pb is the total power
loss across the jacket and includes both Pt and the
kinetic energy lost at the exit. The total power varied
as the 2.61 power of the weight velocity for all the
cylinders and increased as the pitch decreased, below
0.112-inch pitch, for a constant weight velocity. The
data for the 0.166, 0.137, and 0.112 cylinders are repre¬
sented by a single curve. It can be shown from figure
11 and the change in loss out the exit for the three
cylinders, with a constant jacket exit area and weight
velocity over the fins, that the total power required for
278
RETORT NO.
5S7 NATIONAL ADVISORY COMMIl IKK M'H VI.ID'N \i IRS
the 0.166, the 0.137, and the 0.112 cylinders is ap¬
proximately constant.
Further tests are being made to determine the ctleet
of fin pitch, width, and Reynolds Number on the power
required.
Air temperature. — The temperature of the air affects
its specific weight and viscosity. The eiloet of varia¬
tion in specific weight on power has been shown.
Equation (10) shows that the power varies as the 0.31
power of the viscosity. For the range of temperatures
encountered in an ordinary altitude change, the effect
of change in viscosity would be small.
maximum heat transfer for a given weight velocity will
give maximum heat transfer for a given power.
Figure 14 shows curves similar to figure 13 in which
the power lost as kinetic energy in the air leaving the
/». horsepower per nch of cylinder length
Ftc i ii u —Variation ot a vara ce wall baaMranafc* ooadkrtool • itti intal | - ■**» /’,
sportfle trelxhl tif th# atr, 0 OTii poanil p** cttMc Lot.
exit passage of the jacket is included in calcuIatinL’ the
required power. As previously stated, the power h»t
at the exit can lie somewhat decreased by providing a
properly expanding passage. The curves of figure 14
90 i -i - r-
Figure 13. — Variation ot average wall heat-trnnsfer eoeftii-font with power. P*.
Specific weight of the air. 0.0717 pound per cubic toot.
RELATION BETWEEN HEAT DISSIPATION AND BLOWER POWER
The wall heat-transfer coefficient l is shown plotted
against the power Pt in figure 13 for a specific w eight
of the air of 0.0717 pound per cubic foot. Those
results were obtained from figures 9 and 11 and indi¬
cate that for a given power the heat transfer can be
increased by decreasing the pitch up to a limiting value
of approximately 0.08 inch; below this pitch the heat
transfer decreases as the pitch decreases. Thus, with
0.10 horsepower, U increases from 1.24 B.t.u. per
square inch per °F. per hour for the 0.166 cylinder to (
1.885 for the 0.083 cylinder, an increase of approxi¬
mately 52 percent, and then decreases to 1.53 B.t.u.
per square inch per °F. per hour for the 0.057 cylinder.
With a given horsepower, except for the 0.106-inch
pitch, the weight velocity of the air decreases as the
fin pitch decreases. This decrease in weight velocity
tends to decrease U but decreasing the fin pitch tends
to increase U until a limiting value is reached. As the
effect of fin pitch predominates, the fin pitch giving
90 -
.c
>
>
■
u50
£
JO
JO
_ Li
/
i
/
/
/
/
I
9
W
/./
1.3
1.4 (-5
U, B.t u /sg in/*Y/hr
FtovHK \5.— Pvfnetit.igo «v\inc in /*, bj mice fin pitdi 0<iO !tvh ' i '
toU7taeh.
were obtained from figures 9 und 12 and show the same
trends as do those of figure 13.
Figure 15, obtained from figure 13, is a plot of
percentage saving in /’„ the power required for roofing,
HLOWKR C’OOLINd OF FINN FI) CYLINDERS
279
through tho use of a (in pitch of 0.083 inch instead of
0.137 inch at various values of U. The saving in
cooling power is appreciable and, as cylinders used in
conventional practice usually have (in pitches greater
than 0.137 inch, it might he thought that much is to
1)6 gained from a power consideration by decreasing
the pi tcli. The percentage of engine power req uired
for blower cooling of conventional cylinders is, however,
a small percentage of the total engine power. Lohner
(reference 7) gives a value of 3.5 percent of the brake
horsepower required for cooling a multieylindor en¬
gine with blowers and 8.3 percent for a single-cylinder
engine. It has been found in tests of a single-cylinder
engine (reference 8) that the power required for cooling
varied from approximately 2.9 to 8.6 percent of the
engine power, based on a blower efficiency of 7<l percent
and a temperature difference of 405° F. at a point
between the exhaust valve and the rear spark plug, de¬
pending on cylinder and jacket design ami engine-
operating conditions.
< ONC VI SIONS
1. The average surface heat-transfer coefficient q,
based on the temperature difference between the
cylinder and the inlet air, varied ns the 0.667 power
of the weight velocity of the cooling nir for cylinders
with fin spaces from 0.077 hi 0.21 inch. Below 0.077
inch the exponent of the curves increased for each suc¬
cessive decrease in space.
2. '1 he average surface heat-transfer coefficient q,
based on the. temperature difference between the cylin¬
der and the inlet air, was independent of fin width for a
range of fin widths from 0.07 inch to 1.22 inches and
decreased as the space between the tins decreased.
Below approximately 0.048 inch the decrease of q with
fin space was very rapid.
3. I he average surface heat-transfer coefficient q,
based on the difference between t lie cylinder tempera¬
ture and the average air temperature, remained con¬
stant for a given weight velocity of the air, for fin
spaces I mm 0.048 to 0.131 inch; below approximately
0.048 inch q decreased and above 0.131 inch q increased.
4. The power required to force the air around the
cylinder varied directly as the 2. 09 power of the weight
velocity for a constant specific weight and inversely as
l he square of the specific weight for a constant weight
velocity of the cooling air.
5. For a given power expended in cooling, the heat
dissipated from the cylinder could be increased bv
decreasing the space between the tins to approximately
0.045 inch for a cylinder with fins 1.22 inches wide.
Below 0.045 inch space the heat dissipated decreased.
Lanoi.ey M kmobiai. Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
La milky Field, Va., November 14, 1086.
' 4'- > It)
APPENDIX
SYMBOLS
w, fin width, inches.
w', effective fin width (wr =w-\-t/2).
t, average thickness of fins, inclies.
s, average space between adjacent fin surfaces, inches.
p, pitch of fins, p=s-\-t, inches.
I), cylinder diameter at fin root, inches.
lit,, radius from center of cylinder to fin root, inches
(R>=DI 2).
Ra, average radius from center of cylinder to finned
surface, inches ( Ha—Rb-\-w/2 ).
Ab, outside base area of test cylinder, square inches
(7 r/H).
S, total area of heated surface exposed to air stream
(including fin area), square inches.
At, total area of spaces between fins of the test
cylinder per inch of cylinder length, square inches.
Atr, total area of spaces between fins of both the test
cylinder and the guard rings, square inches.
Au area of outlet of jacket, around test cylinder per
inch of cylinder length, square inches.
W t, total weight of air flowing across test cylinder and
guard rings, pounds per second.
pi, absolute total pressure of the air in the orifice
tank, inches Hg.
p2 absolute static pressure of the air in the depression
tank (fig. 2 (b)), inches Hg.
Ti, temperature of the air at the inlet of the jacket,
°F.
T-2, average temperature of the air at the outlet of the
jacket, °F.
Vm, average velocity of the air across the fins, feet
per second.
Tb, average temperature of the root of the fin, °F.
Tm, average temperature of the root of the fin and
fins of the test cylinder, °F. (These two quantities,
Tb and Tm, were calculated from the test data, as
explained in reference 1.)
9b, average temperature difference between the root
of the fin and the air, °F. (9b—Tb—Ti).
dm, average temperature difference between the test
cylinder and the air, °F. (9m=Tm—Tt).
Q, total heat input to test cylinder, B.t.u. per hour.
U, average over-all heat-transfer coefficient, B.t.u.
per square inch base area (Ab) per hour, per °F. tem¬
perature difference between the cylinder wall and the
cooling air (db).
280
q, average surface heat-transfer coefficient, B.t.u.
per square inch total surface area (S) per hour, per °F.
temperature difference between the surface and the
cooling air (9m).
cp, specific heat of the air at constant pressure,
B.t.u. per pound per °F. (cp=1.41 cB).
p, absolute viscosity of the air, pounds per second per
foot.
ka, thermal conductivity of the air, B.t.u. per square
foot per °F. through 1 foot per second.
k, thermal conductivity of the metal, B.t.u. per
square inch per °F. through 1 inch per hour.
Pig, specific weight of the air at the inlet of the jacket,
pounds per cubic foot.
p2g, specific weight of the air at the outlet of the
jacket, pounds per cubic foot.
V2, velocity of the air at the outlet of the jacket,
feet per second.
P t, total horsepower per inch of cylinder length
required by test cylinder to overcome losses.
Pa, horsepower required per inch of cylinder length
to accelerate outlet air.
Pb, horsepower required per inch of cylinder length to
accelerate outlet air and overcome all losses (P„=
Pa + Pt).
REFERENCES
l. Biermann, Arnold E., and Pinkel, Benjamin: Heat Trans¬
fer from Finned 'Metal Cylinders in an Air Stream. T. R. No.
488, N. A. C. A., 1934.
2. Schey, Oscar W., and Rollin, Vern G.: The Effect of Baf¬
fles on the Temperature Distribution and Heat-Transfer Coeffi¬
cients of Finned Cylinders. T. R. No. 511, N. A. C. A., 1934.
3. Schey, Oscar W., and Biermann, Arnold E.: Heat Dissipa¬
tion from a Finned Cylinder at Different Fin-Plane/Air-Stream
Angles. T. N. No. 429, N. A. C. A., 1932.
4. Ware, Marsden: Description and Laboratory Tests of a
Roots Type Aircraft Engine Supercharger. T. R. No. 230,
N. A. C. A., 1926.
5. Brevoort, M. J., and Rollin, Vern G.: Air Flow Around
Finned Cylinders. T. R. No. 555, N. A. C. A., 1936.
6. Dryden, H. L., and Keuthe, A. M.: Effect of Turbulence in
Wind Tunnel Measurements. T. R. No. 342, N. A. C. A., 1930.
7. Lohner, Kurt: Development of Air-Cooled Engines witli
Blower Cooling. T. M. No. 725, N. A. C. A., 1933.
8. Schey, Oscar W., and Ellerbrock, Herman H., Jr.: Per¬
formance of Air-Cooled Engine Cylinders Using Blower Cooling.
T. N. No. 572, N. A. C. A., 1936.
REPORT No. 588
FUEL SPRAY AND FLAME FORMATION IN A COMPRESSION-IGNITION ENGINE
EMPLOYING AIR FLOW
By A. M. Rothrock and C. D. Waldron
SUMMARY
The effects oj air flow on fuel spray and flame formation
in a high-speed compression-ignition engine have been
investigated by means of the N. A. C. A. combustion
apparatus. The process was studied by examining high¬
speed motion pictures taken at the rate of 2,200 frames a
second. The combustion chamber was of the flat-disk
type used in previous experiments with this apparatus.
The air flow was produced by a rectangular displacer
mounted on top of the engine piston. Three fuel-injection
nozzles were tested: a 0.020-inch single-orifice nozzle,
a 6-orifice nozzle, and a slit nozzle. The air velocity
within the combustion chamber was estimated to reach a
value of 420 feet a second.
The results show that in no case was the form of the fuel
spray completely destroyed by the air jet although in some
cases the direction of the spray was changed and the spray
envelope was carried away by the moving air. When the
fuel distribution within the combustion chamber was par¬
ticularly poor, the volume in the chamber reached by the
dame was considerably increased by the air flow. When
the distribution was reasonably good, there was little
change in the distribution of the flame. It was found that
the air movement set up during the induction of air
through ports in the cylinder liner, under a pressure
difference of 26 inches of Ilg, could be controlled so as
materially to aid the airflow set up during the last portion
of the compression stroke.
INTRODUCTION
The distribution of the fuel in the combustion
chamber of a compression-ignition engine can be regu¬
lated to some extent by the design of the combustion
chamber, by the design of the fuel-injection nozzle, and
by the use of air flow. The N. A. C. A. has been con¬
ducting investigations of all three methods, singly and
in combination. Tests have been conducted with
single-cylinder engines and with special apparatus,
by which data unobtainable on the engine may be
procured.
With a special high-speed motion-picture camera
operating at speeds from 2,000 to 2,400 frames a second
in conjunction with the N. A. C. A. combustion appara¬
tus, investigations have been made of some of the effects
of injection advance angle, air-fuel ratio, and nozzle
design on the combustion process. (See references 1,
2, and 3.) Data obtained by the N. A. C. A. on the
effects of combustion-chamber shape and of air How
on combustion in a single-cylinder compression-ignition
engine have been published in references 4 to 8. In
order to explain further the results obtained in these
tests and to coordinate the researches on the com¬
bustion apparatus with the engine tests, a program of
tests was originated to study the effect of air movement
preceding and during the combustion process. In the
present tests it was desirable not only to photograph
the fuel spray and flame formation in the combustion
chamber of the N. A. C. A. combustion apparatus but
also to photograph the air movement.
Any method employed for photographing (lie air
movement must not disturb the normal operation of
the apparatus, for by so doing the variables under
investigation are changed. This condition immediately
eliminates methods using such materials as light metal
projections or strings to show the direction of the air
flow. The use of aluminum dust or some such material
was discarded because of its possible effects on com¬
bustion. A partial solution of the problem was found
in the use of “schlieren” or “striae” photography
(reference 9).
METHODS AND APPARATUS
The N. A. C. A. combustion apparatus has been
described in references 1 to 3. A diagrammatic sketch
showing the engine cylinder, the combustion chamber,
Figure 1.— Diagrammatic sketch of the N. A. C. A. combustion apparatus with
schlieren equipment.
281
282
REPORT NO. 588 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
and the schlieren optical arrangement is shown as
figure 1. The air movement, the fuel injection, and
the flame spread were photographed through the 2 %-
inch-diameter glass windows forming the sides of the
flat-disk combustion chamber. A 750-watt projec¬
tion lamp was placed behind the slit as indicated in the
diagram. The slit was placed at the focus of the first
lens so that parallel light was transmitted through the
combustion chamber to the second lens. The knife
comparisons to be made of the indicated mean effective
pressures developed by the engine.
Three fuel-injection nozzles (fig. 2) were tested: a
0.020-inch single-orifice nozzle, a 6-orifice nozzle, and
a slit nozzle. These nozzles were chosen from those
used in the investigation of the effect of nozzle design
on combustion (reference 3). The fuel oil was the
same as that used in the tests reported in references 1,
2, and 3.
Single orifice.
Figure 2.— Nozzles tested.
m.
edge was located at the image of the slit and in such a
position that two-thirds of the slit image was inter¬
cepted by the knife edge. The image of the combustion
chamber was focused on the motion-picture film. Any
local change in the index of refraction of the medium
between the two lenses caused a deflection in the par¬
allel light rays. This deflection caused the light rays
to strike either below or above the original point in
the image of the slit. Therefore, a change in the index
of refraction of a part of the medium between the
lenses resulted in light or dark areas being formed on
the motion-picture film in the image of the combustion
The following test conditions were maintained
constant:
Engine bore _ inches. _ 5
Engine stroke _ do _ 7
Engine speed _ revolutions per minute. _ 1, 500
Engine-jacket coolant temperature (outgoing)-°F. _ 150
Engine compression ratio (based on total stroke). 14. 1
Air-fuel ratio (except as otherwise stated) _ 17
Start of injection _ crankshaft degrees B. T. C._ 15 to 20
A flat-disk combustion chamber was used with a rec¬
tangular displacer as adapted by Moore and Foster
(references 7 and 8). The displacer was mounted on the
In jection
Figure 3 —Combustion-chamber shapes tested.
chamber. Because any air movement in the com¬
bustion chamber is accompanied by local changes in
the index of refraction of the air, the air movement
showed up as light and dark streaks in the image
recorded on the photographic film. The image of the
fuel-spray silhouette and of the combustion was photo¬
graphed on the film in the usual manner.
The test procedure was similar to that given in refer¬
ence 3. No time-pressure records are presented in the
present report, although they were taken for each test
condition. Such records have been presented in refer¬
ences 1, 2, and 3. As has been previously stated, these
records, although giving the general course of the com¬
bustion, are not sufficiently accurate to permit close
engine piston to produce an air flow of high velocity
within the combustion chamber. The displacer was
arranged so that it could be mounted at either side or
directly in the center of the piston, as shown in figure 3.
In this manner an air jet could be directed along either
or both ends of the combustion chamber. In one test
the displacer was removed and a central oval orifice
installed in the center of the chamber throat (fig. 3E).
The areas between the displacers and the edges of the
combustion chamber and of the orifice in combustion
chamber E were such that the velocity approximated
the value which gave the best performance in the tests
presented in reference 7. The velocity of the air as it
entered the combustion chambers was estimated accord-
FUEL SPRAY AND FLAME FORMATION IN A COMPRESSION-IGNITION ENGINE EMPLOYING AIR FLOW
283
ing to the method given in reference 7 and is shown in
figure 4 as a function of the crank angle. Combustion
chamber A has a width between the glass windows of
0.78 inch and the others a width of 1.01 inches. This
variation in width was necessary to maintain a constant
compression ratio.
In the tests with the single-orifice nozzle the mani¬
fold around the inlet ports of the engine had a single
opening in the plane of the combustion-chamber disk
on the side in which the injection valve was mounted,
and the air entered the cylinder with a definite whirling-
#
motion. In the tests with the multiorifice nozzle this
manifold was removed so that the air could enter
symmetrically with respect to the cylinder. In the tests
with the slit-orifice nozzle the same arrangement was
used and additional runs were made with the intake
ports blocked on first one and then the other side of the
cylinder.
RESULTS AND DISCUSSION
The estimated air flow (fig. 4) shows that, as the
displacer entered the combustion chamber, the air
velocity quickly reached a value of 400 feet a second.
Figure 4. — Air velocity through throat connecting displacement volume and com¬
bustion chamber.
The rate of velocity increase became successively less
and a maximum of 420 feet a second was reached at
about 25 crankshaft degrees B. T. C. The velocity
then decreased to zero at top center. With combustion
chamber E a maximum velocity of 435 feet a second
was reached at 33 0 B . T. C. With combustion chamber A
the velocity reached a maximum of 120 feet a second
at about the same piston position that the maximum
was reached with the displacer. These velocities with
the restriction are those estimated for the air as it
entered the combustion chamber at the narrowest
section. As the air passed from this orifice into the
chamber proper there was, of course, a certain amount
of expansion of the jet and a certain amount of turbu¬
lence was also created. In addition, there was the
effect of any air flow produced during the induction of
the air through the ports into the displacement volume.
The conditions under which the air is inducted are
comparable with those existing in a highly super¬
charged engine because, as was shown in reference 1,
the pressure differential between the displacement
volume and the intake manifold at the time the piston
uncovered the intake ports was approximately 26
inches of Hg.
The photographs showed that two types of air flow
might occur in the combustion chamber. The first was
Figure 5. — Air vortex in combustion chamber D.
a mass rotation of the air as a whole and the second was
the occurrence of a vortex traveling around the com¬
bustion chamber. The first type is not visible unless
the motion pictures are projected, the individual
photographs showing only light and dark areas in the
combustion gases. The vortex occurred most often
with combustion chamber A. Occasionally a vortex
was produced in combustion chamber D (fig. 5).
In the photographic prints reproduced in this report,
mass movement of the air as a whole is indicated by
the deflection of the fuel spray. A description of the
flow as visualized when the motion pictures were pro¬
jected and also as interpreted from the spray shapes is
also included. For assistance in the analysis of the
results, line drawings of the combustion chambers with
arrows indicating the air movement are included with
the enlargements from the motion-picture films. The
enlargements show the fuel spray from the start of
injection and the first three or four photographs of
the combustion.
The effect of some air movement on the fuel sprays
in combustion chamber A was observed in the results
presented in both references 2 and 3. The photographs
showed that the spray tips were twisted first to the
right and then to the left as the sprays proceeded across
the combustion chamber. In the present tests this
motion was found to be caused by the vortex (fig. 5)
moving around the combustion chamber, generally
clockwise in the results reported herein and counter¬
clockwise in the results shown in references 2 and 3.
(This difference in directional rotation does not actually
occur in the engine. Because of space limitations it was
284
REPORT NO. 588 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
necessary to reflect the light through 90° in this schlieren
set-up. Therefore, results showing clockwise rotation
in those photographs correspond to a counterclockwise
rotation in the previous results.) The vortex was
apparently caused by the air movement set up as the
air entered the displacement volume through the inlet
ports. It has been shown in reference 3 that this flow
caused the flame to predominate on the leeward side
of the spray.
Single-orifice nozzle. — With the injection valve
mounted in the top (fig. 6 (a)) of combustion chamber
A, the single fuel spray penetrated across the visible
portion of the chamber. Because of the relationship of
the injection-nozzle area to the other injection-system
dimensions there was a secondary discharge of the fuel
following the first stop of injection. The photographs
indicate that this secondary discharge penetrated
through the already burning gases. When the injection
valve was mounted in the side (fig. 6 (b)) the spray
penetrated across the chamber and impinged on the
opposite wall. In this case there is visible a slight
upward bending of the spray caused by the entering air.
Combustion started at the chamber wall. In neither
case did the flame spread throughout the chamber.
With the injection valve mounted in the side, the motion
pictures show that the combustion was followed by a
cloud of smoke, which seemed to roll backward from the
section of the chamber wall that was struck by the
spray core.
The arrows indicate that in one case the general air
movement was clockwise and in the other case counter¬
clockwise, but the reason for this apparent occasional
reversal of the flow is not known. In no case was it
sufficient to have much effect on the fuel spray or flame
formation.
Combustion chamber B showed a marked difference
from chamber A both in the fuel spray and the flame
formation (fig. 7). The motion pictures showed that
the rotation of the air caused by the displacer, being in
the same direction as that produced during the induc¬
tion of the air, was in the form of a mass rotation of the
air in a clockwise direction as compared with the
rotating vortex obtained without the displacer. In the
upper half of the visible portion of the chamber the
spray is shown blown to the right, and in the lower half
to the left. In the seventh photograph of figure 7 (a)
(3° B. T. C.) the center of the rotating air is well
marked by the spray formation. The flame filled the
chamber reasonably well and a decided improvement
in mixing over that obtained without the piston dis¬
placer is noted. When the injection valve was mounted
in the side (fig. 7 (b)), the fuel-spray core was directed
upward so that there was little impingement on the
opposite wall of the combustion chamber and very
little smoke was visible. The downward motion of the
air on the right-hand side of the chamber did not have
much apparent effect on the spray. Again the chain-
Figure 6. — Fuel sprays and combustion with chamber i*
25 B.T.C. 20 15 10 5 T.C. 5 A.T.C.
(a) Crardkshaft degrees
(a) Injection from top of cylinder B.
25 B.T.C. 20
(b)
15 10 5 T.C. 5 10 15 A.T.C. 20
Crankshaft degrees
(b) Injection from side of cylinder B.
it ti f
20 B.T.C
T.C.
10 A.T.C.
(0
Crankshaft degrees
(c) Inection from side of cylinder C.
Figure 7 —Fuel spray and combustion with chambers B and C.
fuel spray and flame formation in a compression-ignition engine employing air flow 285
286
REPORT NO. 588 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
her was fairly well filled with flame. In neither case
was the spray core destroyed by the moving air, al¬
though the envelope was swept away from the core.
The results show that, even in the highly heated air of
the combustion chamber, high air velocities do not
destroy the core of the spray but nevertheless materially
aid in the mixing of the fuel and air.
With combustion chamber C the air rotation pro¬
duced in the combustion chamber by the displacer was
in the opposite direction to that produced by the in¬
duction of the air (fig. 7 (c)). The motion pictures show
that the air first rotated clockwise and then, as the
displacer entered the combustion chamber, the air
suddenly changed direction and made a rotation in the
counterclockwise direction. As a result of this change
of motion, much of the energy of the moving air was
lost so that the effect on the fuel spray was considerably
less than was the case with combustion chamber B.
The spray impinged on the wall of the chamber as it
did when no displacer was employed and there was
considerable smoke. There is little evidence that with
this arrangement the air flow produced beneficial re¬
sults. The test illustrates the fact that, when designing
a combustion chamber to produce a certain typo of air
flow, extreme care must be taken to insure that the
desired results are not nullified by air movements set
up by the induction of the air into the displacement
volume.
When combustion chamber D was employed (fig. 8),
the movement of the air as a whole was hard to dis¬
tinguish. The rotation of the air before the displacer
entered the combustion chamber was still clockwise but
it seemed to predominate in the right-hand section of
the chamber. With the fuel being sprayed in from the
top of the chamber, there was little apparent effect from
the air flow. The spray tended to have a somewhat
sinuous motion as it penetrated through the combustion
air. The flame showed but slightly better distribution
than was obtained without the displacer. When the
spray was injected from the side, the effect of the air
movement was quite noticeable. As the spray first
issued from the injection nozzle it was blown upward
by the air jet. Its direction was then changed slightly
so that it again traveled in a horizontal direction but,
as the issuing fuel jet became more dense and the air
velocity decreased, the spray core maintained a straight
course inclined upward to the horizontal. The down¬
ward movement of the air in the center of (lie chamber
is noticeable in the photograph taken at 4° B. T. (’.
In this frame the spray shows the effects of the air
blowing up along the side walls of the chamber and down
in the right center. The flame spread throughout most
of the visible portion of the chamber but there was still
considerable smoke during the expansion stroke.
With combustion chamber E it appeared that the air
divided in the center of the chamber, rotating in a clock¬
wise direction in the right half and a counterclockwise
CO
QC
Of
♦ # d
to
o
(a)
B.T.C.
i
20
15
10
5 T.C.
Crankshaft degrees
(a) injection from top.
10 A.T.C.
(b) injection from side.
Figure 9. — Fuel sprays and combustion with chamber E.
% # # #
fb)
15 B.T.C. 10
T-C. 5 10
Crankshaft degrees
(b) Injection from side.
Figure 10 —Fuel sprays and combustion with multiorifice nozzle and chamber A.
15 A.T.C.
*3
H
i
go
T
W
>
kJ
>
Z
c
>
S
H
§
>
O
HH
25
>
o
$3
«
GO
GO
w'
2;
z
H
Z
Q
z
H
H
O
«)
Z
>
0C
^1
(b) Injection from side; air-fuel ratio, 17.
# Cl 0
15 B.T.C.
10
(c)
T.C.
Crank shaft degrees
15A.T.C.
(c) Injection from side; air-fuel ratio. 33
B.T.C. B.T.C.
(d) Injection from side: air-fuel ratio, 65
Figure 11— Effect of air flow on the fuel sprays and combustion at different air-fuel ratios Multiorifice nozzle and chamber B.
a
a
r
CD
>
kJ
>
2
O
a
I
a
a
o
£
>
2
•-H
2
>
a
C\
g
a
a
a
CD
CD
2!
i
a
2
z;
a
2
a
2
a
a
2
>
tc
7:
(b) Injection from side.
Figure 12.— Fuel sprays and combustion with multiorifice nozzle and chamber D.
290
REPORT NO. 588 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Fuel quaniity, lb. /cycle
Figuke 13. — Comparison of performance with and without air flow (reference 7).
direction in the left half (fig. 9). With the injection
valve mounted in the top of the spray chamber the
spray penetration was decreased by the air jet directed
against it. Also the air movement was such that the
spray envelope was blown to the left-hand side of the
chamber. This deflection is quite noticeable in the
photograph obtained 1° A. T. C. The mixing of the
fuel and air was not particularly good. The results
appeared to be little better than with combustion
chamber A. When the injection valve was mounted
in the side of the combustion chamber, the spray was
deflected upward when it met the incoming air jet
about midway across the combustion chamber. The
spray impinged on the opposite wall of the chamber
and was there blown downward by the air swirl in that
half of the chamber. The flame spread to a somewhat
greater area than was the case with the spray entering
at the top of the chamber, but considerable air was still
not reached by the fuel. Again the chamber was partly
filled with a dense smoke during the expansion stroke.
Multiorifice nozzle. — The multiorifice nozzle was
designed according to the proportionality principle dis¬
cussed in reference 6. Engine tests (reference 7) have
shown that in the type of combustion chamber tested
the multiorifice nozzle which gave the best performance
with the quiescent combustion chamber also gave the
best performance with the same combustion chamber
used in conjunction with the displacer piston.
in the tests with the multiorifice nozzle the inlet
manifold around the ports was removed. The vortex
that appeared when the manifold was in place did not
occur so often when the manifold was removed. With
the injection valve mounted in the top of chamber A
(fig. 10 (a)) the individual sprays penetrated through
the highly heated dense air, the side sprays impinging
on the combustion-chamber walls. The flame filled the
visible portion of the combustion chamber. When the
injection valve was mounted in the side of the chamber
(fig. 10 (b)), some of the fuel sprays impinged on the
opposite wall of the chamber but not with the intensity
that accompanied the impingement of the spray from
the single 0.020-inch orifice. The two sprays directed
toward the entrance throat were definitely deflected
upward. The flame again filled the combustion chamber
and, although there was some smoke visible on the
expansion stroke, it was not so dense as in the case with
the single 0.020-inch orifice.
With the nozzle mounted in the top of combustion
chamber B (fig. 11 (a)) the sprays from the 0.014- and
0.018-inch orifices on the side of the chamber toward
the air jet were deflected to the right by the air move¬
ment across the top of the chamber, as they left the
nozzle, and to the left nearer the bottom of the chamber
because of the upward movement of the air in this por¬
tion. The sprays on the other side of the combustion
chamber showed less movement although they were
somewhat bent. On this side of the chamber the air
flow had been decreased because of its greater distance
from the displacer passage and also because the air flow
had already lost some of its energy in deflecting the
first sprays through which it passed.
With the injection nozzle mounted in the side, the
effects of the air movement are visible during the entire
injection period. The sprays are all deflected upward
as they enter the chamber. The envelopes and, in
some cases, the spray cores are deflected downward
when they reach the opposite side of the chamber.
Projection of the film containing the photographs
shown in figure 1 1 showed that in three cases there was
a reversal of rotation of the air flow even though the
intake manifold had been removed. The reversal was
not so violent, however, as it was with the manifold.
In figures 1 1 (c) and (d) are shown the results of tests
made with air-fuel ratios of 33 and 65, respectively.
A comparison of these photographs with those obtained
at an air-fuel ratio of 17 shows that, as the fuel quantity
was decreased and consequently the energy in the
injected spray was decreased, the rotating air turned
the fuel jets through a larger angle so that the sprays
were forced to the upper left-hand quadrant of the
chamber. With the air-fuel ratio of 65 the flame is
(a) Injection from top of chamber B.
(b) Injection from side of chamber B.
FUEL SPRAY AND FLAME FORMATION IN A COMPRESSION-IGNITION ENGINE EMPLOYING AIR FLOW
(a) Air How from both sides.
(b) Air flow from right only.
(c) Air flow from left only.
Figure 15. — Effect of iulet-port arrangement on fuel spray and flame formation. Slit-orifiee nozzle; combustion chamber Ti; injection from top.
292 REPORT NO. 588 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
FUEL SPRAY AND FLAME FORMATION IN A COMPRESSION-IGNITION ENGINE EMPLOYING AIR FLOW
293
visible in two separate sections. One section extends
along the right-hand side of the chamber and the other
is in the region surrounding the fuel-injection nozzle.
In this case the fuel from the main discharge has appar¬
ently been carried to the opposite side of the combustion
chamber by the moving air and so forms a stratified
charge in this area. The small secondary discharge
visible in the photograph taken just before top center
was not blown away because of the decrease in the air
velocity. The original of this strip of film shows that
these two flame areas did not combine. The results
therefore prove that, even with high air velocities in the
combustion chamber, it is possible to maintain a
stratified charge of the fuel and air. For this reason
it is believed that in engines employing air flow there
should be no difficulty in idling the engine. It is
probable that in certain cases where special adapters
have been used in the air-induction system to change
the air flow for idling conditions, the trouble has not
been with the air movement but with the idling charac¬
teristics of the fuel-injection system.
The results obtained with combustion chamber D
and the multiorifice nozzle are shown in figure 12.
With the fuel being injected from the top (fig. 12 (a)) of
the chamber, the sprays appeared quite similar to those
in chamber A. With the fuel being injected from the
side (fig. 12 (b)) of the chamber, the sprays show that
there was a clockwise rotation of the air in the left-
hand side of the chamber and a counterclockwise
rotation in the right-hand side of the chamber. The
air flow did not have much directional effect on the fuel
sprays as a whole except to concentrate them more
in the top of the chamber. Engine tests (fig. 13)
reported in reference 7 of a similar combustion chamber
have shown that this arrangement gives an appreciable
increase in power over the quiescent combustion
chamber without the displacer piston.
Slit nozzle. — In the test conducted by Lee of the
distribution within different types of fuel sprays
(reference 10) it was shown that the distribution within
the spray from a slit nozzle was comparatively good
but that the dispersion of the spray, that is, the total
volume included in the spray, was insufficient and
consequently the air-fuel ratio within the spray was too
low. The suggestion was made that this type of spray
could most beneficially be used with some form of air
flow in the combustion chamber. The results in figure
14 show that, even with the air velocities used in the
present tests, the energy was insufficient to break up
the fuel spray. A comparison of figure 1 4 with figures 1 1
and 12 indicates that the spray from the slit-orifice
nozzle was less affected than those from the multi¬
orifice nozzle. The conclusion is drawn that because
of the large cross-sectional area presented to the air
flow the spray from the slit-orifice nozzle tends to
damp the air movement to a greater extent than do
those from the multiorifice nozzle. With the fuel
being injected from the side (fig. 14 (b)) in combustion
chamber B, the air-flow effects are more noticeable
than is the case when the fuel is injected from the top
(fig. 14 (a)).
A direct comparison cannot be made between the
results shown in figure 14 and those in figures 7 and 8
because of the difference in the air-intake system.
Tests were therefore run with the slit-orifice nozzle in
chamber B in which the inlet ports were blocked first
on one side and then on the other (fig. 15). At the
right of each of the three photographic strips a line
drawing shows which inlet ports remained opened and
which were closed. The three ports on each side of
the engine cylinder are represented by the single
opening. Figure 15 (a) shows the results obtained
with the ports opened on both sides, the same photo¬
graphs being shown in figure 14. When the inlet
ports on the cylinder side adjacent to the displacer were
opened and those on the other side blocked, a counter¬
clockwise rotation of air was produced in the combus¬
tion chamber, that is, a rotation opposed to the air
movement produced by the displacer. Although this
counterclockwise rotation was stopped before the
start of the injection of the fuel, a rotation of the air
in the opposite direction was not visible and the fuel
spray shows no indication of such a reversal. As was
the case in the results presented in figure 7 (c), the
air flow induced during the induction period opposed
that purposely induced during the last part of t he com¬
pression stroke and nullified its effects. With the
air-inlet ports arranged as shown in figure 15 (c), the
air swirl produced during the induction period assisted
that produced by the piston displacer and the maximum
effect of the air flow was obtained.
GENERAL SIGNIFICANCE OF TEST RESULTS
In previous tests (references 3 and 10) it had been
concluded that with high-dispersion fuel-injection
nozzles the lack of spray penetration must be assisted
by air flow. The present tests have shown that with
the nozzles now generally employed and with the
injection pressures commonly used, it is difficult to
obtain a good mixture of the air and fuel even with
air flow. The question that naturally follows is:
How is the compression-ignition engine to be designed
so as to give the power outputs together with the fuel
economy inherent in the high compression ratio? It
was concluded in reference 3 that the chief obstacle to
obtaining this high performance is the slow rate of
diffusion of the fuel vapors. The results presented in
this report support this conclusion. In the use of air
flow to assist diffusion, the air must blow through the
fuel jet and continually pick up the vapors from the
jet. If the air and the fuel rotate about the chamber
as a unit, the mixing of the two is not necessarily im¬
proved. It is necessary to have a continual inter¬
mixing of the fuel and air taking place within the
294
REPORT NO. 588 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
combustion chamber. Ln addition to the controlled
air flow, the purpose of which is to destroy the fuel
jet, it is desirable and probably necessary to have
numerous small eddies throughout the combustion
chamber. The production of such an air flow presents
a difficult problem, and the development of a method
to measure it is probably even more difficult. Whether
or not the use of such flow will actually increase the
initial rate of heat exchange from the air is question¬
able. Such an effect has been indicated, however, by
the decreased ignition lags in engine tests at this
laboratory with the displacer piston. Test results
presented by Selden and Spencer (reference 11) have
shown that the rate of heat exchange between the
injected fuel and the air is not much affected by low-
air velocities. An extensive discussion of the effects
on engine performance of air flow produced by combus¬
tion chambers of different design has been presented by
Alcock in reference 12.
In both the present tests and those discussed in refer¬
ence 2 it has been shown that stratification of the charge
occurs in the compression-ignition engine; it has not been
shown whether or not such stratification is necessary.
When spark ignition is employed as in the conventional
carburetor engine, it is known that the flame will not
propagate across the combustion chamber unless the
air-fuel ratio is less than approximately 20. In this
case the combustion of each successive portion of the
fuel is brought about by the heat from the combustion
of the preceding portion of fuel. In the compression -
ignition engine, in which the number of ignition sources
is infinite, no tests have been conducted to determine
to what extent the air-fuel ratio affects the flame spread.
Although it is probable that each source of combustion
does propagate flame in the normal manner, it is also
certain that new sources of ignition are continually
being formed. It is therefore believed that, although
stratification does occur in the compression-ignition
engine, it is not of so much importance at high air-fuel
ratios as would be the case in a spark-ignition engine
attempting to run on mixtures with an air-fuel ratio
greater than necesssary to support flame propagation.
Since the present tests do not show much difference
in the appearance of the flame using the multiorifice
nozzle with and without the air flow and since those
presented in references 7 and 8 show that a considerable
improvement in engine performance is gained by the
use of air flow' under similar conditions, it can be con¬
cluded that the chief effect of the air flow' in those cases
in which the distribution is reasonably good is not on
the direction and penetration of the fuel sprays but on
the intermixing of the air and fuel b}r the numerous
small eddies. This conclusion is strengthened by the
fact that in references 7 and 8 it was shown that the
nozzle which gave the best performance with the air
flow' w-as the one which gave the best performance in
the quiescent combustion chamber.
An examination of the results presented in this report
and those presented in references 1 to 3 gives an
indication of the rate of diffusion of the fuel vapors but
does not indicate the rate of heat exchange between the
air and the injected fuel. The test results presented in
reference 11 show that the rate of heat exchange is high
from the instant injection starts. Tests have been
conducted at this laboratory on methods of increasing
the effectiveness of this heat exchange, first, by heating
the engine jacket (reference 1) and, second, by heating
the fuel to a high temperature before injection (reference
13). In neither case was there any appreciable improve¬
ment in the engine performance except for a shortening
of the ignition lag w ith its consequent smoother engine
operation, indicating that the rate of heat exchange is
sufficiently fast under normal operating conditions.
Efforts to improve the atomization of the fuel jet
have not shown any marked improvement in engine
performance over that obtained with the atomization
already realized with the conventional injection systems.
In a series of tests conducted at this laboratory (refer¬
ence 14) a jet of high-velocity air was directed through
the fuel spray as it left the injection valve. Tests
conducted by the methods described in reference 14
showed that the combination air-fuel injection decreased
the mean diameter of the fuel drops and, when the fuel
was injected into the atmosphere, it was found that the
combination of the air and fuel jet burned with a much
fiercer flame than did that of the fuel jet alone. Never¬
theless, when the combination air-fuel injection was
used in the engine, there was no appreciable gain in
engine performance. As a result of these tests it was
concluded that the atomization in the conventional
hydraulic injection system is sufficient to result in good
combustion provided that the fuel is correctly
distributed.
Analysis of the results presented in this report,
together with those in the references, leads to the con¬
clusion that the factor about which more information
should be obtained is the actual air-fuel ratio at each
instant throughout the combustion chamber during the
injection and combustion period. These ratios are the
determining factors that control the performance of the
engine. At present it is known that the air-fuel ratio
is extremely uneven and that as a result of this uneven¬
ness too much of the fuel is burned late on the expansion
stroke and, consequently, at a low cycle efficiency.
Not only must the combustion efficiency of the engine
be improved (by combustion efficiency is meant the
percentage of the total fuel injected that is burned
between the start of the fuel injection and the com¬
pletion of the power stroke) but the time at which this
burning occurs must also be controlled to a greater
extent than is done in present-day designs.
FUEL SPRAY AND FLAME FORMATION IN A COMPRESSION-IGNITION ENGINE EMPLOYING AIR FLOW
295
CONCLUSIONS
The analysis of the data on the effect of air (low on
fuel spray and flame formation has led to the following
conclusions:
1. In the combustion chamber of the compression-
ignition engine, air velocities as high as 400 feet a
second were not sufficient to destroy the core of a fuel
spray from a single round-hole orifice.
2. Air velocities of 400 feet a second were sufficient
to change materially the direction and distance of the
spray-core penetration and to blow aside the envelopes
of sprays from a single round-hole orifice.
3. As the air-fuel ratio was increased the effect of the
air flow on the fuel sprays was increased.
4. With fuel-injection nozzles giving poor fuel dis¬
tribution within the combustion chamber, air flow in¬
creased the volume in the combustion chamber reached
by flame.
5. With a fuel-injection nozzle giving good distribu¬
tion, air flow did not result in much change in the
spread of the flame although engine tests showed a large
increase in performance.
6. High-distribution nozzles such as the slit nozzle
did not show much more effect from air flow than did the
sprays from round-hole orifices.
7. High-distribution nozzles damped the air flow
considerably.
8. When air flow is employed in a combustion cham¬
ber, care should be taken that the motion of the air set
up during the induction period is not such as to oppose
the desired air flow produced at the end of the com¬
pression stroke.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., November 25, 1936.
REFERENCES
1. Rothrock, A. M., and Waldron, C. I).: Some Effects of In¬
jection Advance Angle, Engine-Jacket Temperature, and
Speed on Combustion in a Compression-Ignition Engine.
T. R. No. 525, N. A. C. A., 1935.
2. Rothrock, A. M., and Waldron, C. D.: Effects of Air-Fuel
Ratio on Fuel Spray and Flame Formation in a Compres¬
sion-Ignition Engine. T. R. No. 545, N. A. C. A., 1935.
3. Rothrock, A. M., and Waldron, C. D.: Effect of Nozzle
Design on Fuel Spray and Flame Formation in a High-
Speed Compression-Ignition Engine. T. R. No. 561,
N. A. C. A., 1936.
4. Spanogle, J. A., and Whitney, E. G.: A Description and
Test Results of a Spark-Ignition and a Compression-Igni¬
tion 2-Stroke-Cycle Engine. T. R. No. 495, N. A. C. A.,
1934.
5. Moore, C. S., and Collins, J. II., Jr.: Prechamber Com¬
pression-Ignition Engine Performance. T. R. No. 577,
N. A. C. A., 1936.
6. Foster, H. H.: The Quiescent-Chamber Type Compression-
Ignition Engine. T. R. No. 568, N. A. C. A., 1936.
7. Moore, C. S., and Foster, H. H.: Performance Tests of a
Single-Cylinder Compression-Tgnition Engine with a Dis¬
placer Piston. T. N. No. 518, N. A. C. A., 1935.
8. Moore, C. S., and Foster, II. H.: Boosted Performance of
a Compression-Ignition Engine with a Displacer Piston.
T. N. No. 569, N. A. C. A., 1936.
9. Gawthrop, D. B.: Applications of the Schlieren Method of
Photography. Rev. Sci. Instruments, vol. 2, no. 9,
Sept. 1931, pp. 522-531.
10. Lee, Dana W.: Measurements of Fuel Distribution within
Sprays for Fuel-Injection Engines. T. R. No. 565, N. A.
C. A., 1936.
11. Selden, Robert F., and Spencer, Robert C.: Ileat Transfer
to Fuel Sprays Injected into Heated Gases. T. R. No.
580, N. A. C. A., 1936.
12. Alcock, J. F.: Air Swirl in Oil Engines. Proc. Inst.
Mech. Eng. vol. 128, Nov.-Dee. 1934, pp. 123-193.
13. Gerrish, Harold C., and Ayer, Bruce E.: Influence of Fuel-
Oil Temperature on the Combustion in a Precham! er
Compression-Ignition Engine. T. N. No. 565, N. A. C. A.,
1936.
14. National Advisory Committee for Aeronautics: Nineteenth
Annual Report, 1933, p. 17.
REPORT No. 589
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
WITH CHARTS FOR USE IN DESIGN
By Charles H. Zimmerman
SUMMARY
The aerodynamic and mass factors governing lateral
stability are discussed and formulas are given for their
estimation. Relatively simple relationships between the
governing factors and the resulting stability characteristics
are presented. A series of charts is included with which
approximate stability characteristics may be rapidly
estimated.
The effects of the various governing factors upon the
stability characteristics are discussed in dehail. It is
pointed out that much additional research is necessary both
to correlate stability characteristics with riding , flying , and
handling qualities and to provide suitable data for accurate
estimates of those characteristics of an airplane while it is
in the design stage.
INTRODUCTION
The lateral stability of airplanes has been the subject
of considerable mathematical treatment and many
theoretical analyses. (See references.) The main as¬
pects of the problem are therefore well known to stu¬
dents of the subject. Use of the mathematical theory
in design is, however, limited by practical difficulties in
its application. Determination of numerical values for
certain of the aerodynamic quantities is difficult and
the results are uncertain. The required calculations
are extensive and must be carefully made to avoid erro¬
neous and confusing results.
In this report lateral stability will be discussed and
analyzed in a way that, it is believed, will aid in the
acquisition of a working knowledge of the subject with¬
out long and intensive study. The classical equations
have been simplified as much as seems consistent with
reasonable accuracy to permit rapid estimation of the
stability characteristics. Also included is a series of
charts designed to facilitate the rapid estimation of the
approximate lateral-stability characteristics of airplanes
throughout the normal-flight range. It is hoped that
these charts, together with those on longitudinal sta¬
bility presented in reference 1, will aid in putting the
estimation of the complete stability characteristics on
a practical basis.
The material is presented in the following order: (1)
A discussion of the aerodynamic and mass factors that
govern the uncontrolled motion of the airplane together
with formulas for estimating these factors; (2) formulas
for estimating the stability characteristics of the uncon¬
trolled motion having given the governing factors; (8)
charts for the rapid estimation of stability character¬
istics; (4) a discussion of the effects of the governing
factors upon the stability characteristics; (.5) comments
and suggestions for future study; (6) a brief derivation
of the classical stability formulas (appendix I); (7) an
accurate semigraphical method for solving biquadratics
with a useful approximation based on this method
(appendix II); and (8) a list of symbols and their
definitions (appendix III).
FACTORS GOVERNING STABILITY
Both theory and experiment indicate that, with
certain exceptions, the uncontrolled motion of an air¬
plane can be divided into two independent phases.
One phase includes components of the motion that do
not displace the plane of symmetry of the airplane
from the plane with which it coincides during the steady
motion. Stability of this part of the motion is termed
“longitudinal stability.” The other phase of the com¬
plete motion includes all components that do displace
the plane of symmetry. This phase of the motion is
called “lateral motion” and its stability characteristics,
“lateral stability.” Although, in the past, reference
has frequently been made to directional stability as
distinguished from rolling stability (also called “lateral”
stability), both theory and experiment indicate that
no such division is physically possible for the conven¬
tional airplane.
The uncontrolled motion of an airplane quite ob¬
viously depends upon the aerodynamic forces and
moments arising from any deviation from a steady
state together with the inertial forces and moments
accompanying the accelerations coupled with the
deviations. The lateral motion is zero in steady
flight on a straight course. The components of lateral
motion in unsteady flight are a linear velocity v along
the Y axis (see appendix I and fig. 1) and angular
velocities p and r about the A" and Z axes, respectively.
The forces and moments governing lateral motion
therefore arise from the aerodynamic reactions to the
297
298
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
velocities v, />, and r (in the theoretical treatment aero¬
dynamic reactions are assumed to be unaffected by
accelerations) and the inertial reactions to the accelera¬
tions dv/dt, g sin </> cos y, g sin \p sin y, dp/dt, and drjdt,
where </> is the angle of roll, y is the angle of the flight
path, and i p is the angle of yaw.
For convenience the components of the reactions
referred to the coordinate axes are used rather than
the resultant reaction. It appears, then, that a velocity
v should result in a side force AF, a rolling moment A L,
and a yawing moment AN. Similarly there will be
A’s of F, L, and N corresponding to the rolling and
yawing velocities p and r. The basis for the classical
theory of stability is that the algebraic sum of the
values of AF (for example) for a unit value of v when p
and r are zero, for a unit value of p when v and r are
zero, and for a unit value of r when v and p are zero is
equal to the value of AF when the total motion is the
resultant of coexisting unit values of v, p, and r. It is
further assumed that a reaction AF due to a disturb-
Figure 1. — Angular and vertical relationships in flight, power oil.
ance of velocity v is directly proportional to the magni-
dY
tude of v, that is A Y=v~y^- This assumption is ad¬
mittedly an approximation but is valid, in general, for
small values of the velocities of the disturbance. On
this basis the aerodynamic reaction AF to a lateral
disturbance is
1 dv ' 1 dp ' dr
and similar expressions exist for A L and AN.
As a matter of convenience it has been found desir¬
able to express the derivatives dY/dv, dLfdv, etc., in
terms of the nondimensional coefficients CY, Cu and
where
c
v Y~ 1
Cr
~PV2S
L
Lv2sb
n =-
'n
N
T}pV2Sb
In order to make the treatment entirely nondimensional,
it is convenient to consider the ratios v/V, pb/2V, and
rb\2V rather than v, p, and r. For small values v/V
is equal to /3, where j3 is the angle of sideslip (in radians),
and pb\2V is the difference (in radians) between the
angle of attack at the center of gravity and the angle
of attack at the wing tip. Since the velocity at the
wing tip is F+r6/2 the value rb]2V is the ratio of the
portion of the velocity at the tip due to rotation to the
velocity at the center of gravity. Expressed in this
way, the lateral-force coefficient due to lateral motion is
\ s Y JGy , Pf> dCr , rb dCy
2 F 2 V
and similar expressions exist for A Ct and ACn.
. pb rb
Since dCY/d~y and dCY/dyy are small, they are gen¬
erally neglected, leaving the following aerodynamic
factors to be considered:
1. Those depending on sideslip: dCY/d(3, dCJdp, and
dCJdp.
• • • vb
2. Those depending on rolling velocity: dCi\d ~y and
dCJd^r-
rb
3. Those depending on yawing velocity: dCJd^y and
rb
dCJd^
In addition to the aerodynamic factors, others that
depend on the amount and the distribution of the mass
of the airplane must be considered. The important
mass factors, expressed nondimensionally, are p, b/kx,
and blkz- The relative density factor p is equal to
mJpSb and may be considered as being proportional to
the ratio of the mass of the airplane to the mass of air
influenced by it in traveling one chord length. Under
standard conditions p=
AERODYNAMIC FACTORS
Lateral force due to sideslip. — The rate of change of
lateral-force coefficient with angle of sideslip dCYJd /3 can
be accurately determined only by measurement in a
wind tunnel. Assuming the wind-tunnel data to have
been obtained in terms of angle of yaw \p in degrees, the
value of dCY/d(3 is —57.3 ( dCYld\p ), since (3 is in radians
and opposite in sign to i p. In wind-tunnel practice,
cross-wind force rather than lateral force is usually
measured. In such cases dCY/d(3 can be determined
from the relationship
dCY _dCc n
~d$ ~~dp~ D
(1)
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
299
(which follows from the fact that CY=Cc cos p
— CD sin P)-
Diehl gives (reference 2, pp. 254-255) an approxi¬
mate, empirical value of
dCc_
-0.12%
13
(2)
where h is the over-all length. This formula is useful
when wind-tunnel data are not available.
Rolling moment due to sideslip. — The rate of change
of rolling-moment coefficient with sideslip dCJdp must
also be measured in a wind tunnel if accurate values are
desired. Some systematic research has shown the effect
of dihedral and tip shape on the value of dCJdp for the
wing alone (reference 3) but very little is known about
the effect of fuselage interference. In certain experi¬
ments (data unpublished) a model having a wing with
no dihedral mounted in a high-wing position gave a
value of dCi/dp corresponding to 5° of positive dihedral
for the wing alone. The same model with the wing
mounted in a low-wing position gave a very erratic
'dCt
dPU
-. 025
i
I
i
if
iL
/ 1
V
\
\
\
\
A
/
h
1 1
’ i
i
\ V
6 v
\ \
\ \
\
s
1
(/
1
fl
i
i
\
\
\
It
X
1 1
sN.,
it
II l
n i
X-
Rec
1 1 1 n
lane
r
n
n .
/;
o-
— One-chord
tenqth —
funded ftp,
aximum ordi-~
7 ie points
7 mean tines—
in one plane.
1
nrr
l
1
re
1
//
1
i
nc
CL
■w
71 ax (
" Of
/
\ 7 /
I—PCY
□ -
- une-enu
tenqti
funded tip
aximum ore
7 te points
7 upper su
?ce in one
'anr- 1 1
ra
h
s'
-X "
/
/ /
— r
m
>
//-
r-
7*~
■Or " '
TCf
nc
or
7
fc
P3
-8 0 8 16
Angle of attack, cC ,
24 32
degrees
40
Figure 2.— Effect of tip shape on rate of change of rolling-moment coefficient with
sideslip.
curve of Ct against p. The slope of this curve indicated
zero dihedral effect at zero sideslip. The average di¬
hedral effect up to 30° sideslip corresponded, however,
to 4° negative dihedral. These tests were in the nature
ol preliminary tests and are unconfirmed but give ample
evidence of the need for similar additional research.
In the absence of wind-tunnel tests the value of
dCJdp for the wing alone may be computed from the
relationship
where {dCJdp)Y==0 is the value of dCJdp for the wing
without dihedral (see fig. 2) and T is the dihedral angle
in degrees. This formula was developed from data ob¬
tained with wings of aspect ratio 6 and with no taper or
sweepback (reference 3). Tapering the wing decreases
the effective dihedral but the decrease is somewhat less
than would be expected from the geometric proportions
because of the tendency of the wing lift to be evenly
distributed along the span. Sweepback is equivalent
to an increase in dihedral, particularly at high angles
of attack, but the effect is negligible for small amounts
of sweepback such as are used in conventional airplanes.
The wing, including interference effects, is the chief
source of rolling moment due to sideslip and other parts
ol the airplane can normally be neglected. Vertical-
fin area displaced from the longitudinal axis contributes
to dCJdp but the effect is usually small. If, in a par¬
ticular case, the effect upon the value of dCJdp is de¬
sired for parts having considerable projected side area,
it can lie computed from the relationship
dCj_SJ)zl>dC,.p ,,
• dp~~ S b dp
where Sp is the projected side area.
S, the wing area.
z„, the z coordinate of the center of pressure of
projected side area.
Cup, the absolute coefficient of force on the pro¬
jected side area.
In this equation dCLJdp must be estimated, taking
into account the shape of the part and the probable
interference effects.
Yawing moment due to sideslip. — The change of
yawing-moment coefficient with angle of sideslip
dCJdp depends principally upon the fuselage and the
vertical-tail area. The contributions of the landing
gear, interference effects, etc., are small and can gen¬
erally be neglected. The contribution of the wings
is also small and can be neglected at high or cruising
speeds but becomes of increasing importance at slower
speeds (reference 3); the effect due to the wing is an
increase in dCjdp. The center of pressure upon the
fuselage is normally well ahead of the center of gravity
so that the moment due to sideslip is such as to increase
the sideslip. The magnitude of this unstabilizing
tendency varies with the size and shape of the fuselage
but, on the average, is equal to about one-third flu1
stabilizing effect of the vertical tail surfaces.
For accurate stability calculations it is necessary that
dCJdp be obtained from wind-tunnel tests at several
angles of attack by the use of the relation
dCn/dp= — 57 .3 dCJdty. The value of dCn/dp can be
300
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(5)
calculated approximately from the relation
dC*_ l Si (dCit\ ssh
(W ~r]tb s V / 0 Sb
where -qt is the tail efficiency.
/, the distance from the center of gravity to
the rudder hinge.
L, the over-all length of the fuselage.
St, the area of the vertical tail surfaces.
Cl(, the absolute coefficient of force on the verti¬
cal tail surfaces.
Kf 3, an empirical constant (reference 2, p. 203).
Ss, the projected side area of the fuselage.
When using equation (5), it is necessary to estimate or
assume values of r]h clCuldfi, and K$. For modern
types of airplane rjt is about 0.80. The slope of the
tail-force curve dCLiJdfi depends on the aspect ratio of
the tail and to a certain extent upon the end-plate
effect of the fuselage and the horizontal surfaces. For
Figure 3.— Empirical factor for computing effect of fuselage on rate of change of
yawing-moment coefficient with sideslip (from fig. 98, reference 2).
= Sb / ilC„\
^ SJi \ dp / fuselage
conventional arrangements dChJd^ — 2.2 is a good
average value. Values of Kp as determined by Diehl
are given in figure 3. From this figure the value of Kp
can be directly determined from the ratio of the distance
of the center of gravity back of the nose j\ to the fuselage
length /2 and the ratio of the maximum fuselage depth d
to the fuselage length. In a number of computations
made to check the accuracy of formula (5) it was found
that the results were generally conservative, i. e., the
estimated value of dCn/dp was smaller than the meas¬
ured value. The difference arose in most cases from
the fact that the measured effect of the fuselage was
smaller than the estimated effect. The measured
effect of the fuselage apparently varies between zero
S l
and the effect calculated as depending upon the
details of nose shape and fuselage form.
Rolling moment due to rolling. — The rate of change
vb
of rolling-moment coefficient with rate of rolling dCt/d^y
arises from the change of angle of attack along the
wing. The increment in angle of attack at any span-
wise distance y from the center of gravity is py/V (in
radian measure), the increment at the tip being pb/ 2V.
If a uniform span wise distribution of lift and drag be
assumed, simple integration gives
dCt -(. dCJd* + CDw] )
(/A
2 V
G
where CD.„ is the drag coefficient of the wing alone.
If an elliptical distribution is assumed, integration gives
dCt ~(dCL/da+CDw)
d
pb
2 r
8
jpb
Actually, measured values of dCJd^y are considerably
smaller than either formula indicates because of the
tendency of the lift to equalize itself along the span
during the rotation.
In the absence of data obtained from some such device
yb
as a rolling balance, dOi/d^y can be taken as — 0.40
for wing arrangements such as are likely to be used on
conventional airplanes. A survey of test results
reveals values from —0.35 to —0.47 for plain wings
and values as high as —0.50 for wings with tip slots.
It would be expected that rounding the tips or tapering
the wings would reduce dCi/d^y> and such was found to
be the case for the tests reported in reference 3. On
the other hand, there is sufficient conflicting evidence to
indicate that an attempt to calculate dCi/d^y taking
into account tip shape and taper, is likely to give a
result no nearer the true value than is the assumed
average, —0.40.
Yawing moment due to rolling. — -The rate of change
of yawing-moment coefficient with rate of rolling
dCJd.ly arises from the same causes as does dCi/d^y
Simple integration gives for a rectangular- wing force
distribution
,0. -M201
pb
d
6
2V
and for an elliptical-wing force distribution gives
MS
d
dCn
pb
8
2 V
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
301
It will be noticed that the sign of the resulting value of
dCJd—y indicates that the wing being depressed by the
rolling motion is accelerated forward by the resulting
yawing moment. The mistake has frequently been
made (see reference 4) of assuming that the increase in
drag of the wing being depressed would result in a
yawing moment retarding that wing, that is, in a
positive value of dCJd—y • This reasoning fails to
take into account the forward inclination with increase
in angle of attack of the resultant-force vector relative
to an axis fixed in the wing.
Wind-tunnel data cannot ordinarily be obtained for
dCJd^r because there are but few existing balances
capable of measuring the yawing moment on a rolling
model. It is therefore necessary to rely on estimated
values of dCJd^y The empirical relationship
/ dCD,
dC,
iPb
da
')
(6)
d
2 V
has been found (reference 5) to give good agreement
with measured values below the stall, CL and dCDJda
having been obtained from force tests of the wing
alone; but there is need for further experimental data
on this factor.
Rolling moment due to yawing. — The rate of change
of rolling-moment coefficient with rate of yawing
vb
dCifdk) y results from the difference in velocity between
the wing tips, one wing tip having the velocity V-\-rb{2
and the other having the velocity V—rb/2. Simple
. . . vb
integration gives the value of dCifd^y as <7L/3 assuming
a rectangular distribution of lift or as CLj 4 assuming an
elliptical distribution. The rolling moment due to
yawing is of positive sign since a positive rate of yawing
gives a positive rolling moment.
rb
It wall ordinarily be impossible to measure dCifd0^
for a particular design because of lack of equipment.
Either special apparatus for oscillating the model or a
whirling arm equipped to measure rolling moments is
required. In the absence of experimental data, the
computed value must be used. Glauert states (refer¬
ence 6) that
dCi _ CL
, rb 4
a2V
(7)
gives nearly correct values for a rectangular wing.
Experimental results for the Bristol Fighter, a biplane
with substantially rectangular wings, however, gave
dCi/d^y as nearly CLI 3 (reference 7). Measured values
from tests of a biplane model reported in reference 8
were approximately equal to CJ4 for three wing combi¬
nations. It appears that the assumption that equation
(7) gives reasonable values is justified for wings with
faired or elliptical tips and slight to moderate taper.
Yawing moment due to yawing. — The rate of change
of yawing-moment coefficient due to yawing dCJd,
rb
2V
results from the change of velocity along the wing and
the change of sideslip velocity along the fuselage and
at the tail due to the yawing. On the basis of simple
rb
integration the portion of dCn/d^y- due to the wing is
— OdJ 3 for a rectangular distribution and —Cdj4 for
an elliptical distribution. In an extension of work by
rb
Wieselsberger, Glauert shows (reference 6) that dCJd-^y
is equal to —(0.33 (7£>0-f-0.043 CDi) for a rectangular
wing of normal aspect ratio and equal to —(0.25 CDQ-)r
0.33 CDi) for an elliptical wing, where CDq and CDf are
the profile and induced drags, respectively, for the
wing alone.
The change in angle of sideslip at the tail due to a
yawing velocity r is rl/V. The theoretical value for the
vertical tail is
dCn__9 P s, dOi.,
, rb It' S dp
d2V
It will be noted that both the wing and the tail contri-
vb
butions to dCJd^y are negative; that is, they are in the
sense to oppose the rotation.
It is unfortunate that experimental means of measur¬
ing dC„/d-
rb
2V
are not more commonly available.
As will
appear later in the report, an accurate knowledge of
vb • • •
dCJdjy is necessary for reasonable accuracy m esti¬
mating stability characteristics. The sparse experi¬
mental evidence concerning the value of this factor (see
references 7 and 8) indicates that there are, in some
cases, large interference effects. For one model tested
on a whirling arm the value of dCn/d,
rb
2V
for the fuselage
and tail surfaces combined was only one-tliird the value
for the tail surfaces alone. It is quite evident from such
data that computed values can be considered at best
302
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
only as rough approximations. With this limitation in
mind it appears that the most suitable formula for
dCJd— is
dCn_ l 2 st dOLt
j rb ' 3 Vt b2 S dp
d2V
(8)
and that there is no justification for refinements in the
formula.
MASS FACTORS
Relative density of airplane and air. — The relative
density of the airplane to the air is usually expressed as
n—mfpSb. From this definition p is t/4 times the ratio
of the mass of the airplane to the mass of air affected
by a monoplane wing (on the basis of accepted wing-
theory) in traveling a distance equal to the mean chord.
It thus appears that p is intimately tied up with the
performance characteristics of the airplane.
For standard conditions p-
ditions p may be expressed as
l3.l(W/S)p0 (qn
b p
where p0 is the standard mass density (0.002378 slug per
cubic foot) and p is the actual mass density. It appears
that p increases with wing loading and altitude and
decreases with span. The numerical value of p ranges
from 2 for large transports to 10 for pursuit airplanes
under standard conditions. It appears that large air¬
planes are dynamically similar to very lightly loaded
small airplanes, a transport with a span of 120 feet and
wing loading of 25 corresponding to an airplane of
30-foot span with a wing loading of G.25.
Ratio of wing span to radius of gyration about X
axis. — The ratio of the wing span to the radius of
gyration about the X axis, b/kx, has been determined
for 15 airplanes (reference 9) and has been found to
range from G.7 to 9.3, with 8.0 as an average value.
This ratio can be estimated with sufficient accuracy for
stability calculations. For preliminary estimates the
average value of 8.0 is satisfactory for conventional
types because, as will appear later, stability character¬
istics are not critically dependent upon the mass dis¬
tribution.
Ratio of wing span to radius of gyration about Z
axis.— The value of the ratio of the wing span to the
radius of gyration about the Z axis, bfkz, has been found
to vary from 5.1 to G.4, with 5.7 as an average value.
As in the case of bjkx , the average value is satisfactory
for most estimates of stability. The value of bjkz can
be estimated with sufficient accuracy for all stability
calculations from a weight analysis of the airplane.
STABILITY DERIVATIVES
In practice it has been found convenient to combine
the aerodynamic and mass factors that govern lateral-
stability characteristics into stability derivatives. These
derivatives take the following forms, one for each of the
aerodynamic factors:
1 dCY
!,r 2 dp
(by dCj
\kx/ dp
b '
\2 dCn
kz,
) dp
b'
V dCx
kx.
f d- &
a2V
b N
\2 dCn
\kz) jpb
2 V
(b\* dCi
\&.v/ i'b
2V
(b V dCn
h*/ <ipL
Physically these derivatives are, respectively, propor¬
tional to the linear or angular acceleration arising from
a unit angle of sideslip, a unit rolling velocity as ex¬
pressed by T>bj2V, or a unit yawing velocity as expressed
by rb/2V.
The stability derivatives include all the important
factors governing stability characteristics except p.
Since p occurs only in combination with nv and /„ and,
conversely, since these derivatives occur only in com¬
bination with p, the lateral-stability characteristics can
be completely expressed in terms ol the seven non-
dimensional quantities: yv, plv, pnv, lp, np, lr, and nr.
For preliminary estimates it will generally be suffi¬
ciently accurate to use the following values for the
stability derivatives:
yv=— 0.14
x =32^
'• dp
11
10
JCn
v ^dp
Ip— ~ G.4
np = — -0.5 Cl
lr=± Cl
O dCn
n r — 8— r
,rb
^2V
(10)
A rather small value of yv has been chosen in order to
be conservative. Stability characteristics calculated
with this small value of yv can be readily corrected to
correspond to a different yv, a fact which will be sub¬
sequently shown. The derivatives lp, np , and lT may
differ considerably from the foregoing values, particu-
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
303
larlv at angles of attack above that at which the lift-
curve slope begins to decrease. Fortunately the
stability characteristics are not greatly affected by
moderate variation in these particular factors. If
vb
possible, values of dCi/dfi , dCJdfi, and dCJd-^y should
be obtained by actual measurement. There is strong
reason for believing that, unless these factors are
accurately measured, a false impression of the accuracy
of the estimated stability characteristics may be ob¬
tained by refinements in estimating the other factors.
FORMULAS FOR ESTIMATING STABILITY
CHARACTERISTICS
Stability characteristics about which information, is
desired. — The preceding portion of this paper has dealt
with the various aerodynamic and mass factors that
govern stability characteristics. In the following para¬
graphs these factors will be grouped in relationships
which show the effects of the individual factors upon
the stability characteristics and from which these
characteristics can be quantitatively determined.
Instability can manifest itself either as a continuously
increasing divergence from the steady-flight condition
or as an oscillation of continuously increasing amplitude
about the steady-flight condition. On a logical basis
it appears that the questions answered by an estimation
of stability characteristics should be: (1) Will there exist
a tendency to diverge from the steady-flight condition?
(2) Will the oscillations started by a disturbance or by
the use of the controls damp out and, if so, how quickly?
(3) What will be the period of the lateral oscillations?
Approximate relationships to answer these questions
have been developed (see appendixes I and II) and are
presented in the following pages.
Basis for formulas. — The following formulas are
based on the classical theory of small oscillations first
applied to airplane dynamics by Bryan and developed
and expanded by Bairstow, Wilson, Glauert, and others
(references 10 to 13). A brief derivation of the formulas
is given in appendix I. The formulas presented repre¬
sent a first approximation to a semigraphical method of
accurately solving the stability biquadratic given by
the classical theory. This semigraphical method and
the approximation to it are explained in appendix II.
Formulas for predicting a divergence. — Divergence is
not possible in the normal-flight range (to which this
report is confined) if
fll Hfl/ylr (11)
and
(12)
Failure to meet the first of these conditions results in
“spiral divergence,” a form of divergence in which the
airplane tends to go into a spiral dive. Failure to meet
the second condition results in “directional divergence,”
in which the airplane tends to yaw away from the
direction of steady flight.
For purposes of approximate estimation using the
values for the derivatives given in equation (10),
equations (11) and (12) become
i(dcjdff)(dcjd~^>cL(dc,m (is)
and
- CL (dCt/dp) + 3 .2 (dCJd(3) >0 (14)
If the contributions of the wings, the fuselage, and
f'b
interference effects upon dCnjd 0y and upon dCn/d(3 are
neglected, equation (13) further simplifies to
-dCMO
C,b
8 i
(15)
This latter equation is, however, an oversimplification
for any but the most approximate analyses.
Formulas for estimating the damping of an oscilla¬
tion. — The number of seconds required for an oscillation
to damp to one-half its original amplitude is
where is the damping coefficient. The time to damp
to any other proportion of the original amplitude is
given by
T T log en
n~ ‘—0.693
(17)
where n is the desired proportion, such as % or /. To a
fairly close approximation (±15 percent)
In equation (18) the terms in the first pair of brackets
are those which make f' more negative, i. e., decrease
the time required for the oscillation to damp; the terms
in the second pair of brackets are those which make
G less negative.
If the values from equations (10) are used, equation
(18) becomes
304
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(lCn \
Since 8 / - \ is small compared with 6.4 a further
db)
simplification is obtained by letting 8^ — — r-\, where
4/
it appears in the denominator, equal 0.84. On this basis
r'= -0.07
—0.14 G tJ — 1 .2
dO%/ dC„ \
Formula (20) will lead to fairly large errors if the air¬
plane departs very far from the average. The error is
roughly on a percentage basis so that, for small values
of damping approaching an undesirable condition, the
actual error is small.
Formulas for estimating the period of an oscillation.
The period, in seconds, of the lateral oscillation is
where \p' is the period coefficient. To a fairly close
approximation \p' is given by
(— nT—lv )
substituting the values for the derivatives given in
equations (10) and letting s(—dCn/d^^\ = 0.S4: gives
P=
(23)
which is correct for the conventional airplane within
±20 percent.
CHARTS FOR ESTIMATING STABILITY
CHARACTERISTICS
Explanation of charts. — A series of 22 charts for use
in rapid estimation of stability characteristics are given
in figures 4 to 25. In these charts the damping and
the period of lateral oscillations are given by curves of
Tf-y/WJS= constant and of Pj-y/W/S— constant plotted
with —ndC^Jdfi as abscissas and ixdCnJdd as ordinates.
The limits to the region within which both spiral and
static directional stability exist are indicated by straight
lines representing zero spiral stability and zero direc¬
tional stability, respectively. The rates of convergence
or divergence are not given.
vb
The charts cover values of f±(0.2 to 2.0) and dCJd^y
(—0.030 to —0.252) likely to occur in practice with
conventional airplanes.
Each chart covers values of — /idCildfi from 0 to 0.5
and of ndCJdp from —0.05 to 0.3. These ranges are
sufficiently large for most conventional airplanes.
Some extrapolation is permissible in particular cases
without much loss of accuracy other than that due to
the fundamental weakness of increasing inaccuracy as
the damping becomes large.
These charts are based on equations (13), (14), (19),
and (23) and are therefore approximations to the same
extent as the equations. They are intended principally
for use in rapid estimates in design and show fairly
. > . vb
accurately the relative effects of changes in CL, dOnfd—y)
iddCiJdp, and ndCn!d(3. Being based on average values
of dCy/dd, dOJd^y, dCn/d dCt/d~,b/kx, and bjkz,
they cannot be used to determine the effect of changes
in these factors. The charts should not be used where
very accurate values are desired. On the other hand,
there is little justification for using a more accurate
method unless measured values of the various aerody¬
namic factors are available. If dCY/dp is known to
be much larger than —0.28, as, for example, in the case
of an airplane with a split flap at a high angle of attack,
correction for the damping can be made by the pro¬
cedure given in the following section.
Method of using charts.— In order to use the charts
the following data are needed:
W/S, wing loading.
b, wing span.
CL, lift coefficient.
dCi/dfi, rate of change of rolling-moment coefficient
with sideslip, per radian.
dCJdp, rate of change of yawing-moment coefficient
with sideslip, per radian.
. , ,.rb rate of change of yawing-moment coefficient
( 'nl 2y’ with rate of yawing, per unit of rbJ2V.
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
305
Figure 4.
Figure 5.
/'
Cl= 0.2 dCnld—^ -0.060
Figure 6.
Cl— 0.2
dCJdgp' - 0.075
Figure 7.
Figures 4 to 9.— Lateral-stability charts.
306
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Cl =0.8 d Cn/d-^y= — 0.054
Figure 10.
Cl = 0.8 dC„ld~ - 0.072
Figure 11.
Figure 14. Figure 15.
Figures 10 to 15.— Lateral-stability charts.
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
307
Figure 18. Figure 19.
Cl = 2.0 dC„ld~ =-0.108
Figure 21.
Figures 16 to 21,— Lateral-stability charts.
308
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 23.
Figure 25.
Figures 22 to 25. — Lateral-stability charts.
W/S= 16 lb./sq. ft.
6=42 ft. C/,= 0.2
dC„ld.j^r=- 0.060
Figure 26.— Special case of lateral-stability chart
AN ANALYSIS OF LATERAL STABILITY IN POWER-OFF FLIGHT
309
From these data, values of —ydCi/dp and ndCJdp
can be readily determined since n — (standard
conditions).
In general, the value of CL to represent a particular
range of flight conditions can be chosen as 0.2, 0.8, 1.4,
or 2.0. It will be necessary in most cases, however, to
rb
interpolate between two charts for the value of dCJd^y-
Any point given by —ndCt/dp, ndCJdp represents a
value of Pf-y/W/S and a value of TJ-y/W/S. The
period and the time to damp to one-half amplitude are
readily obtained by multiplying these values by V W/S.
The location of the point —/xdCPdp, ndCn/dp also
indicates whether there will be a tendency to diverge.
The charts are computed for standard conditions.
They can be easily applied to a study of stability at alti¬
tude by substituting the value (0.00238/p) W/S for
W/S wherever W/S occurs in the computations.
Correction to a different value of dGy/dp may be
readily made as follows: Compute p for dCy/dp~ — 0.28,
i.e., yv=— 0.14, from the relation p — — 0.3 1 3 WJS)C,._
Add to this value of p the quantity ^(0.28 -\-dCY/dp) to
obtain the corrected value of p. Calculate the corrected
value of T/-yjWfS using the corrected value of p.
in cases where a large number of estimates are to be
made for a given pair of values of W/S and b, it will
sometimes be convenient to convert the charts to read
directly in terms of —dCi/dp, dCn/dp, P, and T. This
conversion can readily be accomplished without re¬
drawing the chart by changing the constants. Figure 2G
represents figure 6 converted to read directly in the
desired quantities for an airplane having 1F/*S'=16
pounds per square foot and b— 42 feet.
Example of use of charts. — It is assumed that the
lateral-stability characteristics throughout the normal-
flight range are desired for a 5,000-pound airplane having
a wing loading of 1G pounds per square foot and a span
of 42 feet. Values of dCnfd\p and dC pip are available
from wind-tunnel tests. Values of dCn/d—y must be
estimated. The airplane is a modern type with a fairly
high top speed and is equipped with split flaps. Flaps
were considered to be down at CL~ 2.0 but up at
Cj~ 0.2, 0.8, and 1.4.
The stability characteristics will be estimated for
each of the CL values of 0.2, 0.8, 1.4, and 2.0. Values of
~ndCi/dft and ndCn/dp are determined at each value of
Cl from the relationships
and
-^(7,/rfff=13'X*16X57.3 X (dCJdf)
ndCM = X 57.3 X (—dOJdip)
,rb
alues of dCn/d^y are determined from the relationship
dCH/d
rb
2V
J2 St dCLt
“b2 S dp
where CDw is taken from wind-tunnel tests of a similar
wing, l/b and St/S are dimensional characteristics of
the airplane, and dCLt/dp is estimated using the
relationship
dC,t
dp
o.o
~ 9
where bt is the height of the vertical tail surface. The
rb
values of CDw, dCn/d0y, — ixdCJdp , and ndCJdp are as
follows:
C -L
C D u>
rb
dCn/d jp:
— MdCi/dP
fid CM 9
0.2
0.008
-0. 051
0. 20
0. 180
.8
.025
-. 057
.25
. 180
1. 4
.070
-. 072
.45
. 165
2.0
. 400
-. 182
. 55
. 130
From the various charts, values of T and P are de¬
termined, interpolations and extrapolations being made
where necessary. The values of the stability charac¬
teristics at each value of CL follow.
Cl
T
(sec.)
P
(sec.)
Divergence
0.2 •
2. 1
3. 0
None.
.8
3. 1
5. 5
Spiral.
1. 4
3. 1
5.8
Do.
2.0
1 2.2
• 6.4
None.
1 Correction for the increase in dCr/di 3 due to the high drag gives the corrected
value of Tas 1.3 seconds.
EFFECT OF THE GOVERNING FACTORS ON THE
STABILITY CHARACTERISTICS
AERODYNAMIC FACTORS
lateral force due to sideslip. — The lateral force due
to sideslip is small, in general, but beneficial in its
effect upon stability characteristics. As appears
in equation (18), dCyfdp adds directly to the damp¬
ing coefficient, Ap = %AdCy/dp. For the value of
dCy/dp=—J^28, Ap = — 0.07, which is sufficient to
damp the lateral oscillation to one-half amplitude in
8 seconds for an airplane with a wing loading of 1G
Hying at 17G miles per hour. The effects of dCy/dp
on the period and on the tendency to diverge are
negligible.
Rolling moment due to sideslip. — The rate of change
of rolling-moment coefficient with sideslip plays a great
part in determining the stability characteristics, as is
apparent from a glance at the charts of figures 4 to
25. It is necessary for stability that dCi/dp be negative;
the term ~ dCi/dp will be used, as in the charts, for
simplicity in discussion.
310
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Increasing —dCi/dfi increases the range of values of
dCJd(3 within which there is no divergence, there being
less likelihood of either spiral divergence or directional
divergence as —dCi/dfi is increased. Increasing —dCi/dp
increases the time for an oscillation to damp and short¬
ens the period. These effects are sufficiently small to
be of no practical importance at high speeds but are
appreciable at low speeds.
Yawing moment due to sideslip. — From the con¬
siderations of tendency toward divergence the value of
dCn/dp should be small and positive. Too large a
positive value of dCnJdp results in spiral divergence.
Too large a negative value will lead to undamped
lateral oscillations as indicated by the curve of
T/ ^(W/S) = co (oscillatory divergence) or to direc¬
tional divergence. The range of permissible values of
dCn/dfi is quite narrow for small values of —dCtI</ ft and
- dCJd
Increasing dCn/d(3 increases the damping and shortens
the period of the lateral oscillations. The effect upon
the period is very pronounced, particularly at small
values of the lift coefficient corresponding to cruising
and high speeds, as is especially apparent in equation (23)
where
0.146
P=
3.2
( dO t/d (3) T (j-dCJdfi
It appears that for CTj= 0.2 the effect of dCn/d(3 upon
the period has 16 times the effect of — dCi/dfi. The
effect upon T is less pronounced. It is of interest to
note that the theory indicates stability with dCn/dp
rb
zero or slightly negative if dCY/dp and dCJd.jy are
moderate or large.
Rolling moment due to rolling. — Differences in the
value of dCi/d^y of the order of those likely to exist
between conventional airplanes in the normal-flight
range have but slight effect upon the tendency toward
divergence or the oscillatory characteristics. This fact
tends to justify the use of an average value for this
factor in equations (20) and (23) and in the charts.
I'he small effects occurring are such that increasing
dCi/dijjf decreases the time required to damp, in
general, and increases the period.
vb
Near the stall dCi/d^y changes sign and tends to
result in violent instability. This report does not deal
with stability near the stall, which is amply discussed
in references 14, 15, and 16.
Yawing moment due to rolling. — As is the case for
dCi/d^jf) differences in dCn/d~y likely to exist in
practice have comparatively slight effect upon the
stability characteristics below the stall. Increasing
7)b
dCn/d-^y may either increase or decrease T, depending
upon the magnitudes of other quantities, and increases
P slightly. Here again the selection of an average
value for this factor seems justified. Near the stall
vb
dCJd^y changes sign and becomes an important
factor in producing instability.
Rolling moment due to yawing. — The rolling moment
due to yawing is chiefly of importance in connection
with the likelihood of spiral divergence. Increasing
dC\/d^ decreases the range of values of dCnfdfi for
which spiral convergence exists for a given set of
values of —dCj/dft and dCJd—y • Increasing dCJd ^
generally decreases T but has no noticeable effect upon
P or the likelihood of directional divergence.
Yawing moment due to yawing. — Increasing dCn/d~y
increases the permissible range of values of dCn/dfi for
spiral convergence and decreases the time required for
the oscillation to damp to one-lialf amplitude. It is
apparent from equations (20) and (13) and from the
charts that an accurate knowledge of dCJd~y is
essential to accurate calculations of T and of the
limiting values of dCn/d(3 within which spiral conver-
vb
gence exists. On the other hand, dCn/d-^y has only a
very slight effect upon the directional convergence
or upon the period of the oscillations.
MASS FACTORS
Relative density of airplane to air. — The relative
density p has no effect upon the likelihood of either
spiral or directional convergence. Its effect upon the
period and damping of the lateral oscillation can best
be understood by considering the separate effects of the
factors which determine p, namely W/S, b, and p.
Since a decrease in p has precisely the same effect as
an increase in W/S, the effects of altitude are the same
as the effects of increasing the wing loading and will
therefore not be discussed separately.
The effect of wing loading upon the time required to
damp the oscillation to one-half amplitude can best be
deduced from equations (16) and (20). From equa¬
tion (20) it appears that if, for the case at hand
is greater than 0.3 (— dCi/dfi ), then
increasing W/S (since p is proportional to W/S) will
make greater in the negative sense. This will be the
case only for very small values of — dCi/d(3 . In gen¬
eral, therefore, increasing W/S will increase T both by
decreasing S and by increasing the numerator in the
relationship
T
-0.313 i/(W/S)CL
f'
311
AN ANALYSIS 0I< LATERAL STABILITY IN POWER-OFF FLIGHT
On the other hand, wing loading has no appreciable
effect upon the period, at a given CL, as is apparent from
equation (23).
From the charts it appears that, since increasing b
decreases m dCJdfi and —isdCi/dfi, increasing the span
will decrease the time required to damp the oscillations
over most of the range of values of the parameters. As
pointed out in the preceding paragraph, the effect de¬
pends upon the relative magnitudes of dCJdfi, dCn/d~y>
and —dCi/d(3. Only in the case of very small values of
— dCifdp , will increasing the span increase T. For prac¬
tical purposes the period of the lateral oscillation is
proportional to the square root of the span, as is shown
by equation (23).
Ratio of wing span to radius of gyration about X
axis. — In the discussion of the effects of changing:
O O
b it was assumed that the ratios b/kx and b/kz were kept
constant. The effects of changing these ratios can be
most readily explained on the basis of keeping b
constant.
The value of kx has no effect upon either spiral or
directional convergence. Although not readily appar¬
ent in equations (18) and (22), increasing kx results in
small increases in T and P. There is, however, no
justification for extensive labor to determine kx accu¬
rately in the absence of accurate data on all the aero¬
dynamic factors.
Ratio of wing span to radius of gyration about Z
axis. — The effects of increasing kz are similar to the
effects of increasing kx. It has a slight but unimportant
effect upon directional convergence. Its effect upon
the period is greater than the effect of increasing kx, but
not great enough to be of practical importance in most
cases.
GENERAL COMMENTS
The present state of knowledge does not justify
positive assertions as to the desirability of any given
set of stability characteristics. Very little has been
done to determine quantitatively the stability charac¬
teristics that result in the most satisfactory riding and
handling characteristics. Such research (reference 17)
has given more or less negative results, at least with
respect to the period and the damping of oscillations.
It is definitely known, however, that very great instabil¬
ity, such as that at the stall, and very great stability
are both undesirable. There is strong reason to believe
that any tendency to diverge is undesirable but that,
if such a tendency is of small magnitude, it will not
seriously inconvenience the pilot.
When the foregoing facts are taken into considera¬
tion, it seems desirable that for airplanes designed for
most purposes, excepting machines intended as pur¬
suits, fighters, or for acrobatics, there should be no
38548 — 38 - 21
tendency to diverge, oscillations should be moderately
to heavily damped, and the period of the oscillations
should be as long as practicable. It is believed that
such characteristics will require a minimum of effort
from the pilot and will result in a maximum of passenger
comfort.
Reference to the charts of figures 4 to 25 reveals that
these characteristics can be attained only by making
dCJdp small while keeping dCJd^y and dCY/d(3 large.
borne additional advantage is gained by keeping
— dCi/dfi small, particularly at high angles of attack.
Probably the best value of —dClldfi is from small to
moderate, the moderate values giving more pronounced
spiral and directional convergence. The best method
of keeping dCn/d |3 small while retaining large values of
fb
dCJd^y and dCY/d(3 appears to be the use of a fuselage
giving an unstable yawing moment of rather large
magnitude. The unstabilizing effect of the fuselage
depends on its length, breadth, the distance of the
center of gravity from the nose, and on the shape.
The shape of the fuselage, and possibly interference
effects, play an important part, which can be deter¬
mined accurately only by wind-tunnel tests. A large
value of l tends to make dCJd^y large and a large,
deep fuselage tends to give a large value of dCY/d(3.
The dihedral of the wings can he adjusted to bring
dCddf3 to the desired value but here again, with
present knowledge, it is necessary to make wind-tunnel
tests.
Although control is outside the intended scope of
this paper, it should be pointed out that appearance of
instability may, under certain circumstances, be brought
about by the influence of the controls. The two most
common instances are that of directional divergence
arising out of an attempt to hold the wings level witli
conventional ailerons, the rudder being held neutral;
and that of increasing or poorly damped oscillations
arising out of operation of the rudder in improper
phase relationship to the change in attitude of the
airplane. The directional divergence is caused by the
adverse yaw of the ailerons and can be avoided by re¬
ducing the adverse yaw, by increasing dCn/dp, or by
holding the ailerons neutral and allowing the airplane
to roll. The increasing oscillations are most likely to
occur when the natural period of the airplane is short
and when the rudder is operated in such a manner as to
prevent yawing. They can be avoided by holding the
rudder neutral or by operating it in such a manner as
to produce sideslip opposing the roll, i. e., by trying to
hold the wings level rather than by trying to prevent
yawing.
312
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
SUGGESTIONS FOR FUTURE STUDY
A systematic correlation of stability characteristics
with riding and handling qualities is needed. It is
possible that these qualities are more directly related
to certain of the governing factors than to the tendency
to diverge or to the characteristics of the oscillations;
investigations should be conducted with this possi¬
bility in mind.
There is need for adequate comparison between com¬
puted values and measured values of stability char¬
acteristics as a check upon the accuracy and validity
of the mathematical treatment.
At present some of the aerodynamic governing factors
cannot be estimated with assurance. A great deal of
systematic study will be necessary to provide sufficient
data for the formulation of satisfactory empirical con¬
stants to be used in estimating these factors.
In this report no consideration has been given to the
effect of power on the lateral stability. This problem
should be the subject of a study sufficiently thorough to
reveal the effects of power on the stability derivatives
and upon the mathematical treatment necessary to
estimate the stability characteristics.
More satisfactory means of measuring the separate
aerodynamic factors and also the final stability char¬
acteristics of models are necessary for rapid progress.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley I ield, Va., November 17, 1936.
DERIVATION OF FORMULAS
APPENDIX I
The theory of small oscillations. — The theory of
small oscillations was first applied by Bryan to the
dynamics of mechanical flight (reference 10). On the
assumption that the direction and magnitude of changes
in the aerodynamic characteristics due to changes in
motion from the steady-flight condition are known,
equations of motion in unsteady flight are written for
the case of small deviations from the steady condition,
one equation for each of the degrees of freedom of the
motion. Simultaneous solution of the equations gives
values that describe the motion of the airplane after a
disturbance.
Assumptions in the application of the theory. — In
the application of the theory of small oscillations to
quantitative estimations of stability characteristics, a
number of assumptions are necessary in order that the
mathematics may not be too involved and the compu¬
tations too extensive for practical applications. The
primary assumptions are as follows:
(a) The combined aerodynamic effect of two or more
components of motion is assumed equal to the alge¬
braic sum of the separate effects of the individual
components.
( b ) The changes in aerodynamic forces and moments
due to a deviation are assumed proportional to the
deviation, i. e., the slopes clCi/dp, dCi/d^yt etc., are
assumed to be constants.
(c) The lateral motion involving p, q, and r is as¬
sumed to be independent of the longitudinal motion, i. e.,
the machine is assumed to be symmetrical.
(d) Secondary effects such as those involving the
products of two or more small quantities are neglected.
( e ) The values of the aerodynamic factors are
assumed to be unaffected by the linear and angular
accelerations.
Equations of lateral motion. — The equations of
lateral motion will be written for the axes shown in
figure 1 using the symbols and notation given in
appendix III and on the report covers. The A^ axis
is taken in the direction of the relative wind during
the steady-flight condition. The axes are assumed
fixed in the airplane. During steady flight,
Y=L= N=0
v= p— r =0
u=V
After a disturbance,
dY dY . dY .
+ B sin \f/ sin y — m ^ + m r u
dL ,
vTv+V
dL , dL
dj>+r 7b
dN . dN . dN . dr
rW^dI>+rdF = mk*\it
p—dfp/dt
r=d\pjdt
(25)
It is assumed in these equations that the principal
axes of inertia are coincident with the reference axes,
which is not true in the general case. A number of
supplementary calculations made as part of the study
leading up to this report have indicated, however,
that to neglect the angularity of the principal axes to
the reference axes will not introduce serious error in
the normal-flight range and will give slightly conserv¬
ative results. Consequently, the terms including the
product of inertia were omitted to make the equations
as simple ns possible.
Since dY/dp and dYjdr are small, they are generally
neglected. For the small deviations considered, u may
be taken equal to the steady-fliglit velocity V and the
sines of the angles of roll and yaw may be replaced by
the angles themselves. Since in power-off flight the
lift is equal to IF cos y and the lift times the tangent of
the angle of glide is equal to IF sin y, the first of the fore¬
going equations v ill be rewritten,
dY
X>X (lift) + tAX (lift) X tan y
dv T -r
The equations of equilibrium finally become,
— +0 (lift) + (lift) tan y-^mV
dL . d<t> dL d24> 7 2 . dL dL, _
v7k + dt^rWmkx' + dt Tr=°
dN . d(f> dl N , d\p dN d2L , ,
vHi+7t -di+dilF~Wmkz=0
Replacing
~ by b pV 2 S
dv -1 2 dv
(Lift) by i PV*S CL
0
(26)
313
314
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
clL 1 rroo » d(L i
Hvhy2f’l'Sb^’ etC'
dl\ , 1 irjo ldCn
~dv by 2pV Sblh’ etc'
m .
pSb by M
m
-7 by
PS\
dCy , 1 dCy
~ch by V ~W
Writing in determinant form and simplifying gives,
dv CL CL , x . di/
Vyv~Tdt ~2^ Y (tanT) ^ —
f] A\ A\ fl i/y
; d(f) o?20
lpTdi~T~W
i drp
l'Tdi
v pnB
where ?/„=
I
dcf)
UpTdi
1
2 rf/3
1 / 6 Ydtf,
dp
1 / 6 Y dCn
P
nTr
dip ,d2\p
dt T dt 2
— 0 (27)
=1 ("AY
0 2 \kj
1 / 6 V </<
W'~2U) d
, 1 / 6 Y dCt
t /> ^
' 4V.A-.v7 ,p4
d2V
1 / 6 YrfC,
a2V
71 v ~ 4 U*
,1/6 V <K7,
r"4 VW
a2V
1 / 6 Y dCn
, rb
( 2V
- 4 (0
Substituting r0 ex* for r, <£0 cxz for <j>, etc., and simplify¬
ing give
yv — t x
dv
pTl v
CL
Ipt\ — T" A”
npr\
tan 7 — r\
nrr\ — r2\2
=0
(28)
which can be expressed as
A(X,)5+5(X')4+C'(X')3+^(Y)2+S(Y)=0 (29)
where,
X' = rX
.4 = 1
5 — 1/ d Hr Ap
0= /p?ir — /rHp + y v (lp + n r) + pn t
D=yv(lrnp— lpnT)+dv(nP— y)— tan 7+4
(7
E=p-^ (l»nr lTYid) Y M 2 tan 'y(lpiiv
The solution X' = 0 is readily apparent in equation
(29) and results from the fact that the airplane has no
inherent tendency to return to any fixed compass course,
being, as the solution shows, neutrally stable in that
respect. This solution, X' = 0, is generally neglected
and the lateral-stability characteristics are considered
as those given by the biquadratic
/l(X')4+il(X')3+C,(X/)2+T>(X') + ^=0 (30)
The deviation of each one of the components of the
lateral motion varies with time according to the rela¬
tion,
v, p, or r=C]_eKlt-\-C2eK2l-\-CzeK'it +
where X., X2, X3, and X* are the four roots of the bi¬
quadratic. In lateral motion the constants B, C, D,
and E are generally such that there are one pair of real
roots and one pair of conjugate complex roots indicating
motion of the type,
v, p, or r=C5e^( cos \f/t— C6) -j-C3eX3t4- C^1
where f and / are the real and imaginary parts, respec¬
tively, of the conjugate roots. This motion represents
an oscillation superimposed upon two rates of con¬
vergence (or divergence) . It is evident that for stability
$*, X3, and X4 must be real and negative so that the
values of v, p, and r will reduce to zero. In order that
the real parts of the roots shall all be negative it is
necessary and sufficient that B, C, D, E, and
(BCD—D2—B2E) each be positive. In order to
determine the rates of convergence and the damping
and period of the oscillation, it is necessary to solve the
biquadratic. A convenient semigrapliical method of
solving stability biquadratics was pointed out in
reference I and is described in detail in appendix II.
APPENDIX II
SOLUTION OF STABILITY BIQUADRATIC
Semigraphical method of solving biquadratics. — The
biquadratic
A4+£ \3-f C\2+D\+ E= G
can be expressed as
(X2T^i^“h^i) “h®2^T^2) ~ 0 (31)
from which
are roots of the general equation. It appears that
i?=a1+a2
C= a 1Q0 -f- b\ T b2
D—a1b2Jra2bi
E=bxb2
Eliminating values of a2 and b2,
a
and
bx2B-bxD
ai~ b2—E
(33)
■=f±V(f )2~c+b'+bi (34)
(35)
Note that, if t}ie minus sign in equation (34) is chosen
for d\ , the plus sign will correspond to a2.
Values of cq and bx that will satisfy these equations
separately are plotted on charts having values of a
as abscissas and values of b as ordinates. The inter¬
section of the resulting curves represents values of ax
and &i that satisfy both equations. There are two
intersections in the general case, one corresponding to
eq and 5,, the other to a2 and b2. Ordinarily it is more
convenient to find one of the intersections by plotting
and to solve for the remaining values by the use of
equations (33).
Figure 27 gives a solution of a typical stability bi¬
quadratic and illustrates the use of this semigraphical
method. For most cases time can be saved in locating
the intersection by letting ax equal zero in equation (35),
thus determining the intersection of the plot of equa¬
tion (35) with the b axis. The resulting value of bx
when substituted in equation (34) will give an approx¬
imate value for cq. The final values can then be de¬
termined as accurately as desired by locating the point
of intersection of the curves. This method has been
applied to several hundred solutions of stability bi¬
quadratics in the course of the study leading up to this
report and has been found to be very satisfactory,
particularly so if systematic changes in factors are being
studied.
a
Figure 27.— A semigraphical method of solving stability biquadratics. Solution of
biquadratic:
X4+5.52X3+5.36Xs+13.90X+0.74 = (X2+fliX+6i)(\2+«2X+62)— 0
From intersection of curves
From equations (33)
o,=0.46; bi=2.72
a2= 5.52-0.46=5.06; 62= 0.74/2. 72 = 0.027
From Xs+0.46X+2.72 =0, X = -0.23±i 1.0
From XH-5.06X+0.027 = 0,X=-5.05
x=— 0.01
Approximate formulas for the damping and the
period of the oscillation. — As was stated in the preceding
paragraph, an approximate value of 6, can be found by
substituting flq=0 in equation (35) giving
(36)
Substitution of this value of bx in equation (34) gives
the approximate value for eq of
B,
«1=9 ±
EB
D
(37)
This latter equation can be further simplified without
loss
\ of accuracy by
removing the radical
and assuming
o
01“ =
= 0. The resulting equation for eq is
ODE
a'~B B2 D
(38)
Since
\ =
-W (!)■-*■
=
r'ii*'
(39)
f' =
2
(40)
315
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
316
Since (f ) is normally small compared with bu it is
sufficiently accurate for practical purposes to put
(40
From equations (38) and (36),
n /n
(42)
,, _ i rg_D_E-]
i ~~ 2\_ B B2 D_\
/==V
D
B
(43)
Supplementary study lias indicated that further simpli¬
fication can be had with but slight loss in accuracy by
neglecting values of yv in the expression for B and D
and neglecting tan y in the expression for D and E
giving
B——nr—lp
C=lpnr — l/rip + y a {Ip + nr) + pn v
D=ixll(np—^fSj — n n ,lp
C
E = p „ (/ pii r lrn r)
(44)
Substituting these values in equations (42) and (43)
and simplifying where possible gives
f 9
I l-pflf IpPp i M^r( Hr)
-y'+(-n,-lt) + (-nr-l,Y
I OBr'Hv
and
2lv(np-^-2nvlp
pi v [lip 2~ ^ E jJ vHt
(— nT—lp )2 2lv[np — ~^~2nvIp
\y j pl v[llp P'llJ'p
V (— nr—lp )
(45)
(46)
The time in seconds to damp to one-half amplitude is
given by
loge 0.5 — 0.693
T=
(since f'=Tf).
r
r
Expressed in more convenient form, this equation
becomes
T
_-°-3i:iV(f)^ ^
f'
The period in seconds of the lateral oscillation is
27T _ 2 7TT
J~~V
Approximate formulas for the convergence char¬
acteristics. — Since <q is small, a2 is approximately equal
to B.
Letting a2=B
as the solution for the pair of the roots of the stability
biquadratics corresponding to the convergence charac¬
teristics. Since B is always positive and large in the
normal-flight range, it appears that this equation repre¬
sents two convergences if EBJD is positive and less than
(/i/2)2, a heavily damped oscillation if EB/D is positive
and greater than (/i/2)2, a divergence and a convergence
if EBjD is negative and less than (BJ 2)2, and two di¬
vergences if EBjD is negative and greater than (Z//2)2.
Instability is therefore possible if either E or D be¬
comes negative. For most cases E is small but may
be either positive or negative and D is positive and
large. These circumstances give the usual solution
of (49) as a large negative root approximately equal
to — B=nr-\-lp and a small root approximately equal
to — EJD.
In the usual case it is desired to know whether or
not there will be a divergence rather than to know the
rapidity of the convergence. For such a case it is
sufficient to know that
and
D> 0
£>0
By the use of the relationships of equations (44), these
conditions are represented by
i(np — ^j—nvlpy0
and
l pflr'E>En t
(50)
(51)
These equations neglect the effects of yB and tan y, a
procedure that is conservative for power-off flight.
APPENDIX III
SYMBOLS
X, Y, Z, axes of reference fixed in the airplane having
the origin at the center of gravity, the X
axis in the plane of symmetry and along
the relative wind in steady flight, the Y
axis perpendicular to the plane of sym¬
metry, and the Z axis in the plane of
symmetry and perpendicular to the X axis.
A', Y, Z, forces along the respective axes, X being
positive when directed forward, Y positive
when directed to the right, and Z positive
when directed downward.
L, M, N, moments about the X, Y, and Z axes, respec¬
tively, L being positive when it tends to
depress the right wing, M positive when it
tends to depress the tail, and N positive
when it tends to retard the right wing.
u, v, tv, components of linear velocity of the airplane
along the X, Y, and Z axes, respectively,
having the same positive directions as the
X, Y, and Z forces.
V, resultant velocity.
\), q, r, components of angular velocity about the X,
Y, and Z axes, respectively, having the
same positive directions as L, M, and N.
4>, d, \p, components of angular displacement from a
given attitude about the X, Y, and Z
axes, respectively.
a, angle between the relative wind on a plane
parallel to the plane of symmetry and the
wing chord, positive when corresponding
to positive rotation 0 of the airplane
relative to the wind.
d, angle between the relative wind and a plane
parallel to the plane of symmetry, equal to
sin 1
v_
V;
angle of sideslip in radians.
7, angle of flight path to horizontal, positive in
a climb.
T, dihedral angle, degrees.
Y
C y=~c h coefficient of lateral force.
qS
p —
< i —
C —
L
qSb ’
N
qSb’
Co
C,
coefficient of rolling moment.
coefficient of yawing moment.
coefficient of drag for the wing alone,
coefficient of force on projected side area,
coefficient of force on vertical-tail area.
S, wing area.
Ss, projected side area of fuselage.
St, vertical-tail area.
Sp, projected side area.
d , maximum depth of fuselage.
y, spanwise distance from plane of symmetry.
xx, distance from fuselage nose to center of
gravity.
I, distance from center of gravity to rudder
hinge.
lu over-all length.
l2, over-all length of fuselage.
Po, mass density of air under standard condi¬
tions.
P, mass density of air under condition of flight.
t, subscript denoting vertical tail surfaces.
bt, height of vertical tail.
Vt, tail efficiency.
zp, the Z coordinate of the center of pressure of
projected side area.
Kp, empirical factor for estimating dCn/d(3 for
fuselage.
7YI
M = -or, relative density factor.
For standard atmosphere, /*= — —
Tfi b
T~~Xv~^y’ kmie conversion factor.
1 dC
yv= g nondimensional derivative of lateral force due
to sideslip.
C—Tjfrr') nondimensional derivative of rolling
moment due to sideslip.
nondimensional derivative of yawing
moment due to sideslip.
p~^(jx) nondunensional derivative of rolling
A/ d^jr moment due to rolling.
nondimensional derivative of yawing
2 d^y moment due to rolling.
n
Ur
1/6 \2dCi
■<t)
, > nondimensional derivative of rolling
dyy moment due to yawing.
1 / b \ 2 dC
. r~ ) —tt’ nondimensional derivative of yawing
dryy moment due to yawing.
B, C, D, E, coefficients of stability biquadratic.
318
REPORT NO. 589— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
x, v/ 1/
h — — = £± i\p = — ± t— > root of stability equation.
T T T
T, time for oscillation to decrease to one-
half amplitude, seconds.
rr —0.693
/=T~Xr
= -0M3^W[ SJCl (Standard a tmos-
^ phere).
P, period of oscillation, seconds.
2ttt
p=
r
^2.83 4(WJS)Cl (Standard atmos-
^ phere).
a, b, coefficients of stability quadratic.
REFERENCES
1. Zimmerman, Charles H.: An Analysis of Longitudinal Sta¬
bility in Power-Off Flight with Charts for Use in Design.
T. R. No. 521, N. A. C. A., 1935.
2. Diehl, Walter S.: Engineering Aerodynamics. The Ronald
Press Company (revised edition), 1936.
3. Shortal, Joseph A.: Effect of Tip Shape and Dihedral on
Lateral-Stability Characteristics. T. R. No. 548, N.
A. C. A., 1935.
4. Wilson, Edwin Bidwell: The Variation of Yawing Moment
Due to Rolling. T. R. No. 26, N. A. C. A., 1919.
5. Bradfield, F. B.: Lateral Control of Bristol Fighter at Low
Speeds. Measurement of Rolling and Yawing Moments
of Model Wings, Due to Rolling. R. & M. No. 787,
British A. R. C., 1922.
6. Glauert, H.: Calculation of the Rotary Derivatives Due to
Yawing for a Monoplane Wing. R. & M. No. 866, British
A. R. C., 1923.
7. Halliday, A. S.: Stability Derivatives of the Bristol Fighter.
R. & M. No. 1277, British A. R. C., 1930.
8. Halliday, A. S., and Burge, C. H.: Experiments on the
Whirling Arm. Yawing and Rolling Moments on the
Hornbill and Various Aerofoils Also Pressure Distribution
and Flow Tests on R. A. F. 15. R. & M. No. 1642, British
A. R. C., 1935.
9. Soule, Hartley A., and Miller, Marvel P.: The Experimental
Determination of the Moments of Inertia of Airplanes.
T. R. No. 467, N. A. C. A., 1933.
10. Bryan, G. H.: Stability in Aviation. MacMillan and Co.,
Ltd. (London), 1911.
11. Bairstow, Leonard: Applied Aerodynamics. Longmans,
Green and Co. (London), 1920.
12. Wilson, Edwin Bidwell: Aeronautics. John Wiley and Sons,
Inc., 1920.
13. Glauert, H.: A Non-Dimensional Form of the Stability
Equations of an Aeroplane. R. & M. No. 1093, British
A. R. C., 1927.
14. Weick, Fred E., and Jones, Robert T.: The Effect of Lateral
Controls in Producing Motion of an Airplane as Com¬
puted from Wind-Tunnel Data. T. R. No. 570, N. A.
C. A., 1936.
15. The Stability and Control Panel: The Lateral Control of
Stalled Aeroplanes. General Report by the Stability and
Control Panel. R. & M. No. 1000, British A. R. C., 1926.
16. Bryant, L. W., Jones, I. M. W., and Pawsey, G. L.: The
Lateral Stability of an Aeroplane Beyond the Stall. R. &
M. No. 1519, British A. R. C., 1933.
17. Soule, Hartley A.: Flight Measurements of the Dynamic
Longitudinal Stability of Several Airplanes and a Corre¬
lation of the Measurements with Pilots’ Observations of
Handling Characteristics. T. R. No. 578, N. A. C. A.,
1936.
REPORT No. 590
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
By H. A. Pearson
SUMMARY
Results are given of pressure-distribution measurements
made over two different horizontal tail surfaces and the
right wing cellule, including the slipstream area, of an
observation-type biplane. Measurements were also taken
of air speed, control-surface positions, control-stick forces,
angular velocities , and accelerations during various abrupt
maneuvers. These maneuvers consisted of push-downs
and pull-ups from level flight, dive pull-outs, and aileron
rolls with various thrust conditions.
The results from the pressure-distribution measurements
over the wing cellule are given on charts showing the varia¬
tion of individual rib coefficients with wing coefficients;
the data from the tail-surface pressure-distribution meas¬
urements are given mainly as total loads and moments.
These data are supplemented by time histories of the meas¬
ured quantities and isometric views of the rib pressure
distributions occurring in abrupt maneuvers.
The results indicate that there is little if any dissym¬
metry of load on the tail due to slipstream rotation and that
the up loads may be as much as the down loads. From the
results of the wing investigation it was found that the rela¬
tive efficiency of the wings depended upon the type of
maneuver.
INTRODUCTION
Following the completion of pressure-distribution
tests made of a PW-9 pursuit airplane in 1928 (reference
1), similar tests of an observation biplane were requested
by the Army Air Corps. The original object of this
request was to institute a program that would lead to
information on an observation type of airplane corre¬
sponding to the information already obtained on the
pursuit type. An 0-211 airplane was made available.
Pressure of other work at the N. A. C. A. laboratories,
however, delayed work on the rather extensive installa¬
tion of apparatus, and flight tests could not be started
until 1932.
Although the 0-2H airplane was by then an obso¬
lescent, type and although the results of other related
research projects had led to an improved understanding
of many questions concerning external loads and their
distribution on airplane structures, it was decided to
complete the tests of the 0-2 H because it was believed
that they would constitute a useful set of data with
which modern methods of computing loads and load
distribution might be compared.
The results are presented in a two-part paper, the
first part giving the results of tests made of two tail
surfaces and the second the results of an investigation
over the right wing cellule and slipstream area.
APPARATUS
Airplane. — The airplane used in these tests (figs. 1
and 2) was a standard Army 0-2 H observation airplane
with the following modifications: (1) The fabric covering
on the fuselage from just abaft the engine hood to
38548—38 - 22
Figure 1.— The 0-2H airplane.
319
320
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the rear of the observer’s cockpit was replaced by
thin duralumin sheets that could easily be removed;
(2) the original 9. 5-foot, propeller was replaced by a
10.5-foot propeller; and (3) a boom carrying a swiv¬
eling pitot head was attached to the interplane struts.
The two horizontal tail surfaces are shown in figures
3 (a) and 3 (b) and the wing surfaces are shown in
figure 4. These figures give the location of the pressure
points and other pertinent dimensions. Additional data
(b) Modified.
Figure 3.— Tail surfaces with pressure-rib and orifice locations.
concerning both the airplane and the various surfaces are
given in table I.
Pressure orifices and tubing. — The orifice and tubing
installation is much the same as that described in refer¬
ence 1. For the tail-surface investigation the metal
pressure tubes from both the elevator and the stabilizer
were brought out in bundles near the fuselage (fig. 5),
from which point they were connected by short lengths
Ribs D,E,K & L £
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN O 2H AIRPLANE IN FLIGHT
321
of rubber tubing to metal tubes leading directly to the
manometers. For the wing investigation the tubing
from the lower wing was carried through the wing root
to the manometers and that from the upper wing was
faired around the cabane struts and brought to the
manometers. The tubing from the aileron ribs was
grouped in small bundles, midway between the pressure
ribs, and was connected by short pieces of rubber tubing
to metal tubes within the wing.
Instruments. — Each pressure orifice was connected to
a pressure cell on either of two N. A. C. A. type 60
multiple recording manometers located in the observer’s
cockpit midway between the upper and lower longerons.
The pressure cells were similar to those of reference 1
Figure 5.— Tail-surface tubing installation
but were corrected for temperature effects by the method
given in reference 2.
In the tail-surface investigation the load distribu-
tion occurring over each tail surface was measured
during steady flight, dive pull-outs, and pull-ups from
level flight. For the steady-flight condition the fol¬
lowing standard N. A. C. A. photographically record¬
ing instruments were used: air-speed meter, control-
position recorder, control-force recorder, inclinometer,
and tachometer. For the pull-ups and pull-outs an
accelerometer and a turnmeter, both located near the
center of gravity of the airplane, were substituted for
the inclinometer and tachometer used in the steady
flights. All instruments were synchronized by an
N. A. C. A. timer incorporated into their circuit.
In the wing-cellule and slipstream investigations the
load distribution was measured in steady flight, push¬
downs and pull-ups from level flight, dive pull-outs,
and aileron rolls. With the exception of an additional
accelerometer mounted 18 inches in from the right wing
tip for the aileron rolls, the instruments were the same
as used for the tail-surface investigation.
I. PRESSURE-DISTRIBUTION TESTS OVER TWO SETS
OF HORIZONTAL TAIL SURFACES
METHOD
In the tests made of the modified tail (fig. 3 (b)),
resultant pressures were recorded at 74 points. The
remaining pressure cells were connected to wing ribs
for the purpose of correlating the tail-surface and wing
results. Subsequent tests showed this precaution to
be unnecessary as the various stabilizer and elevator
settings did not measurably affect the pressure distri¬
bution on the wing ribs. Consequently, in the series of
tests of the original tail (fig. 3 (a)), the full 120 pres¬
sure cells were used on the tail alone.
Steady dives. — In order to obtain information on
certain flap parameters, tail loads were measured dur¬
ing steady dives with the stabilizer in various settings.
For the most part, the effect of the slipstream was
minimized by running the tests near zero propeller
thrust. Several tests were made, however, with the
throttle fully closed and also with the throttle open to
a position corresponding to what was considered to be
a maximum safe engine speed. The method used to
obtain zero thrust was to compute the V/nD for zero
propeller thrust from an analysis of full-scale propeller
tests. The pilot was then instructed to dive at a cer¬
tain steady air speed and with a definite engine speed
before taking records. Actually, this procedure re¬
quired that the throttle be slightly opened.
In the tests of the modified tail, the stabilizer set¬
tings specified to the pilot were full nose heavy, full
tail heavy, and trim.1 Obviously, when trim was
specified, several settings in the range of adjustment
were possible depending upon the pilot’s “feel” and
the altitude at which he trimmed the airplane. This
procedure led to complications in the analysis of the
data owing to the number of variables involved. Con¬
sequently, in the tests of the original tail only three
stabilizer settings were used: The two extreme settings
and one midway between them.
With the exception noted, the test procedure for the
two tail surfaces was the same and consisted of steady
glides starting from 120 miles per hour and increasing
by increments of roughly 10 miles per hour up to the
maximum diving speed considered to be safe. The
pressures measured at each point were the algebraic
sum of those on the top and bottom of the airfoil sur¬
face (resultant pressures), no attempt being made to
separate them. Simultaneously with these measure¬
ments, air-speed, control-force, control-position, in¬
clinometer, and tachometer records were taken.
1 “Stabilizer set tail heavy” as used here means that the stabilizer is set so as to
make the tail seem heavy. From this definition the meaning of ‘‘trim” and ‘‘full
nose heavy” settings is readily deduced.
322
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The rib pressure-distribution curves for each tail rib
were mechanically integrated to obtain the load and the
moment of the load about the elevator-hinge center
line. The rib loads and moments were then plotted
against their span location and these curves, in turn,
were integrated for the total load and moment of the
tail. These results were then converted to tail load
center of pressure with respect to the hinge line and
finally to the moment exerted by the tail surfaces about
the center of gravity of the airplane. A similar pro¬
cedure was followed to obtain the load carried by the
elevator and its hinge moment. The velocity used in
all calculations for normal-force and liinge-moment
coefficients was that given by a swiveling air-speed
head located on a boom one wing chord length forward
of the leading edge of the upper wing (fig. 1).
Pull-ups. — Pressure measurements were taken in
abrupt pull-ups from steady level flight throughout
the speed range with various stabilizer settings. Several
graduated pull-ups from high-speed level flight and
several pull-outs from shallow dives were also made.
In these miscellaneous tests the stabilizer was set
to trim.
In addition to the pressure measurements taken in
the pull-up, records were also taken of the air speed,
normal acceleration, angular velocity, control position,
and control force. In most of the pull-up tests the
results were computed from the records for only the
time corresponding to the maximum down tail load.
For the purpose of showing time histories, however,
the results were in some cases computed for an interval
that included the initial tail load and the subsequent
maximum downward- and upward-acting tail loads.
The method by which total loads and moments
were obtained from point pressures is the same as that
p re vi o usly expl ain ed .
PRECISION
A number of possible sources of error are present and
may be listed as follows:
Individual pressure measurements may be incorrect
because of
(а) Orifices not flush with surface.
(б) Tube stopped or leaking.
(c) Lag in tube and diaphragm.
(< d ) Shrinkage of film.
(e) Changed pressure-cell calibrations due to
aging and temperature effects.
(/) Personal errors in plotting and reading
records.
(g) Excessive width and haziness of pressure
record line due to dust or oil on lens, small
rapid pressure fluctuations, or vibration.
Rib loads and moments may be incorrect because
of —
(a) False individual pressures due to above
errors.
(6) Errors in plotting.
(c) False fairing of curves due to insufficient
points.
(< d ) Integration errors.
(e) Error introduced by neglecting the fore¬
shortening of the chord line with a control
displacement. The resultant pressure at
each point was, in all cases, plotted normal
to the original chord line.
Sufficient checking was done to insure that errors in
the individual pressures arising from sources (a) to ( d )
were negligible in these tests. The error due to source
(e) was minimized by frequent calibrations and the use
of temperature-compensated pressure cells. Errors due
to (/) were practically eliminated by checking at all
phases of the work. The largest source of error in the
individual pressures is due to the haziness and width of
the lines on the pressure records. Generally, the
records taken in the dives were better in this respect
than those in the pull-ups; also, those farther out on the
tail were better than the ones close to the fuselage. The
widths of the record lines were in some cases, where the
deflections were small, so large as to make it impossible
to tell whether a small positive or negative pressure
existed. From the foregoing, it is obviously impossible
to express the accuracy of the individual pressure on a
percentage basis, since it varies with the amount of the
local pressure, location of the pressure point, and the
type of maneuver. The estimated maximum absolute
error in the individual pressures was no more than 3
pounds per square foot for the higli-range cells, which,
in general, were connected to orifices located near the
leading edges and close to the hinge center line. The
error in the low-range cells was estimated to be no more
than 1 pound per square foot. The low-range cells
were connected to orifices located near the middle of the
stabilizer ribs and at the trailing edges of the elevator.
The errors in rib loads due to source (e) were small
in the case of the dives since the elevator displacements
rarely exceeded 15°. In the abrupt pull-ups, however,
where the elevator may be deflected as much as 30°, the
error in the total tail load may he as much as 7 percent.
This error does not enter into the elevator loads or
moments.
The principal source of error in the rib-load curves
is known to be in the fairing of the curves. The magni¬
tude of this error varied with the type of pressure dis¬
tribution obtained. In the steady dives with the stab¬
ilizer in the full nose-heavy setting, the error in the tail
load due to fairing is believed to he a minimum and that
obtained with the stabilizer in the other extreme
position a maximum. In the nose-heavy case the
maximum error in the tail load at speeds above 150
miles per hour is probably no more than 25 pounds as
compared with GO pounds for the full tail-heavy position.
The maximum down tail loads occurring in the pull-ups
Moment about c.g., / b.-ft .
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
323
and pull-outs are estimated to be correct to within 50
pounds.
The indicated air-speed measurements are believed to
be correct to within 1% miles per hour as shown by
several flights over a measured course. The recorded
accelerations are accurate to within 0.2 g and the
control-force measurements correct to within 3 pounds.
Angular displacements, as given by the control-position
recorder, are correct to within y2° and 2° for the stabi¬
lizer and elevator, respectively, while angular velocities
about the center of gravity were measured to within
0.05 radian per second. Although tachometer readings
were taken in the dives, no estimate of their accuracy is
needed since it was found that the erratic effect of the
various degrees of thrust in the tail-surface pressure-
distribution tests did not exceed the effect that might
arise from other errors. Consequently, in the following
discussion, no discrimination is made regarding the
various thrust conditions.
RESULTS AND DISCUSSION
Steady dives. — The variation of the tail moment
about the center of gravity with air speed is given in
Figure 6.— Tail moment about airplane center of gravity (modified tail).
figures 6 and 7 for the modified and original tail surfaces,
respectively. From these figures it appears that the
moment furnished by the tail, at a given air speed, is
considerably affected by the stablizer setting. Since the
tail surfaces provide a moment about the center of
gravity of the airplane that balances the resultant
moment due to all other parts, it would be expected
that the moment furnished by the tail would be approx¬
imately constant. The tail-moment curves, however
(figs. 6 and 7), indicate that, as the stabilizer moves
toward the tail-heavy position, the moment becomes
smaller and the scattering of the experimental points
becomes greater.
Typical curves for the pressure distribution meas¬
ured over the tail-surface ribs are given in figures 8 to
12. Figures 8 and 9 are for the modified tail surfaces
and figures 10, 11, and 12 are for the original tail. The
ordinates of these rib pressure-distribution curves are
given in terms of the ratio p/q where p is the local
pressure difference and q is the dynamic pressure meas¬
ured at the air-speed head. A comparison of the
results for identical stabilizer settings either in figures
8 and 9 or in figures 10, 11, and 12 shows an increase in
peak pressure at the stabilizer leading edge with an
increase in air speed. Although tins difference in peak
pressure is due to the cumulative effect of several
factors, such as possible changes in interference, down-
wash, and elevator angle, it is thought that the greater
Figure 7.— Tail moment about airpfane center of gravity (original tail).
structural deflection which occurs at the highest speed
would account for a good portion of the variation with
air speed. Static tests with a loading corresponding to
that of the full tail-heavy setting for the modified tail
indicated that at 170 miles per hour the change in
stabilizer angle due to this structural deflection was
approximately 1°.
The pressure distributions shown over ribs ZR and
ZL (figs. 8 and 9) seem to indicate that with small ele¬
vator deflection the balance portion is of little value
in reducing the stick loads. A similar conclusion is
inferred in reference 3, in which calculated balance co¬
efficients obtained by the usual methods were not veri¬
fied by the pilots’ observations. The rib-pressure
diagrams for the original tail (figs. 10, 11, and 12) show
that in the dives the peak pressure on the elevator occurs
nearer to the hinge line than to the leading edge; how¬
ever, in the dives the elevator leading edge seldom pro¬
jects either above or below the stabilizer surfaces.
The form of the rib-pressure diagrams for the full
tail-heavy setting explains the tendency to the wide
scattering of the experimental points given in figures 0
and 7 for this setting. Figures 8 to 12 show that for
the tail-heavy setting the resultant tail load is the
difference between upward- and downward-acting
loads, either one of which is larger than the resultant.
324
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
r 2
Mid position
Full tail heavy
Figure 8.— Distribution of resultant pressures on modified tail surfaces for different stabilizer settings at 130 miles per hour.
Pressure , p/q
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
325
Mid position
%
Full tail heavy
Figure 9.— Distribution of resultant pressures on modified tail surfaces for different stabilizer settings at 170 miles per hour.
Pressure , p/q
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
0
I
I
I
r
i
i
W
Figure 10.— Distribution of resultant pressures on original tail surfaces for different stabilizer settings at 130 miles per hour.
Pressure , p/q
PRESSU RE- D I STRI BUTTON M E A SU RE M E NTS
ON AN 0-‘2H AIRPLANE IN FLIGHT
Pressure , p/q
328 REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
■ 0
i-/
Pressure , p/q
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
329
Because of this condition, small inaccuracies in fair¬
ing may lead to considerable dispersion in the final
results. Aside from the inaccuracy due to fairing, the
individual rib loads, and consequently the tail loads,
are likely to be low for the lull tail-heavy setting owing
to the fact that the large down pressures at the leading
edge could not be measured. Since the rib-pressure
curves for the stabilizer set full nose heavy are not sub¬
ject to these sources of discrepancy, it is felt that the
moment curves for this setting (figs. 6 and 7) are more
indicative of the true moment than any of the others.
In order to gain an idea as to how the experimental
moment curves for the nose-heavy settings compare
with the computed ones, several curves, representing
varying degrees of refinement, are given (fig. 13).
Curve A is for the case when only the moments of the
two wings about their quarter-chord points are taken
into account; in curves B the moment about the
airplane center of gravity has been computed for the
case when the additional moments due to the lift and
drag vectors are also included. These vectors were
assumed to act at the wing quarter-chord points and
their magnitudes were determined from the relative
lift distribution between the wings, which was deter¬
mined in the wing investigation. As the airplane
centers of gravity were different (table I) for the two
tail-surface investigations, two separate curves were
required.
Curves C also include the probable effect of the fuse¬
lage on the moment about the center of gravity, assum¬
ing that the fuselage exerts a constant moment given by
A/ f = Cm/jAfC f
where Cmf is the moment coefficient, 0.01.
Af, horizontal projected area, 65 square feet.
cf, fuselage length, 27 feet.
The value of the moment coefficient defined by the fore¬
going equation was taken to be 0.01 after an analysis of
the data contained in reference 4. The final compari¬
sons (curves C and D) could no doubt be improved if it
were possible to include the effect of the landing gear
and tail surfaces. The moments that they introduced
were, however, of opposite sign and tended to cancel.
The span load distribution across the tail for the fore¬
going rib pressure-distribution plots is given in figure
14. These curves show irregularities that are more or
less to be expected owing to the irregular nature of the
flow over the tail surfaces and to the comparatively
small loads measured in the steady dives. An analysis
of the data indicated that, in spite of the irregularity of
the loading, the average difference in load between the
two halves of the tail was of the order of 3 percent and
5 percent of the total load for the original and modified
tail, respectively. Inasmuch as the sides that carried
the most load varied between the two tail surfaces, it
must be concluded that the difference in load is due to
slight differences in rigging rather than to a slipstream
effect.
In these tests the elevator moments about the hinge
axis were obtained from both the pressure distribution
and the control-force-recorder measurements; the
results are compared in figure 15 for the original tail.
In order to make this comparison between the twro
hinge moments, however, it was necessary to correct
the measurements given by the control-force recorder
for the moment exerted by the elevator (because of its
unbalanced weight) about the hinge line and for the
moment exerted by the unbalanced weight in the stick
about its pivot point. Although the magnitude of the
friction moment was known, it was impossible to correct
for it in the steady dives because its direction was
unknown. Even with these corrections the moments
given by the control-force recorder were found to be
more consistent than those given by pressure-distribu¬
tion measurements and hence were used for computing
hinge-moment coefficients.
The variation of the hinge-moment coefficient with
elevator angle is given in figures 16 and 17 for the
Figure 13. — Computed and experimental tail moments about the center of gravity .
modified and original tail surfaces, respectively. These
coefficients have been computed from the relation
where Me is the elevator hinge moment given by the
control-force recorder.
ce, the average elevator chord obtained by
dividing the elevator area behind the
hinge line by the elevator span.
Se, the elevator area behind the hinge line.
Although the points for the modified tail (fig. 16) show
a fairly close grouping to a common line, those for the
original tail (fig. 17) indicate considerable dispersion.
Even though the scattering of these points is fairly
large, it can be seen that there is a tendency for the
points to move upward as the tail normal-force coeffi¬
cient increases negatively. This shift is in qualitative
agreement with the theory for an airfoil with a flap.
Load, lb. Load, lb.
330
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Full nose heovy - Midposition - Full tail heavy
Figure 14.— Span load distribution in steady dives.
PRESSl RE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
331
Pull-ups. — Typical results of the pull-up tests of the
original tail are given in figures 18 to 24. Figures 18
and 19 are time histories of the measured quantities
in abrupt pull-ups from level flight at various air speeds
with the initial stabilizer settings full nose heavy arid
full tail heavy, respectively. Figure 20 presents time
histories of two fairly abrupt pull-outs from dives at
approximately 170 miles per hour with the stabilizer
trimmed.
The time histories shown in figures 18 and 19 indicate
that the maximum down tail loads occurring in the
abrupt pull-ups vary with stabilizer setting. At a
given air speed the loads with the stabilizer in an initially
frequently in airplanes performing acrobatics and the
horizontal tail surfaces for such airplanes should
consequently be designed to withstand the same load
in both directions.
The evolution of the rib pressure distribution oc¬
curring in the abrupt pull-ups from level flight at
approximately 115 miles per hour is shown in figures
21 and 22. These diagrams correspond to runs 67
and 70 of figures 18 and 19, respectively. Similarly,
figure 23 shows the rib pressure distribution occurring
in the dive pull-out represented by run 77 of figure 20.
It can be seen from these diagrams that with the larger
elevator displacements the horn balance performs its
Hinge moment from control force, lb.- ft.
140 120 100 80 60 40 20 0
Figure 15. — Comparison of elevator hinge moments obtained from pressure-dis¬
tribution measurements with those obtained from control-force measurements
(original tail).
full tail heavy setting are greater than those when the
stabilizer is in the other extreme position, but it should
be noted that in the nose-heavy setting the total eleva¬
tor displacements are less. Regardless of stabilizer
setting, however, the tail load reaches a maximum
with the maximum elevator displacement and before
the airplane has had a chance to pitch. The load
then quickly decreases and reaches a positive maximum
as the airplane gains angular velocity. This positive
maximum is generally less than the down load and
occurs at about the same time as the maximum ac¬
celeration at the center of gravity. In the space of
1.0 second the tail has thus undergone two peak
loadings of opposite sign.
The most interesting item occurring in figure 20 is a
measured up load greater than the maximum down
load. In this run (run 79) it may be observed that the
acceleration mounted rapidly toward (jg, where it was
abruptly checked when the pilot returned the elevator
to neutral. This condition probably occurs quite
Elevator anqle, 6. degrees
-2 0 2 4 6 8 !0 12 14 16
Figure 16. — Elevator hinge-moment coefficients with the modified tail.
Elevator angle , 6, degrees
0 2 4 6 8 10 12 /4
16
18
V
A
0
£
Hj
O'
o
c
-
5
o
5
o ’
o.
,c
-.01
-.02
.03
■04
-.05
3
C -
o
a
q
-0.05
O o- o- - .06
O Q ~ -07
<> q q - .08
O p p - .09
■o
P
O
fag
O
-o
-a
tu
O
O
^ £
U
r
o /
Tu!
n
? h
&Q'
'V
□-
£
oraon/zer i
s&tfinn 1
o Mid position
(
* c
pp
t;
□ /
u /
t tc
7///
iec
ivy
_
Figure 17.'— Elevator hinge-moment coefficients with the original tail.
proper function. The Handley Page part of the balance,
however, does not contribute so much toward balancing
during the first phase of the pull-up as would be ex¬
pected and during the latter phase it works against
balance.
A typical variation of the change in the spanwise load
distribution with time is given in figure 24 and cor¬
responds to the results given in figure 22. The shape of
the loading curve is more regular than in the steady
dives mainly because the larger loads result in larger
recorded deflections, which may be read with a greater
percentage of accuracy. Another reason for the
greater regularity may be that in the pull-up the tail
surfaces tend to swing out of the relatively irregular
slipstream area.
332
REPORT NO. 590 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
333
Figure 19. — Time history of pull-ups from level flight (stabilizer full tail heavy, original tail).
334
REPORT NO. 590 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Pressure, / b./s 9. ft. '
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
335
Figure 21.— Distribution of resultant pressures at various stages of a pull-up from level flight at 115 miles per hour (stabilizer full nose heavy).
^essure, /b./s<?. ft.
336
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
1 igure 22.— Distribution of resultant pressures at various stages of a pull-up from level flight at 117 miles per hour (stabilizer full tail heavy).
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
Figure 23. — Distribution of resultant pressures at various stages of a pull-out from a dive at 160 miles per hour (stabilizer set to ti ini).
338
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Although the foregoing figures (figs. 18-24) have given
results for the original tail, they also typify those ob¬
tained with the modified tail. In figures 25 and 26,
however, over-all loads and coefficients are given for
both tail surfaces. Figure 25 gives the variation with
air speed of the maximum loads measured in abrupt
pull-ups from level flight and figure 26 is a plot of the
!20\
same order of magnitude, about 1,200 pounds, for both
tail surfaces. For the original tail, however, the maxi¬
mum unit loading per square foot is higher (26.6
pounds) because of its smaller area. At a given air
speed there is a large variation in the maximum loads
80
440
A
<a
e 0
£
^40
o
^ 80
120
Ru
n 67
/
\ I ' /
\
N
/
\ L5° 7
X
-V
r\ \
/
/
X
.95,
.95
^ N
\
X
A
\K
urrr'-
4'-
4
4 -
0.10
/
\
\
o./o
!
/
\
r
50
. \
7
\
/ Time
!
’
?ec.\
\
A
—
s _
~A
\
- -
y
_
J
UJ
MNO P Q R S
T U V W XYZ
$
0
-400
70
80
Air speed, rri:p. h.
90 100 HO
120
130
V
c
D
-800
-1,200 —
X*
O
X
X
*x |
O
*
X
X
o
X
X
O
o
X
X
* X
^ X
o
X
K
X
o
X
Mo
Or
difi
ed 1
ail
o
o
X X
g/noj
i i
li
o
Figure 25. — Maximum down tail loads measured in abrupt pull-ups from level flight •
Air speed, m.p. h.
70 80 90 100 HO 120 i30
0
X-.2
,<h
.0
$
g-.4
0)
£
v6
5
h
0
^ -.8
X
£
-1.0
X
Mot
Ori
difie
ginc
>d tc
7/
lit
o
X
X
X
X
XX*
X
o
X *
c
*
X
X
O
X
X
X, X
O
X
_
o
o
o
X
X
O
X
O
C
Vr
q S
Fjgure 24.— Distribution of normal force along the span of the original tail during a
pull-up from level flight at 117 miles per hour (stabilizer full tail heavy).
Figure 26. — Maximum values of the tail normal-force coefficient measured in abrupt
pull-ups from level flight.
corresponding normal-force coefficients, computed from
the relation
tail load
where S is the actual tail area including the balances, in
square feet. The maximum loads measured are of the
.0
■V
0
c
4?-
Oj
u
o
o
.5
x
7 —
[ 1 - 1 -
Average
/
7~,
'72 n
i.p.h.
/'
y
4
’
y
/
/
t ~
/
. tc
V
y
/'
/
/c
Lm‘
7
T“
U 93
?
^
/
Y
934
4s?
1
82
/
^ 82
o 82'
^ 1 - 1
72
/
/
<4
^7
4o
8% 4
- V
/
— ^
4
7/
7/
/
i
1
i-
j
1
O 20 40 60 80 iOO
St ick- force increment, tb.
120
140
Figure 27.— Delation between acceleration and stick-force increment in abrupt
pull-ups from level flight (modified tail). Numbers refer to air speed at start of
pull-up.
1 measured that is due to slightly different rates of stick
movement and to differences in the applied forces.
Differences in the rate of stick movement are difficult
5
tf
4
5
Qj
!J o
O 4
C
■§*
I
r "
Aver
—
~oqt
■A
2m}p.h.
i\\>
O
173
/
X
166
/
/
O
H6
4
4
7/7
y
/
178
O
'16
>
4
/
y
— /
7-Jt
_
<
05^
_
_
j
X
4
*
/
/
4 /
i /
■i
J
/
/
/
4
y
o
"0 77,
-7-
uA
7 O -
/
A
_ y
/
.
4
J
^4
1
_
j
_
_
_
_ -
O 20 40 60 80 too 120
Maximum stick-force increment, tb.
140
Figure 28.— Relation between acceleration and stick-force increment in abrupt pull-
ups from level flight (original tail). Numbers refer to air speed at start of pull-up.
to detect because of the steep gradient of the control
records.
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
339
An average line through the points of figure 25 would
indicate that the maximum load obtained in the abrupt
pull-ups varies nearly linearly with the air speed
instead of as the square and, as a consequence, the
normal-force coefficients increase inversely with the air
speed.
The variation of the maximum acceleration in the
abrupt pull-ups with the increment in stick force is
plotted in figures 27 and 28 for the two tail surfaces
with each point labeled for the air speed that existed at
the start. The increment given is the difference be¬
tween the maximum force recorded during the pull-up
and the initial force on the stick prior to the maneuver.
If straight lines are drawn, as indicated, through the
average of each group of points for a given air speed
and the 0-1 g point, it is apparent that the increment of
force required to produce a given acceleration increases
with a decrease in air speed. Since no graduated pull-
ups were made, the relation between acceleration and
stick-force increment may not be linear as indicated by
the lines in figures 27 and 28.
cn is the rib normal-force coefficient.
n, rib load normal to chord, pounds per foot
of span.
g, dynamic pressure, pounds per square foot,
pitching moment about leading edge, foot¬
pounds per foot.
cm, pitching-moment coefficient about lead¬
ing edge.
c, rib chord, feet.
The rib loads were then plotted against their span
location and the resulting curves integrated for total
wing load. These loads were converted to individual
wing and wing cellule normal-force coefficients from
the relations
AT.
qSu ’
AT
qSL
and
Cellule C
AT
Cvj/SVy T Cnj^L
II. PRESSURE DISTRIBUTION OVER THE RIGHT WING
CELLULE AND SLIPSTREAM SECTIONS
where
METHOD
The tests of the wing cellule were carried out in two
parts in order to make the best use of the available
pressure cells. In the first section, called the “wing
hook-up, ” pressure measurements were taken on all ribs
on the upper wing outboard of, and including, rib Si and
all ribs, excepting R1? on the right lower wing (fig. 4).
In the next section, called the “slipstream liook-up,”
pressure measurements were taken on ribs Si, B, and
H, in addition to all the ribs previously omitted. Thus
ribs Si, B, and H furnished a means for tying in the data
between the two sections, a procedure simplified by
making similar runs with the two arrangements.
The flight tests with each arrangement were divided
into three groups consisting of: (1) a series of level-
flight runs starting from just above stalling speed and
increasing by approximately 10-mile-per-hour incre¬
ments up to high speed, (2) a series of abrupt pull-ups
and push-downs from level flight at the foregoing speeds,
and (3) a series of abrupt right and left aileron rolls with
rudder neutral at various speeds throughout the speed
range. Several shallow dives at about 170 miles per
hour were also made with the engine fully throttled.
The method of working up the results was somewhat
similar to that employed in the tail-surface tests. For
the symmetrical-loading conditions the rib-pressure
curves were mechanically integrated to obtain the rib
load and the rib moment about the wring leading edge.
The rib loads and moments were then converted into
coefficient form by the relations
(1) cn—n/gc
(2) Cm — m^eJqc2
AT and AT are the integrated loads for upper
and lower wings, pounds.
Sc and SL are the upper and lower wing areas,
square feet. The lower wing area does not
include the part intercepted by the fuse¬
lage.
In the aileron rolls, the rib-pressure curves were inte¬
grated for both load and moment but the results were
not converted into coefficient form.
Since the tie-in rib Si on the upper wing was some
distance out from the center, it was necessary, in order
to obtain the cellule and upper wing normal-force
coefficients, to extend the span loadings to the wing
center. In the symmetrical-flight conditions they were
extending by plotting the values of the normal-force
coefficients of the slipstream ribs against that of the
tic-in rib. The span load for the upper wing was then
continued by means of these intermediate plots together
with the appropriate value of the normal-force coeffi¬
cient for rib Si. In the aileron rolls, the span loads
were continued across the slipstream sections by inter¬
polation between the partial-span load curves for the
slipstream section by the use of the values of normal-
force coefficients given by the tie-in ribs Si and H.
PRECISION
The individual rib pressures in the wing investigation
are subject to the same errors listed for the tail pressures.
The magnitudes of the different sources of error are the
same with the exception of that due to width and hazi¬
ness of the record lines, which is less for the wing tests.
The errors in rib loads due to fairing are also smaller
because of the larger number or orifices per rib.
340
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The loads on the individual wings are believed to be
correct to within 75 pounds and individual rib loads to
within 7 pounds. A good idea of the accuracy of the
load results may be obtained by noting the dispersion
of the points in figures 33 and 34.
The air speeds in level flight are correct to within
lb miles per hour. In the push-downs, pull-ups, and
rolls, the air-speed head, although measuring the dy¬
namic pressure at the head correctly to within 2 percent,
does not record the correct dynamic pressures for cal¬
culating coefficients since the speed varies along the
span. Control positions and control forces are believed
accurate to within 2° and 3 pounds, respectively.
RESULTS AND DISCUSSION
Symmetrical-flight condition. — Results for the sym¬
metrical-flight condition, which includes push-downs,
pull-ups, dive pull-outs, and steady flight, are given in
figures 29 to 35.
Typical span load and span cn variations are given in
figure 29 for steady flight at air speeds ranging from 58
to 171 miles per hour. The span loadings over the
upper wing in level flight (fig. 29 (a)) show compara¬
tively little variation with air speed. At the center the
loads tend to be low owing to the center-section cut¬
out; also, owing to a clockwise rotation of the slip¬
stream, there is a tendency for the loads just to the
right of the center line to be lower than those to the
left. The load curves for the lower wing show a similar
but increased slipstream effect, which is due to the low
position of the thrust line. Although the rotation
effect is present on the wings, the tests of the tail
surfaces indicated that there it had been practically
damped out since little dissymmetry of load occurred.
In the throttled dive (fig. 29 (a)) the span loading
is much more irregular than in the level-flight condi¬
tion owing to the fact that a negative thrust is present
and that the wing had a slight twist, the effect of a
small twist on the load being much more noticeable at
the smaller wing lift coefficients. Measurements of the
profiles of the extreme tip ribs (G and N) on both wings
showed them to be at a smaller effective angle than
those farther inboard while ribs F and M were found
to be at a higher angle. This twist at the tip was due
to the fairing used in forming the rounded portion of
the wing, although there may also have been an actual
twist of the wing structure in flight.
The curves given by figure 29 (b) indicate that the
cn values at the center tend to be high, even though
these sections are effectively washed out with respect
to the rest of the wing, because of the tendency for the
lift to be maintained across a cut-out. This washout
arises from the fact that the ribs in the center section
were formed by simply cutting off the trailing edge of
a Gottingen 398 airfoil and fairing in the bottom
surface, as shown by figure 4.
The distribution of load on the individual wing ribs
is given in figure 30 where the local pressures are given
in terms of the dynamic pressure at the air-speed head.
These distributions, which correspond to some of the
previous span-loading curves, are similar to those ob¬
tained in other investigations and require no comment
as to their shape. It will be noted, however, that the
pressures at the leading edge show' a peculiar variation,
indicating that there the flow is extremely critical.
Although figures 29 and 30 showed typical results
for the load distribution, the final averaged results for
the symmetrical-flight condition are contained in figures
31 and 32. The results of these figures, which give the
variation of rib cn with individual wing CN and of rib
cm with rib cn respectively, were determined from curves
similar to those given in figures 33 and 34, which indi¬
cate both the average scattering and the number of
experimental points used to establish each of the curves
given in figures 31 and 32. It will be noted (figs. 31
and 32) that ribs S2 and S3 show two distinct curves at
the higher lift coefficients. The points that form the
second, or dotted, curve occurred in some but not all
of the pull-ups. An analysis of the points determining
the two curves showed no tendency for one curve to be
associated with pull-ups at one end of the speed range
or vice versa; also, since these pull-ups were made from
power-on flight, a difference in slipstream conditions was
not an explanation. The only cause to which this
peculiar flow could be attributed was that the flow past
the top of the fuselage nose, which incidentally had
louvers, was critical to the shutter opening on the
radiator.
In these tests the maximum individual wing CN meas¬
ured was 1.9 (upper wing); the maximum individual rib
cn values measured were over 2.1 for ribs S2, S3, and SA.
These high values are common in abrupt maneuvers and
occur if the angular velocity in pitch is sufficiently great
to carry the lift past the normal burble angle before the
wing stalls.
The relative efficiency of the wings is given in figure
35 where the ratio CNu/Cnl is plotted against the cellule
Cn- These curves were determined from the results of
an integration of individual wing-load curves, known
wing areas, and an air speed measured one chord length
ahead of the upper wing. It is obvious, however, that
in a pull-up or push-down the wings are actually travel¬
ing at different air speeds owing to the angular velocity
in pitch and that the effect, if a single air speed is used,
is to change the apparent relative efficiencies between
the wings of a biplane. Figure 35 shows three distinct
curves, rather than a series of transition curves, because
the points determining them were obtained from records
that were read near or at the peak loads, which occur
practically simultaneously with the maximum angular
velocity. If the records had been read at intervening
time intervals, a gradual transition from the level-flight
to the pull-up curve would have been indicated.
Normal force, lb./ ft
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
341
342 REPORT NO. 590— -NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 30. — Rib pressure distribution in steady flight.
Scale for rib c
PRESSURE-DISTRIBUTION
MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
343
Figure 31— Variation of rib cn with individual wing C.v.
38548-38-
23
Scale for rib cm
344
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Rib Cn
-.4 -.2 0 .2 .4 .6 .8 10 1.2 1.4 1.6 1.8 2.0
Figure 32.— Variation of rib cm with rib c„.
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
In order to reconstruct the span cn or cm distributions
obtained in the symmetrical-flight conditions a cellule
coefficient is first chosen and reference made to figure 35
to find the relative efficiency. With this ratio and the
formula
Cellule CN
OnTjSu-\- ChlSl
Su~{-SL
the individual wing CN values may be found. Figures
31 and 32 are then referred to for the variation of rib
cn and cm along the span.
Aileron rolls.— The results of the aileron rolls are
given in figures 3G to 41 and in table II. Time histories
of the measured quantities are given in figures 3G and
37 for G right and 6 left aileron rolls made at various air¬
speeds. Figures 38 to 40 give the variation with time
of the span load distribution, rib load distribution, and
individual wing load during abrupt right and left
aileron rolls at 120 miles per hour. These results,
which correspond to runs 43 and 39 (figs. 36 and 37),
are typical of those measured at other speeds. The
maximum measured air loads on aileron ribs D and K
are given in figure 41. The wing rib characteristics,
Wing CH
2.0
1.6
1.2
S3
ct
0
-.4
Figure 33.— Typical wing rib c„ curves showing scattering of experimental points
for ribs Si and K.
i. e., rib loads, rib moments about the leading edge, and
rib centers of pressure, are tabulated in table II for all
the aileron rolls.
The irregularity of the span-load curves in the roll
(fig. 38) is d ue to the combination of an effective twist
introduced by deflecting the ailerons and a twist intro¬
duced by the subsequent rolling motion. In a left roll,
the load on the right wing is first increased owing to
the down aileron; then, as the airplane rolls, the load
decreases owing to the rolling action and also to the
decrease of the component of airplane weight normal
to the span. In a right roll, the load on the right wing
is first decreased by the aileron action; subsequently
it tends to increase as rolling occurs and finally to de¬
crease as the lift component becomes smaller. This
variation is indicated both by the time histories of the
accelerometer mounted inside the wing near the tip
(figs. 3G and 37) and bv the results shown in figure 40.
The load distribution over the aileron ribs (fig. 39)
indicates that the peak pressure at the leading edge of
the aileron is greater during the left aileron roll than
during the right. This variation is due to a smaller
aileron deflection and is shown in figures 36 and 37.
Since the ailerons had no differential action, the smaller
deflection is a direct result of piloting technique.
The results shown in figure 41 indicate that the loads
measured on aileron ribs D and K tend to increase
Rib cr,
Figure 34.— Typical wing rib cm curves showing scattering of experimental points
for ribs Si and K.
linearly with initial air speed as did the maximum load
on the tail surfaces in the abrupt pull-ups. The load
on the upper aileron rib (rib D) is larger than that on
the lower aileron rib regardless of the direction of deflec¬
tion. Since the resultant load on the aileron is upward
for zero deflection (fig. 30), the magnitude of the up
loads with the aileron down is greater than the corre¬
sponding down loads when the aileron is up.
Figure 35. — Relative efficiency of upper and lower wings.
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
346
Figure 37. — Time histories of six left aileron rolls.
Load, to. per ft.
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0 211 AIRPLANE IN PLIGHT
347
Upper wing
Strut tine
L ower wing
Strut tine
Strut line
Lower wing
Strut tine
Distance, ft.
Figure ^.-Distribution of normal force along wing span obtained in abrupt aileron rolls at 120 miles per hour
REPORT NO.
590 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Time , sec.
Figure 40.— Variation of individual wing loads measured in abrupt aileron rolls at
120 miles per hour.
Figure 41.— Aileron rib load in abrupt aileron rolls.
349
PR ESSU RE-DIST RIBUTION M E ASURE M E
CONCLUSIONS
The pressure-distribution tests over the two tail sur¬
faces showed that:
1. Although for large elevator deflections horn-type
balances performed their intended function of reducing
hinge moments, they actually increased the hinge
moment for small deflections.
2. The difference in the load on the two sides of the
tail surfaces due to slipstream rotation was of minor
importance.
3. The tail moment in the steady dive was calculated
with fair accuracy by static-equilibrium equations that
took into account the moments exerted by the wing
and fuselage.
4. In abrupt pull-ups the maximum up tail loads
may be as great as the maximum down tail loads.
5. In abrupt pull-ups the maximum tail normal-force
coefficients developed decreased with an increase in air
speed.
6. The acceleration produced with a given increment
of stick force increased with the initial air speed.
The pressure-distribution tests over the right wing
cellule and slipstream area showed that:
1. The effective relative efficiency between biplane
wings varied considerably with the type of maneuver.
2. The maximum unsymmetrical load in the abrupt
aileron roll occurred as soon as the aileron reached its
maximum deflection.
3. The unit loadings on the ailerons of a biplane are
affected by the relative efficiency between the wings.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., December 8, 1936.
sTTS ON AN 0-2 h airplane in flight
REFERENCES
1. Rhode, Richard V.: The Pressure Distribution over the
Wings and Tail Surfaces of a PW 9 Pu rsuit Airplane in
Flight. T. R. No. 364, N. A. C. A., 1930.
2. Theodorsen, Theodore: Investigation of the Diaphragm-
Type Pressure Cell. T. R. No. 388, N. A. C. A., 1931.
3. Roche, J. A.: Study of Balanced Rudders. A. C. T. C. No.
586, Materiel Division, Army Air Corps, 1927.
4. Rhode, Richard V., and Lundquist, Eugene E.: Pressure
Distribution over the Fuselage of a PW 9 Pursuit Airplane
in Flight. T. R. No. 380, N. A. C. A., 1931.
TABLE 1
CHARACTERISTICS OF DOUGLAS 0-2H AIRPLANE
Engine— Liberty. _ _ _ _ „ 420 hp. at 1,760 r. p. m.
Airfoil - - ..... _ .. . GQttingen 398
Weight during pressure-distribution measurements of
Modified tail _ .. _ ......... . 4,6601b.
Original tail _ . 4,7361b,
Wing cellule _ _ 4,708 lb.
Areas:
Upper wing _ _ _ _ . 190.4 sq.ft.
Lower wing _ _ _ ----- 182.4 sq. ft.
Total _ 872.8 SQ. ft.
Elevator, modified tail (including 2.06-square-foot balance) 27.00 sq. ft.
Stabilizer, modified tail . . . . __ 23.82 sq. ft.
Total horizontal surfaces, modified tail _ _ 50.82 sq.ft.
Elevator, original tail (including 4.53-square-foot balance)- 25.70 sq. ft.
Stabilizer, original tail _ _ .... ... 21.24 sq.ft.
Total horizontal surfaces, original tail _ _ - . 46.94 sq. ft.
Rudder, all tests (including 0.93-square-foot balance) _ . 11.81 sq.ft.
Fin, all tests _ _ _ _ 6.41 sq. ft.
Total vertical tail surfaces _ ... . . . .. 18.22 sq. ft.
c. g. location back of leading edge of lower wing during tests:
Modified tail _ _ ... 8.20 in.
Original tail _ _ _ _ _ .. 9.65 in.
Wing cellule _ _ _ _ _ _ . . 6.80 in.
Ole . . . . . . . ... _ _ 1.2
Stagger _ _ . 17° or 22 in.
Dihedral. _ _ _ _ . _ 2°
Decalage _ _ _ _ _ _ _ _ _ 0.
Incidence _ ... - - - . - - 2*
Thrust-line location above leading edge of lower wing - . 2 ft. 1.4 in.
Distance from leading edge of lower wing to center line of tail-hinge
axis _ _ _ _ _ _ _ 20ft. 3in.
Tail-hinge location above thrust line _ _ _ 2 ft. 0 in.
350
REPORT NO. 590— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE
WING RIB LOADS AND MOMENTS
Run 38 (air speed 62 m.
P. h.O
Run 39 (air speed
74 in.
p. h.
)
Run
40 (air speed 85 m. p. h.1)
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
\Time,
Rib
1.09
77
75
8!
73
07
63
72
75
70
80
04
40
22
58
05
54
55
53
51
46
34
18
1 .90
2.50
1 .09
1.90
2.50
1.09
1.90
2.50
0.90
1.90
2.50
0.90
1.90
2.50
0.90
1 .90
2.50
1.40
2.09
2.90
.1.40
2.09
2.90
1.40
2.09
2.90
Sb
51
Sa
S3
52
A
Si
B
C
D
E
F
G
Rs
S11
H
Ri
J
K
L
M
N
77
75
80
73
07
03
60
04
63
71
54
32
16
42
44
55
00
51
40
43
31
15
72
70
72
65
56
54
38
44
47
58
42
25
10
35
37
49
53
50
42
40
29
12
-112
-109
-117
-92
-91
-88
-109
-117
-119
-153
-120
-64
-24
-94
-102
-100
-98
-95
-104
-97
-01
-28
-99
-97
-103
-70
-74
-74
-92
-103
-101
-147
-112
-49
-17
-65
-69
-101
-112
-90
-90
-92
— 5f
-20
-95
-93
-93
-02
-55
-03
-70
-77
—87
-120
-89
-38
-9
-54
-55
-89
-101
-94
-89
— 86
-52
-17
1.45
1.45
1.45
1.26
1.30
1.40
1.51
1. 50
1.57
1.91
1.97
1.01
1.09
1.62
1. 57
1.85
1. 78
1.79
2. 04
2. 11
1. 79
1.55
1.28
1.29
1. 29
1.04
1.10
1. 17
1.53
1. 01
1.60
2. 07
2. 08
1.53
1.06
1. 55
1.57
1.84
1.87
1. 76
2. 09
2. 14
1.81
1.33
1.32
1.33
1.29
.95
.98
1. 17
1.84
1. 75
1.85
2. 07
2. 12
1. 52
.90
1. 54
1. 49
1.81
1.91
1.88
2. 12
2. 15
1. 79
1.42
84
84
82
75
64
65
73
76
78
92
74
42
23
57
64
52
54
54
63
57
40
22
69
69
07
55
32
29
45
52
54
68
51
26
9
38
41
44
47
46
50
41
28
12
60
62
56
40
22
16
14
21
28
40
32
17
6
17
15
33
36
39
34
34
22
8
-125
-120
-124
-94
-85
-93
-112
-120
-129
-193
-158
-65
— 22
-94
-102
-102
-101
-98
-141
-129
-70
-30
-107
-108
-104
-70
-60
-60
-81
-96
-106
-156
-125
-44
-9
-72
— 77
-90
-97
-94
-123
-lOf
-60
-19
-98
-99
-90
-49
-36
-38
-44
-58
-78
-129
- 103
-36
-4
-33
-28
-67
-80
-96
-101
- 100
-53
-15
1.49
1.50
1.51
1. 25
1.33
1.43
1. 53
1. 58
1. 65
2. 10
2. 14
1. 55
.96
1.65
1.59
1. 90
1.87
1.81
2. 24
2. 20
1. 75
1. 3(
1. 55
1.56
1.55
1.27
1.87
2. 27
1.80
1.85
1. 96
2. 30
2. 45
1.69
1. 01
1.90
1.88
2. 04
2. 00
2. 04
2. 4(
2. 59
2. 14
1.58
1.63
1.60
1.61
1.22
1.64
2. 37
3. 14
2. 76
2. 78
2.81
3. 22
2. 12
.67
1.94
1.87
2.03
2. 39
2. 40
2. 97
2. 94
2.41
1.87
98
94
89
82
68
08
70
77
78
94
74
40
19
59
63
52
55
53
05
58
38
19
83
79
74
67
53
53
56
63
65
78
57
29
10
51
55
43
4f
49
37
44
29
12
03
62
58
46
20
26
10
24
31
54
38
19
7
23
21
32
31
42
41
37
25
10
-156
-144
-137
-105
-99
-116
-120
-137
-142
-213
— 175
—68
-20
-119
-125
-122
-120
-111
-164
-142
— 78
-28
-137
-125
-118
-86
-80
-92
-101
-116
-129
-191
-153
—56
-11
-95
-99
-102
-103
-109
-109
-128
-71
-22
-111
-105
-99
-61
-47
-91
— 56
-71
-95
-168
-132
-45
-8
— 54
-53
— 77
-91
-112
-134
-127
-69
-18
1. 59
1.53
1. 54
1.28
1.45
1.71
1.71
1.78
1.82
2. 26
2. 30
1.70
1.05
2. 02
1.98
2.35
2. 18
2. 09
2. 52
2. 45
2. 05
1.47
1.65
1.58
1.60
1. 28
1.51
1.74
1.80
1.84
1.98
2. 45
2.68
1.93
1. 10
1.86
1.80
2. 37
2. 24
2. 22
2.95
2.91
2. 45
1.83
1.76
1.61
1.71
1.33
1.81
3. 50
3. SO
2. 96
3. 06
3.11
3.47
2. 37
1. 14
2. 35
2. 65
2.41
2.94
2.66
3. 27
3. 43
2. 76
1.80
x 'I'ime,
Y. sec
Rib\
Run 44 (air speed 63 in.
p. hd)
Run 45 (air speed 74 m.
p. h.O
1!
ead-
ft.
Run 46 (air speed 83 m.
p. h.')
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from
ing edge
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
1.40
2.10
3.90
1.40
2.10
3.90
1.40
2.10
3.90
1.10
1.90
2.90
1.10
1.90
2.90
1.10
1.90
2.90
1.60
2.15
3.10
1.60
2.15
3.10
1.60
2.15
3.10
Sb
61
66
11
-106
-105
-46
1.74
1.59
4. 18
58
03
33
-101
-109
-76
1.74
1.73
2.30
55
63
34
-108
-120
-87
1.96
1.91
2.56
Si
00
05
12
-104
-103
-47
1. 73
1.58
3.92
52
57
28
-86
-94
-61
1.65
1.65
2. 18
56
62
34
-105
-110
-82
1.87
1.87
2.41
Sa
07
72
24
-106
— 105
— 56
1. 58
1.46
2.33
61
66
38
-99
-107
-73
1.62
1.62
1.92
58
65
38
-100
-112
-79
1.72
1.72
2. 08
S3
(j?
71
28
-89
-88
-43
1.33
1.24
1.53
03
68
43
-83
-91
-61
1.32
1.34
1. 42
59
66
43
-81
-92
-63
1.37
1.39
1.46
S2
58
63
28
-85
-84
-36
1.46
1.33
1. 29
57
62
41
-83
-91
-61
1.46
1.47
- 1.49
64
71
50
-96
-107
— 76
1.50
1.51
1.52
A
06
70
43
-94
-93
-63
1.42
1.33
1.46
62
07
50
-86
-94
-70
1.39
1. 40
1.40
63
70
56
-98
-109
—87
1.55
1.50
1.55
St
72
77
43
-106
-105
-72
1.47
1.30
1.07
75
80
59
-114
-121
-95
1.52
1.51
1.61
75
83
64
-122
-133
-109
1. 63
1.00
1.70
B
77
81
44
-114
-112
-73
1.48
1. 38
1. 06
SO
84
59
-126
-130
-101
1. 57
1.55
1. 71
81
88
66
-135
-143
-115
1.07
1.62
1.74
C
04
69
30
-83
-89
— 45
1.30
1.29
1.50
06
09
41
-89
-90
-64
1.35
1.30
1. 56
04
73
48
-89
-101
-74
1.39
1.38
1.54
D
60
59
13
-43
-53
-6
.86
.90
. 46
51
57
21
-40
-48
-11
. 78
.84
.52
43
55
21
-28
-42
-8
.65
. 76
.38
E
40
49
15
-31
-44
-8
. 77
.90
.53
41
48
24
-37
-41
-16
.90
.85
. 67
37
52
28
-24
-42
-14
. 65
.81
.50
F
40
50
19
-54
-65
-32
1.35
1.30
1.68
40
49
27
-58
-68
-42
1.45
1.39
1.55
39
54
32
-58
— 73
-48
1. 49
1. 35
1.50
G
28
40
17
-30
-47
-20
1.07
1. 17
1. 18
25
36
20
-28
-41
-24
1. 12
1. 14
1. 20
24
35
22
-25
-40
-26
1. 04
1. 14
1. 18
R2
60
53
28
-98
-81
-52
1. 63
1.53
1.86
65
53
34
-116
-99
-55
1.78
1.86
1.62
63
59
33
-128
-125
-60
2. 03
2. 12
1.82
Sh
07
60
20
-104
-87
-36
1.55
1. 45
1.80
64
51
28
-106
-88
-37
1. 66
1. 73
1.32
03
59
28
-118
-115
-40
1.87
1.95
1.43
H
56
49
-11
-102
-86
-6
1.82
1. 75
— . 54
54
42
9
-113
-96
-35
2. 09
2. 28
17.50
51
47
1
-115
-111
-17
2.26
2. 36
17.00
Ri
55
48
-5
-94
— 77
-10
1. 71
1. 60
-2. 00
57
45
8
-105
-88
-28
1.84
1.95
3.50
63
58
12
-128
-125
-30
2.03
2. 16
2.50
J
40
47
4
-69
-67
-14
1. 50
1.42
3. 50
49
43
12
-84
-70
-30
1.71
1.63
2. 50
47
48
16
-85
-84
-40
1.81
1. 75
2. 50
K
34
39
4
-30
-37
3
.88
.95
— . 75
34
35
9
-34
-30
-3
1.00
.80
.33
29
36
12
-20
-25
-1
. 69
.69
.08
L
31
40
5
— 22
— 32
7
. 71
.80
-1. 40
28
35
10
-21
-24
4
.75
.09
-.40
27
37
10
-11
-20
-10
. 41
. 54
1.00
M
40
44
15
-61
-64
-29
1. 52
1. 45
1.93
38
44
21
-00
—07
-36
1.58
1. 52
1. 71
39
48
25
-64
-74
-44
1.04
1.54
1.76
N
31
39
12
-38
-47
-17
1.22
1. 21
1.42
30
37
17
-34
-44
-22
I. 13
1. 19
1. 29
29
39
20
-33
-47
-26
1. 14
1.20
1.30
1 Denotes air speed at start.
PRESSURE-DISTRIBUTION MEASUREMENTS ON AN 0-2H AIRPLANE IN FLIGHT
351
ii
DURING AILERON ROLLS
Run 41 (air speed 103 in. p. h.'l
I
Run 42 (air speed 114
m. p.
h.>)
Run 43 (air speed 122 m
. p. lid)
Rib load, lb.
Rib moment,
lb. -ft.
C. V
from leading 1
edge, ft.
Rib load, lb.
Rib moment,
lb. -ft.
c.p. from leading
edge, ft.
Rib load
,1b.
Rib moment,
lb. -ft.
c. p. from lend¬
ing edge, ft.
1.93
2.92
3.38
1.93
2.92
3.38
1.93
2.92
3.38
1.90
2. 92
3.53
1.90
2.92
3.53
1.90
2.92
3.53
1.90
2.90
3. 73
1.90
2.90
3.73
1.90
2.90
3.73
Time
see: Rib
88
57
30
-161
-121
-116
1.83
2. 12
3.87
84
60
46
-162
-149
-145
1.93
2.48
3.15
88
71
55
-182
-158
-151
2. 07
2. 23
2. 75
Sb
86
64
35
-154
-135
-134
1.79
2. 11
3.83
83
52
49
-151
-142
-140
1.82
2.73
2.86
87
73
60
-176
-155
-150
2. 02
2. 12
2. 50
Si
74
54
28
-131
-113
-112
1.77
2.09
4.00
72
49
46
-126
-113
-111
1.75
2.31
2.41
75
60
48
-148
-127
-122
1.97
2. 12
2. 54
Sa
69
38
12
-97
-59
-55
1.41
1.55
4. 58
65
38
35
-88
-67
-64
1.35
1.76
1.83
72
58
29
-111
-81
-71
1. 54
1.40
2.45
Si
53
11
-15
-101
-52
-46
1.91
4.73
-3. 07
55
17
13
-96
-58
-56
1.74
3.41
4.31
65
40
11
-112
-76
-62
1.72
1.90
5. 64
S2
57
16
-16
-134
-92
-87
2. 35
5. 75
-5. 44
39
3
1
-80
-42
-41
2.05
14.00
41.00
48
18
1
-88
-61
-52
1.83
3. 39
52. 00
A
49
-11
-22
-114
-49
-41
2. 32
-4. 45
-1.86
51
-3
-8
-128
-67
-62
2.51
-22. 33
-7. 75
61
10
-9
-146
-97
— 75
2.40
9. 70
-8. 33
Si
57
-3
-8
-131
-70
-62
2. 30
-23. 33
-7. 75
60
11
1
-148
-99
-82
2. 47
9.00
82. 00
74
27
12
-180
-128
-110
2.43
4.74
9. 17
B
64
13
0
-158
-109
-94
2. 47
8. 38
OO
66
19
5
-180
-129
-106
2. 73
6.79
21.20
77
36
18
-208
-160
-138
2. 70
4. 45
7.66
C
85
45
22
-252
-216
-171
2. 96
4.80
7. 77
85
54
23
-272
-241
-157
3.20
4.46
6.83
90
65
38
-310
-273
-204
3. 13
4.20
5.37
D
64
30
14
-203
-173
-141
3. 17
5. 77
10. 07
64
38
18
-225
-199
-150
3.52
5.24
3.33
72
50
26
-250
-227
-177
3.47
4.54
6.81
E
31
13
6
-73
-62
-52
2. 36
4.77
8. 67
25
10
5
-71
-61
-55
2.84
6. 10
11.00
27
17
8
-76
-69
-63
2. 82
4. 06
7.88
F
10
5
2
-15
-13
-10
1. 50
2. 60
5.00
8
2
2
— 15
-13
-15
1.87
6.50
7.50
10
7
3
-18
-16
-13
1.80
2. 29
4. 33
G
45
1
— 15
-110
-53
-28
2. 44
53. 00
-1.87
53
12
4
-110
-78
-74
2. 07
6.50
18.50
60
49
-9
-150
-120
-79
2. 50
2.45
-8. 78
Rs
45
-6
-26
-113
-50
-24
2.51
-8.34
-.92
52
11
1
-110
-78
-72
2. 12
7.08
72.00
58
47
-14
-142
-115
-80
2. 45
2. 45
-5. 72
Sh
37
15
4
-113
-70
-45
3.05
4.66
11.25
29
12
8
-104
-83
-79
3.58
6. 92
9.88
33
21
10
-127
-106
-89
3.85
5. 05
8. 90
H
41
15
-2
-122
-103
-71
2.98
6. 87
-35. 50
39
11
5
-128
-111
-107
3.28
10.09
21.40
42
31
8
-152
-133
-120
3. 62
4. 29
15. 00
R.
41
14
4
-122
-103
-92
2. 98
7. 35
23.00
35
14
11
-128
-119
-118
3. 66
8. 50
10. 72
38
23
12
-146
-135
-127
3. 84
5. 87
10. 59
J
56
26
19
-197
-166
-158
3. 52
6. 38
8.31
57
32
17
-226
-202
-154
3. 97
6.31
9.06
62
47
30
-250
-241
-198
4.03
5. 13
6. 60
K
50
32
21
-182
-174
-157
3. 64
5. 44
1.48
49
34
18
-204
-195
-150
4. 16
5. 74
8. 33
51
47
29
-215
-230
- 190
4. 22
4. 90
6. 55
L
30
18
13
-94
-92
-90
3. 13
5. 11
6. 92
26
18
14
-98
-100
-96
3. 77
5. 55
6. 85
31
28
21
-116
-122
-122
3. 74
4. 35
5. 81
M
12
5
2
-26
-24
-24
2. 17
4.80
12.00
9
6
1
-29
-30
-25
3.22
5.00
25. 00
8
8
4
-31
-31
-28
3.87
3. 87
7. 00
N
Run 47 (air speed 103 m. p. h.1)
Rib load, lb.
1
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
1.75
2.50
3.10
1.75
2.50
3.10
1.75
2.50
3.10
02
46
20
-136
-112
-88
2. 20
2. 44
4. 40
60
44
19
-127
-103
-79
2. 12
2. 34
4. 16
66
50
26
-122
-98
-74
1.85
1. 96
2. 84
73
57
34
-111
-87
-63
1.52
1. 52
1.85
79
63
41
-121
-97
-73
1.53
1. 54
1. 78
88
72
50
-143
-119
-95
1.62
1.65
1.90
100
83
61
-169
-146
-121
1.69
1. 76
1.98
106
88
61
-183
-164
-130
1. 73
1.87
2. 13
87
64
41
-121
-104
-81
1.39
1.63
1. 98
54
29
3
-34
-3
16
.63
. 10
-5. 33
62
37
17
-49
-24
1
. 79
. 65
-.06
66
43
26
-96
-68
-51
1.45
1.58
1.96
41
27
14
— 45
-33
-19
1. 10
1.22
1.36
76
32
-3
-169
-101
-76
2. 22
3. 16
-25. 33
74
29
-6
-143
-75
-53
1.93
2.58
-8. 84
51
4
-20
-141
-72
-50
2. 76
18.00
-2. 50
65
15
-13
-156
-87
-60
2. 40
5.80
-4.62
59
21
-1
-117
-67
-43
1.98
3. 19
-43.00
46
18
-2
-42
-10
8
.91
. 55
4.00
49
18
0
-39
2
20
.80
-. 11
CO
64
39
22
-101
-71
-50
l 58
1.82
2. 27
45
28
13
— 56
-38
-22
1.24
1.35
1.69
Run 48 (air speed 117 m. p. h.1)
Run 49 (air speed 125 m. p.
h-O
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
Rib load, lb.
Rib moment,
lb. -ft.
c. p. from lead¬
ing edge, ft.
Time /
s QC. /
1.08
1.92
2.60
1.08
1.92
2.60
1.08
1.92
2.60
1.60
2.10
2.90
1.60
2.10
2.90
1.60
2.10
2.90
' Rib
78
66
-1
-181
-164
-125
2. 32
2. 48
-125. 00
76
72
22
-186
-179
-131
2. 45
2. 49
5. 95
SB
78
66
-3
-171
-154
-115
2.20
2. 34
-38.30
75
71
22
-174
-167
-122
2.32
2. 35
5. 55
S,
66
54
-3
-152
-135
-95
2.30
2. 50
-31. 70
73
69
26
-152
-145
- 100
2. 08
2. 10
3. 86
Sa
84
72
22
-134
-117
-82
1.59
1.62
3. 73
86
82
45
-135
-128
—87
1. 57
1. 56
1.93
S3
72
60
33
-119
-102
-71
1.65
1. 70
2. 15
83
79
46
-137
-130
-89
1.65
1 . 65
1.93
s2
87
75
42
-162
-145
-112
1.86
1.93
2. 67
91
87
58
-157
-150
-114
1. 73
1.72
1.97
A
99
86
54
-183
-166
-137
1.85
1.93
2.54
106
102
72
-199
-191
-155
1. 88
1.87
2. 15
S,
108
91
61
-203
-182
-159
1.88
2. 00
2.61
115
111
77
-217
-211
-175
1.88
1.90
2. 27
B
86
64
37
-135
-116
-103
1. 57
1.81
2. 79
93
83
52
-147
-134
-107
1.58
1. 61
2. 06
C
56
25
7
-42
0
-4
.75
0
.57
59
41
10
-42
-10
9
.71
.24
-.90
D
60
34
19
-47
-16
-23
.78
.47
1.21
62
53
24
-47
-36
-9
.76
.68
.37
E
67
46
26
-99
— 76
-62
1.47
1.65
2.38
74
61
37
-111
-96
-68
1. 50
1.57
1.83
F
39
26
12
-43
-32
-22
1. 10
1.23
1.83
42
35
19
-45
-40
-24
1.07
1. 14
1.26
G
50
29
9
-149
-121
-118
2. 98
4. 17
13. 10
55
36
29
-169
-136
-128
3. 07
3. 78
4. 41
R 2
50
28
5
-137
-101
-90
2. 74
3. 61
18.00
55
34
21
-157
-124
-100
2. 85
3. 65
4. 77
Sh
48
7
-21
-145
-99
-74
3.02
14. 10
-3. 52
51
23
-3
-161
-129
-99
3. 16
5.61
-33.00
H
59
20
-12
-156
-110
-85
2. 64
5. 50
-7.08
62
34
5
-172
-139
-106
2. 77
4.09
21. 20
R.
59
21
4
-134
-84
-81
2. 27
4. 00
20. 20
63
42
10
-116
-116
-79
2.32
2. 7r>
7.90
J
43
15
1
-49
-12
-18
1. 14
.80
18.00
45
29
1
-51
-24
1
1. 13
.83
-1.00
K
47
18
1
-37
0
3
.79
0
-3. 00
50
38
8
-43
-31
11
.86
.82
-1.37
L
67
43
26
-112
-81
-73
1. 67
1.88
2.81
73
59
36
-123
-106
— 77
1.69
1.80
2. 14
M
45
28
16
-57
-39
-30
1.26
1.39
1.87
51
41
22
-64
-53
-34
1 . 25
1. 29
l. 54
N
1 Denotes air speed at start.
38548-38-
24
REPORT No. 591
AN ANALYTICAL AND EXPERIMENTAL STUDY OF THE EFFECT OF PERIODIC
BLADE TWIST ON THE THRUST, TORQUE, AND FLAPPING
MOTION OF AN AUTOGIRO ROTOR
By John B. Wheatley
SUMMARY
An analysis is made of the influence on autogiro rotor
characteristics of a periodic blade twist that varies with the
azim uth position of the rotor blade and the results are com¬
pared with experimental data. The analysis expresses
the influence of this type of twist upon the thrust, torque,
and flapping motion of the rotor. The check aga inst ex¬
perimental data shows that the periodic twist has a pro¬
nounced influence on the flapping motion and that this
influence is accurately predicted by the analysis. The
influence of the twist upon the thrust and torque could be
demonstrated only indirectly, but its importance is indi¬
cated.
INTRODUCTION
The resultant of the air forces and the mass reactions
on an autogiro rotor blade produces a couple tending
to twist the blade unless the chordwise center of gravity
of the blade and the center of pressure of the air forces
are coincident. This fact lias been known for some
time, but it has not been generally realized that, except
in particular cases, the resultant twist is periodic and is
a function of the angular position of the blade in azi¬
muth. The periodic twist may be of a magnitude com¬
parable with or even exceeding the pitch setting of the
rotor, which demonstrates the necessity of including it
as a factor in the analysis of autogiro-rotor characteris¬
tics.
It is the purpose of this paper to present an analysis
of the periodic twist and to support the validity of the
analysis by a comparison of predicted results with ex¬
perimental information obtained from flight tests of a
direct-control wingless autogiro. The scope of the
paper will be limited to a study of the influence of a
known periodic twist upon the thrust, flapping motion,
and torque of a rotor; the effect of such a twist upon
rotor vibrations and stability and the problem of pre¬
dicting the twist will be treated in a subsequent report.
ANALYSIS
It has been experimentally shown in previously
unpublished data that, except in special cases, the air
forces acting on a rotor blade cause a twist of the blade
and a consequent change in the blade pitch angle.
The twist is not constant but is a function of blade
azimuth angle because of the variation of the air forces
on the blade with this angle. In the following analysis
the basic equations expressing the rotor characteristics
will be generalized to include the factor of periodic
twist. The notation of reference 1 will be used through¬
out this paper except for minor changes; for con¬
venience, the list of symbols is appended at the end of
this section.
The following additional notation is used:
r=xR (1)
dr — Rdx (2)
The problem is now the solution of the equations for the
autogiro rotor when the pitch angle 6 has the form
0=0o+2'0,-f;reo+.re1 cos \p-\-xi sin \p-\-xeo cos 2\p
flxr]2 sin 2\f+ . . . (3)
where en and i)n are coefficients descriptive of 0.
It will be noted that an assumption is here made
concerning the distribution of the twist along the
radius; equation (3) shows that a linear distribution,
starting from zero at the blade hub, has been used.
Actually the twist reaches zero just outboard of the
vertical pin and is not, in general, absolutely linear
from there to the tip; the assumption used, however,
does not introduce a serious error and is considered
justified for its simplicity.
It is obvious that the expressions of reference 1 for
interference flow angle of attack a, blade flapping
angle /3, and the dynamic equation of flapping are un¬
altered; they are
CtQR
2(X2+m2)^
(4)
tan a
h I _ Cr _
m^2m(\2 + M2)5
(5)
/3=a()~ai cos \p — bx sin f — a2 cos 2f
— b2 sin 2 1 p— ... .
7,(^4
353
(6)
(7)
354
REPORT NO. 591— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Using the notation of equation (1), the velocity com¬
ponents at the rotor blade are:
TJ t
hr
=uT—x- \-p sin ip
(8)
q£=‘ Up~ X + 4 2^0^) cos
+ (j-xai+^b^\ sin p-\-(^pax-\-2xb^ cos 2i p
4 ( .)M&i — 2 xaA sin 2 \p -)- ~ pa2 cos 3 ip -f- ^pb2 sin 3 ip (9)
Also
uT2=x2J--^p2-\-2px sin 4/~\r2 cos 2ip (10)
UrUp — a:A-f-^M2^2 + ^ — M£Ck)4^i|jE24 4 M'J- '2 Pxa2^ cos p
+ (^mX— c/ij^x2 — sin^
+ (iixaiJr2x2b>) cos 2 n2a0 4 pxbx — 2 x2a^) sin 2 ^
4 ( — 4 M‘^i 4 2 cos + (4 M2(h 4 9 pxb^\ sin 3 p
— ^ /x24> cos 4^4t m2«2 sin 4 ^
(ID
The rotor thrust is calculated upon the assumptions
that the elemental force on the blade lies in a plane
perpendicular to the blade-span axis and that the force
depends only on the velocity in that plane; it is further
assumed that uP is small compared with uT, so that the
angle <p between uT and the resultant velocity (wr24
Up2) 1 may be equated to its sine and tangent. As an
approximate allowance for tip loss, it will be assumed
that the thrust becomes zero at a radius x= B where it
is arbitrarily assumed that 5=1— Then
b n* CB 1
r=4- dpi ±pcH2RHT2CLdx (12)
2ttJo Jo 2
It is further assumed that CL is a linear function of the
blade-element angle of attack ar, which is, of course,
accurate below the stall; then
the error so introduced was negligible. Another error
in the thrust expression exists where uT is negative;
this error can be approximately nullified by the follow¬
ing correction. When uT is negative, the normal
expression for the blade-element angle of attack must
be altered to
oiT' = — 0— <p (15)
and equation (15) must be used in the part of the disk
bounded by x——p. sin p and z=0 and by p=ir and
p=2ir. The expression for the thrust is now, after
substituting for CL, 6, and <p=uPluT,
1 h f2r CB
pcaHJR2, — d\p ur2 (0O 4 a$i 4 2*0 4 #ei cos \p
2 2ttJo Jo
+xrji sin p+xe2 cos 2^4a:?72 sin 2p + . . . )dx
1 b (‘2t <'B
4 o pcaHJR2, =- dip uTuPdx
2 2 T Jo Jo
1 b f*27r P-m sin -A
— g pcafirR3- j dip uT2 (dQ -\-xdr 4 XtQ-\-xex cos ip
+xvi sin ipj-xe2 cos 2 ^4^2 sin 2^4 . . . )dx
1 b C2* P-MSiniA
— ^ pcaHrR 3- dip \ uTuPdx (16)
2 7r Jtr Jo
T=\ bcpa x(B2+|/)+e0QB3+| m2B-^ms)
+ <3 B' + 1 — ~ M1) + 1 umB3 - 1 ,wj (17)
It has already been shown (reference 1) that an and
bn are of the order pn; it can similarly be shown that en
and yn are of the order p,n.
The expression for thrust has been integrated upon
the assumption, which experience has shown to be
valid, that terms of higher order in p. than the fourth
are negligible. This same assumption will be used
throughout the remainder of this analysis.
The change in thrust caused by twist is
A T= \bcpattW {e„(4 + 3 M2#2 - k*') + \^B‘ - |i“2^S2}
(18)
The thrust moment MT is, from reference 1,
CL=a.ar (13)
ar=6J-<p (14)
Errors are introduced by the assumption that
CL~aar ; however, a graphical evaluation of the thrust
made without this assumption and using a curve of CL
against a derived from wind-tunnel tests disclosed that
CB 1
Mr =1 ^ pcaH2Ri { Qu T2 4 uTuP] xdx
r sin 1 p 1 |2tt
—2 ^ pcaHP2Ri{QuT2-\-uTuP}xdx (19)
do 2
where the second integral is added to thrust moment
only in the interval p= % to ip— 2 ir. The integrated
value of Mt is
355
EFFECT OF PERIODIC BLADE TWIST ON AUTOGIRO-ROTOR CHARACTERISTICS
Mn
+ e, (!/#> + +| AB2+ «/|b» +
%£3
~h 1 2 M X#2 — g M3 X + ^OoB3 + 0 .053m4#o -f- ~/x0! Z?‘
- a ,( |b4 - |m2B2) - ^mM3 + f^B4
+>!jQb5+ — jM«2B4}sin t
+ { - ^avB3- 0.035M4a„+ 6,(Ib4 + |mM
— g (i«2-B3 + « i( jB5 + y^B3) + JMI2B4 jcos f
+ 1 “ yM7X)B~ + ~f yi-AB3 — ^a2B4 + ^ /J2|/y'
+ KgB3 + ~ n 2#
+{-0.053m3X-jms«>Bs+^,90-5/9iB8
4“ qM^iB3 + 2^-^4 — hjfrB4
+ e!(5Bs+gM2fi3) + j/i»3B4]cos 2*
(20)
Equation (7) can now be expanded into
7iU2(a0+3a2 cos 2^-f 352 sin 2\f/)=MT—Mw (21)
The coefficients of the flapping angle /3 can now be
obtained by substituting for Mr in equation (21) and
equating the coefficients of similar trigonometric func¬
tions; then, letting y=cpaR4/Ix
“0=^11 ^+O.O8OMX + j0o(b4-|VB2Mm
+ 0, ( \B> + ~m2B3) + <0 Qb5 + ^2B3)
+p»,B4-^2e2Bl-LU
(22)
2 (2
f2{ x(b2 - iM2) + «0(|b3 + 0. 1 06/23) + e, B4
' B'-IPB
-i62B3+eoB4+^(|B3+I^)-ie2B4
^1 =y^i _j_i ^2 /^h''(yB3^ 0.033u3)-|- ga2B3
(23)
(24)
The expressions for a2 and 62 must be expanded in
powers of m before solution is possible; it will be
shown later that expansion to the order of m2 is suf¬
ficient to express the thrust and torque to the order
of fx*. To this order the equations for a2 and b2 are
®62+ia2B4=M2(-hoB2+^B3+^/?4+f®B4
7
4m
O M J
6
— I
7
-a2-
1
M?4 = M2 { - 1 e0 B> - i e , B3 + 1 ^ B3 - jboB3
-\-lBl +i^|B5
4 M 5/X
(26)
Equations (25) and (26) may be solved for a2 and
b2 after substituting for a0, aX) and bx to the appropri¬
ate order of m; then
a ~ ^ \\b( l(M-7 y2B*\ + 0 B2( 46 4- 7 y'Ir )
a2“72JB8+144lX7\16+ 108 )+doB\j+lu)
+exB^ 12
7 - y2B8\
180 )
+
soB'(l2 +
7 y2B8\
180 )
-4s yBs+y B4 + 24 -,-Y B”! (27)
30 m 5 m 5 m 5 m J
b’=^TUl™s+T^’+&B7+n^
+ |-5!B4+T2!B8+|£2gi!_24 2|Bsj (28)
5y m 30 m 5 m 57 m ]
The changes in the expressions for the blade-motion
coefficients arising from the twist are:
A«„=i ThfjB’+gMB3 j-f JM-!,B4— -M2^3 j (29)
1
1
1
Acq
l
£4+^(f 55 + ^M2£3)-~e2£4} (30)
j54-^M2M6°
A6l=54+|tM2^2{7eo(30jB8+36M2jB
~ “ (|^5 + ^ M253) M7^7 - 4 ^4} (3 1 )
A u 2
;7258+144r
2
M 7
-M-Ibs+I^b9!
A 62 =
O M O M‘
{r- k/7+t e7u+ -^'/u
7‘B°-)- 144 1 15 57M 30 m
(32)
5 m 57 m“
(33)
356
REPORT NO. 59! — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The air torque on the rotor blade is the sum of the
accelerating torque arising from the lift elements and
the decelerating torque arising from the drag elements.
It has been assumed that the lift elements are zero
between x~ B and x—]; it is thought reasonable,
however, to assume that the drag exists over the entire
blade. An average value of the blade-element drag
coefficient 5 will be used; this value is assumed con¬
stant with respect to the angle of attack. The torque
Q, which must be zero bv hypothesis, since the rotor is
in a state of steady rotation, is then
Q= 0= <hp A pcWR'u r2(pCLxdx
“Tt./o Jo 4
b n* r 1 1
— o I d\p I 0 pcU2WuT28xdx
-7T Jo Jo *
(34)
This expression after substitution for 0, CL, and n
integrates into
1
3
+ MX a, yr-Ar -Mol -ah2&
8
T
16
• M
+«,0+1V^)+».<gB*+iV/p'
-«/{ Xaji- + \nb, fl») I- \,h3B'
+ + ),bm'
1 I" Pr ) ^ f<,( 4 .yj v'b Y^V'blB’
6
4 a
+ .>,(v + &.[?«'+ U«2/(
+h,(|(* bB3 - a ,[ '/?' - _ 1m62B 4
+ 2*2(4^ X' 4 -bx4
+ A( - 1/cioB 3 + \»bX‘- \<kB-
(35)
Equation (35) is a quadratic in A with the coefficients
of the quadratic dependent upon p, y, /?, 0O, 9\, and the
e and v coefficients describing the periodic twist. The
evaluation of equation (35) requires the substitution of
known values of e and rj in the expressions for an and bn.
The scope of this study includes only the prediction of
the effect of a known twist upon rotor characteristics;
consequently, the solution of equation (35) is possible
when the drag term ---
& 4a
is known.
Examination of equations (17) and (35) shows that
the thrust and torque are expressed to the order p4 if
a2 and b2 are expressed to the order p2, inasmuch as en
and Vn are of the order pn. This last condition has been
analytically proved but will not be included in this
paper; the analysis of the e and 77 coefficients of twist
will be the subject of another paper.
LIST OF SYMBOLS
R, blade radius.
b, number of blades.
c, blade chord, feet.
r, radius of blade element.
*, r/R.
0O, blade pitch angle at hub, radians.
0i, difference between hub and tip pitch angles,
radians.
en, coefficient of cos rup in expression for 0, radians.
7]n, coefficient of sin n\p in expression for 0, radians.
0, instantaneous pitch angle, radians.
8, mean profile-drag coefficient of rotor-blade airfoil
section.
\p, blade azimuth angle measured from down wind
in direction of rotation, radians.
v, rotor induced velocity.
9, rotor angular velocity, drp/dt, radians per second.
A HR, speed of axial flow through rotor.
pV.R, component of forward speed in plane of disk,
equal to V cos a where V is forward speed,
feet per second.
/3, blade flapping angle, radians.
a„ , coefficient of cos n\p in expression for 13, radians.
bn, coefficient of sin n\p in expression for /3, radians.
I\, mass moment of inertia of rotor blade about hor¬
izontal hinge.
a, rotor angle of attack, radians.
M T, thrust moment about horizontal hinge.
M w, weight moment of blade about horizontal hinge.
urilR, velocity component at blade element perpendic¬
ular to blade span and parallel to rotor disk.
uP9.R, velocity component at blade element perpendic¬
ular to blade span and to uT9R.
T, rotor thrust.
Q, rotor torque.
Q
Q p92irR:>
a, slope of curve of lift coefficient against angle of
attack of blade airfoil section, in radian
measure.
. -1 ur
(f>= tan 1 • —
^ uT
aT, blade-element angle of attack, radians.
cpaRi
7 =
/1
j mass constant of rotor blade.
B= l — factor allowing for tip losses.
EFFECT OF PERIODIC BLADE TWIST ON AUTOGIRO-ROTOR CHARACTERISTICS
357
EXPERIMENT
Flight tests were made of a Kellett KD-1 autogiro
having the following characteristics:
Gross weight, II _ 2,100 pounds.
Rotor radius, R _ 20.0 feet.
Number of blades, b _ 3.
Blade chord, c _ 1.00 foot.
Blade weight, v'b - 61.5 pounds.
Blade- weight moment, Mw _ 482 pound-feet.
Blade moment of inertia, A _ _ 175 slug-feet.2
. . be
Rotor solidity, tr=—p _ 0.0478.
7 r/v
Blade mass constant,
(sea level) y=~p~- _ 12.74.
J i
Blade airfoil section _ Gottingen 606.
Pitch setting, 0O (0i = O) _ 0.0960 radian.
Airfoil section moment co¬
efficient, Cma c (about aero¬
dynamic center) _ —0.056.
Blade chordwise center-of-
gravity location, cr (aft of
aerodynamic center) _ 0.038 foot.
Figure 1.— Rotor speed and rotor thrust coefficient of KD-1 autogiro as measured
in flight.
The flight tests included the measurement of rotor speed
as a function of air speed (fig. 1) from which, since the
autogiro had no fixed wing, the thrust coefficient could
be calculated. Simultaneous measurements of the
blade flapping angle and twist were made with a motion-
picture camera mounted on and turning with the rotor
hub. The data for twist are shown in figure 2. The
flapping-angle data are represented by the experimental
O ./ .3 .3 .4
Tip-speed ratio, p
Figure 2.— Blade twist coefficients of KD-1 autogiro rotor as measured in flight.
points of figure 3. Both the flapping angle and the
twist have been presented as the coefficients an, bn, en,
and rjn of the expressions used in the previous section to
represent /3 and 9.
The effect of periodic twist upon the thrust coefficient
CT was obtained by calculating the increment in Cr
caused by the periodic twist and deducting the incre¬
ment from the experimental value. The results are
shown in figure 4.
In order to check the derived expressions for the
effect of periodic twist upon the flapping motion, the
inflow factor A was calculated from the expression for
the thrust (equation (17)) in which A was the only
unknown; the calculation was made using the experi¬
mental values of the periodic twist, and it was also made
on the assumption that all e and r? coefficients except t0
358
REPORT NO. 591— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
were zero. The two results are shown in figure 5.
These values of X were then used in equations (22), (23),
(24), (27), and (28) to calculate the blade flapping co¬
efficients both with and without the effect of the peri¬
odic twist; these results are shown in figure 3, together
with the measured values of the blade-flapping-angle
coefficients. Since the measured values of the periodic
twist were obtained from targets placed at 3/4 B, they
Figure 3. Blade flapping coefficients of KD-1 autogiro rotor as measured in flight
and as calculated with and without periodic twist.
were multiplied by 4/3 before insertion in the equations.
The effect of the periodic twist in the torque equation
was estimated in the following manner: Known values
of X, an, bn, en, rjn, 60, and dx were substituted in equation
(35); the resultant expression was used to evaluate the
remaining unknown term -r~
& 4a
1 -f-,u
2-1,4
8
The cal¬
culation was then repeated with the assumption that the
periodic twist was zero and that X rather than the 8 term
was unknown; the factors an, bn, 0o, 9U and e0 were
assigned the same values in both calculations. The
results of these calculations are shown in table I.
0
./
.2 .3
Tip-speed ratio, p.
A
Figure 4.— Calculated periodic twist effect on thrust coefficient of KD-1 autogiro.
Figure 5. — Inflow factor X of KD-1 autogiro as calculated from thrust coefficient
with and without periodic twist effect.
DISCUSSION
The influence of periodic blade twist on the rotor
characteristics is illustrated in figures, 3, 4, and 5.
The data in figure 3 afford convincing proof not only of
the validity of the twist analysis but also of the effect of
periodic blade twist upon the rotor characteristics.
EFFECT OF PERIODIC BLADE TWTST ON AUTOGIRO-ROTOR CHARACTERISTICS
359
The data demonstrate that the type of twist developed
in this rotor has a pronounced influence on the coning
angle a0 and on the flapping angle ax. The influence on
the lag angle bx and on the second harmonics a2 and b2
is considerably smaller. The agreement between the
values of a0 and ax calculated from the expressions
including the periodic twist and the experimental values
is quite good. The calculated values of the lag angle bi
are in radical disagreement with experiment; this same
condition was encountered in previous work (reference
1) and has been partially explained. In the reference
it was shown that a variation of the rotor-induced
velocity along the chord of the rotor disk had an appreci¬
able effect upon the variation of bx with n; an induced
velocity increasing from the leading edge to the trailing
edge increases bx. Since this type of asymmetry
exists (reference 2) and varies inversely in magnitude
with n, the evaluation of its influence upon bx would
improve the qualitative agreement between the calcu¬
lated and measured values.
Figure 4 illustrates the magnitude of the periodic-
twist contribution to the thrust coefficient. A different
result was obtained in figure 5 by showing the difference
in the values of X calculated when the periodic twist was
considered and when it was neglected.
In table I the calculated influence of periodic twist
upon the torque equation and upon the resultant value
of X is shown to be the least in magnitude of the effects
studied. The effect is not, however, small enough to be
neglected and would be an important factor if it were
extrapolated to higher tip-speed ratios.
TABLE 1.— EFFECT OF PERIODIC BLADE
TWIST ON TORQUE EQUATION
X
(experimental)
£('+>’ -I'O
X
(calculated with¬
out periodic
twist)
0. 15
0. 0182
0. 000700
0.0177
.20
.0186
. 000794
.0175
.25
.0189
. 000845
.0171
.30
.0189
.000800
.0161
CONCLUSIONS
1. The effect of periodic twist upon rotor-blade
flapping coefficients is satisfactorily predicted by this
analysis.
2. The influence of periodic twrist upon rotor char¬
acteristics as calculated from and checked with available
data is an important factor in rotor analysis and can be
adequately evaluated by the methods presented.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Ya., January 28, 1937.
REFERENCES
1. Wheatley, John B.: An Aerodynamic Analysis of the Autogiro
Rotor with a Comparison between Calculated and Experi¬
mental Results. T. R. No. 487, N. A. C. A., 1934.
2. Wheatley, John B., and Hood, Manley J.: Full-Scale Wind-
Tunnel Tests of a PC A- 2 Autogiro Rotor. T. R. No. 515
N. A. C. A., 1935.
REPORT No. 592
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
Bv Theodore Theodorsen, M. J. Rrevoort, and George W. Stickle
SUMMARY
A comprehensive investigation has been carried on with
full-scale models in the N. A. C. A. 20-foot wind tunnel ,
the general purpose of which is to furnish information in
regard to the physical functioning of the composite pro¬
peller-nacelle unit under all conditions of take-off, taxying,
and normal flight. This report deals exclusively with the
cowling characteristics under conditions of normal flight
and includes the results of tests of numerous combinations
of more than a dozen nose cowlings, about a dozen skirts,
two propellers, two sizes of nacelle, as well as various types
of spinners and other devices.
The optimum shape of a, low-drag cowling has been
determined. The shape of the leading edge and the con¬
tours of the exit passage are the cause of large losses when
improperly designed. The importance of providing
means for regulating the quantity of cooling air to the
minimum that will prevent excessive losses at high speeds
has been demonstrated. The N. A. C. A. cowlings
show a remarkably high efficiency when considered as a
pump for the cooling air. The superiority of a baffled
over an unbaffled engine has been verified and it has,
furthermore , been shown that tightly fitting baffles are
superior to the deflector type.
INTRODUCTION
The general purpose of a cowling lias been known for
some time. The original tests of N. A. C. A. cowlings
are given in reference 1 and later studies in references
2, 3, and 4. The actual design of the engine cowling
has, however, been based on a very inadequate scientific
knowledge of its functions, owing largely to a lack of
conclusive experimental data. The two basic functions
of the engine cowlings are: (1) To provide an engine
enclosure having minimum air resistance and (2) to
act as a pump for the air that is to cool the engine or
the radiator.
The cowling is usually designed to fit tightly about
the engine unit with a rearward taper gradually faired
into a wing or with a slightly expanding section that
forms the front portion of a fuselage. The design of
the portion ahead of the engine has been quite hap¬
hazard and often aerodynamically poor. As the cowling
has a leading edge quite similar to that of an airfoil,
it must be expected to react aerodynamically in much
the same manner. The leading edge being fairly thin,
the cowling must be sensitive to the “angle of attack”
of the local air flow at the leading edge. This question
has, in fact, been considered as a direct consequence
of the findings of reference 5, in which an “ideal angle
of attack” is defined.
No information has been available until quite recently
on the function of the cowling as an air pump.
Since the summer of 1935 the N. A. C. A. lias been
conducting a very extensive investigation of propellers,
nacelles, and cowlings with numerous special devices
ncluding a dozen different cowlings with a variety
of skirts. Attention is being paid to the mutual
interference of the parts and to their effect on engine
cooling. This first report comprises the results of the
tests of cowlings, nacelles, and spinners under normal-
flight conditions.
ANALYSIS OF THE PROBLEM
As previously stated, the two primary functions of
the cowling are: (1) To provide an engine enclosure of
minimum drag and (2) to pump the cooling air through
the engine or the radiator. These functions are distinct
because the definite amount of work required to be
done on the cooling air is distinctly different from the
ordinary aerodynamic drag of the cowling itself. In
order to cool the engine, a certain quantity of air Q has
to be forced through the engine per second at a certain
pressure difference Ap. A related increment is observed
in the drag D — D0 at an air speed V. The work done
per second is thus QAp and the work expended exclusively
for cooling is ( D — D0 ) V, which gives an efficiency of
pumping
= _QAp _
Vr (D-D,)V
The quantity DQ, which is given considerable signifi¬
cance, is defined as the drag of a closed cowling with
major dimensions similar to those of the actual cowling
as indicated by the sketch in figure 1. (See also the
actual design in fig. 4, nose 19, skirt 5.)
Writing the total drag of the cowling-nacelle unit
the problem is stated. It is, of course, evident that
Up should be as large and D{) should be as small as
possible.
361
362
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Thus far the presence of a propeller has been ignored.
On first consideration one might be led to believe the
propeller to be nonessential in the sense that all con¬
clusions drawn from a test without a propeller might
readily be applied. That such a procedure is not permis¬
sible will be evident from the results. The main inter¬
action may, however, be fairly well isolated and de¬
scribed. In order to determine the pump efficiency with
a propeller, the net efficiency of the propeller-nacelle
unit will first be defined as
RV
Vn p
where R is the thrust of the unit and P the power sup¬
plied to the propeller shaft. The value rjn thus includes
the useful expenditure to cooling.
As the propeller is a secondary consideration, it will
be treated very simply as a disk capable of producing
the desired pressure difference or forward thrust. The
velocity increase and the contraction of the slipstream
Figure l.^Basic cowling shape for determining minimum drag.
are found to be proportional to the unit disk loading,
defined as
P =—? —
c qSV
where q is the dynamic pressure ~pV2 and S is the disk
area ^Z)2.1
Any combinations of P, S, and q (or of V) that give
fixed values of Pc are therefore essentially similar in
geometrical appearance of the flow field. In the study
of the effect of the propeller on the cowling, the para¬
meter Pc will frequently be employed, or rather the
more convenient expression
It may be noted that large values of
correspond to
small contractions and vice versa.
An expression for the pumping efficiency of the
cowling for the power tests is obtained by recognizing
the fact that part of the apparent loss in aerodynamic
efficiency reappears as useful work in cooling the engine.
The net efficiency pertaining to a certain installation
has been given as t;„, which is experimentally determined
for several values of Pc. The mechanical cost of the
cooling is determined by employing the closed cowling
in figure 1 to obtain a series of points on the net-
efficiency curve for this limiting case of no cooling or
pumping losses. This particular net efficiency is
denoted as rj0. A comparison of these net efficiencies
at a value of Pc representing a desired standard
condition gives the pump efficiency at Pc as
Vp =
Q&P
{Vo Vn) P
Consider for a moment the product QAp. The
engine or the radiator permits a rate of flow Q at a
pressure difference A p. For a given engine the pressure
drop across the baffles is obviously very nearly pro¬
portional to the square of the volume and to the
density p. A nondimensional quantity can easily be
obtained. Let A be the cross-sectional area of the
portion of the main air stream in front of the engine,
which actually enters the engine as cooling air. (See
fig. 21(d).) For a given engine or radiator the
volume per unit time AV is proportional to Ap; that
is, the area is proportional to
V
Ap
< Z
proportionality may be defined as
The constant of
k
where k is seen to represent an area. In order to obtain
a nondimensional expression, k may be expressed in
terms of some representative area, such as the cross-
sectional area of the nacelle F. Thus
A
v <z
The term K, which shall be termed “the conductivity
of the engine,” is now a pure number. It is easy to
visualize when Ap is equal to q: when the available
head is used across the resistance.
A
In this case K=p
and the conductivity K may be defined as the fraction
of the total air column with a cross section equal to that
of the nacelle that enters the inside of the cowling
when the pressure drop across the resistance is equal
to the velocity head q.
The term “conductivity” has been used from time to
time in various forms by other authors. It is adopted
because of a certain analogy to electrical terminology,
as will be discussed later.
The value of Ap/q is nearly unity in baffled engines
and K normally lies between 0.05 and 0.1. Most of
the reported tests were conducted with tightly fitted
baffles, in which case the value of K is 0.0424. This
value of K is referred to as “standard baffling.” Sub¬
sequent tests were run with loosely fitting baffles in
which K was 0.0909. A final series of tests was made
with the baffles removed and K, approximately 0.5.
1 It is noted that the power supplied to the air stream as thrust is somewhat less than
P and that the effective disk area is reduced by the Goldstein effect. (See reference 6.)
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
The great convenience of having the engine-flow
resistance given by a single number can be realized.
If the defined quantity K is used to obtain an
expression for the quantity of the cooling air
Q=K-y/^f FV (2)
a form is obtained that is particularly convenient
inasmuch as a single calibration suffices to determine K
for each engine baffle or radiator. The method of
calibration will be described later.
Introducing K in the efficiency formulas, there is
obtained for the nacelle tests with D=Cd Fq
Kmm
Vp
C
D
-a
£>0
(3)
as the final formula for the pump efficiency. Similarly
for the propeller tests
(f)3,Wg k(
K
’’""(go -V.)P
Ap\3/2
q )
Vo—Vr,
F
P,S
or
Vp
= C
ST
V0~V n
(4)
where C=
KF
SPr'
This formula is convenient as K is a
constant, as are the disk area S and the nacelle cross-
sectional area F. It will later be shown that the value of
-17=- = 1.8 has been chosen as a standard of reference.
V Pc
The influence of the exit area on the flow through
the cowling is best explained by reference to figure 2.
Pz’ h
Observe that p2 and V2 are the pressure and velocity,
respectively, in the exit. The static pressure p2 is
practically identical with the static pressure of the
outside flow at the slot because the flow line dividing
the external and internal fields is nearly straight.
The expression for the total available drop is thus
AP= Apfl- Ap2
where A P is the total head on the front minus the
static pressure at the exit. The static pressure at the
exit, as will be seen from a number of pressure plots, is
usually slightly negative and may in some cases reach
a value of —0.3 q. The frontal pressure is fairly close
to q on all normal cowlings. The pressure A P thus
ranges from approximately 1 q to 1.3 q. The right-
hand terms of the foregoing equation are the pressure
363
drop across the engine and the pressure to produce the
velocity head in the exit. The preceding equation
written in nondimensional form is
AP^Ap . A p2
q~ c + q
For the pressure drop across the engine there has already
been obtained the relation
Q=kJ ^ FV
V q
or
Ay ( Q V
q \KFVJ
For the pressure that produces the velocity head in the
exit, there is simply
^lh—^pV2
as the internal-friction loss in the passage is considered
negligible. Inasmuch as V2=^~ and q=h pV2, there
may be written
The area of the exit of the slot A2 may be written in
coefficient form as a fraction of the maximum cross-
sectional area F, as K>F. Then
aP2 ( Q Y
q \K2FVJ
and for the total pressure drop the final relation
A P ( Q Y
q \KFV )
representing the case of two resistances in series. The
A P
pressure drop — corresponds to the voltage I , the
/ Q \2
square of the rate of flow \jSr) the current «/, and
the conductivities K to - yjC .
A few remarks on the foregoing equation of flow
regulation may be in order. Restating, the left-hand
side is independent of air speed and is equal to slightly
more than unity. Even with the use of cowling flaps
the increase is only from about 1.1 to 1.3. The associ¬
ated increase in Q is thus of the order of 10 percent and
the increase in cooling is very slight. Indeed, if K is of
the usual small value of baffled engines, not much is
gained by increasing also the exit conductivity K2.
Representative values of K and K2 as used in the most
efficient and satisfactory installations tested are 0.05
and 0.15, respectively. The pressures across the resist¬
ances are therefore and /f, l or in the ratio3
(0.05)2 (0.15)-
of 9 to 1. Any possible increase in K2 results in only
a negligible increase of Q.
2 Note the electrical analogy, \ = J ’
3 For constant cooling, this ratio decreases as the air speed increases.
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
364
(a) Nacelle 2, nose 7, skirt 6, propeller B, inner cowling 6 (7 — 6 — B— 6 — 0).
(b) Nacelle 1, nose 7, skirt 5, propeller B, inner cowling 3 (7 — 5 — B -3 0).
(c) Front view of engine cylinders with baffles and center section of the cowling. (d) Rear view of engine cylinders with baffles and center section of the cowling.
Figure 3.— The test set-up.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
365
The conductivity K completely represents the engine
as regards the aerodynamic tests of the nacelle-propeller
unit.
The choice of the value of 1.8 is made strictly for
the convenience of comparison. Each individual pro¬
peller was tested over a complete range of angles of
attack. A plot of the net efficiency against -==
vPe
shows that the range of -57= extends from 0 to about 3,
VPC
the net efficiency becoming zero at the latter point.
This particular shape of the efficiency curve is, of course,
a function of the present test set-up, which consists
solely of an engine-nacelle unit. It is obvious that the
presence of a wing section or of an entire airplane would
ard equipment is described in reference 7. The full-
scale cowling model was attached to the standard
balance frame by the supports shown in figures 3 (a)
and 3 (b). The supports were shielded from the air
stream in the regular manner to minimize tare drag.
The cowlings were built to enclose a Pratt A Whitney
A asp engine having a maximum diameter of 52 inches.
The dummy engine used in the main series of tests
consisted of Wasp engine cylinders mounted on the
front half of the crankcase (figs. 3 (c) and 3 (d)). The
engine was pivoted on an axis at the top (fig. 4) and the
force was taken by a bell crank connected to a scale
at the bottom. This arrangement permitted the direct
determination of the axial force on the engine and the
ring-cowling assembly.
<£ propeller £ cylinders
change the shape of the entire curve. It is fairly safe
to assume, however, that the differences in propellers,
cowlings, spinners, etc., would manifest themselves in
the same relative manner.
The condition -jy= =1.8 might be more easily kept
VPC
in mind as a fixed slipstream contraction; it is used to
permit a comparison of the effect of the propeller on the
cowling-nacelle unit under equal or similar conditions of
flow.4
APPARATUS
The cowling investigation was conducted in the
N. A. C. A. 20-foot wind tunnel, which with its stand-
4 For example, the value l/v/Pc = 1.8 is represented by a 550-horsepower engine
and a 10-foot propeller at about 180 miles per hour or by a 200-horsepower engine and
an 8-foot propeller at about 150 miles per hour.
A 150-horsepower, 3-phase, wound-rotor induction
motor was mounted in the nacelle behind the dummy
engine (fig. 4). This motor was calibrated in a special
brake test over the entire range of speed and torque.
The propeller was mounted in proper relation to the
engine by an extension shaft, which replaced the engine
shaft. The speed and the power output were controlled
by resistance in the rotor circuit. This arrangement
permitted a flexibility and accuracy far superior to those
obtainable on an engine run on its own power. Another
important reason for the electric drive is its dependa¬
bility. With the complex installation comprised of
more than 100 pressure tubes and several dozen ther¬
mocouples all over the unit, mechanical repairs would
have been cumbersome.
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
366
The heat transmission through the cylinders was
obtained by the employment of a 2-kilowatt electric
heater of fixed output mounted inside cylinder 1, which
was completely sealed. The measured surface temper¬
atures thus furnished an accurate index of the coeffi¬
cient of heat transmission, not subject to the multi¬
plicity of errors associated with tests of a gasoline
engine. These temperatures will be referred to in the
text and tables as ‘ ‘index” temperatures l\. A short
preliminary series was run on an actual engine, a Pratt
& Whitney Wasp SlHl-G, baffled in the average man¬
ner and run by its own power. Conductivity and
temperature distribution were measured in several
cases for reference purposes.
Cowlings. — AH cowlings used in this investigation
are surfaces of revolution about the propeller axis. The
struction. Noses 1 and 4 had the same size of front
opening but had very different angles of attack at the
leading edge. Nose 5 differed from nose 4 by having
the leading edge designed as an airfoil section. Nose
6 was identical with nose 5 except for a shortening of
6 inches in the axial length. Nose 7 was designed with
a greater radius of curvature than nose 6, representing
a cowling very neutral to the direction of the oncoming
air flow. Nose 8, which was built on the basic form
of nose 1, represents a completely closed nose used for
special purposes. Nose 9 is built on nose 6 with a
forward reversed curvature. Nose 15 is especially
designed for housing a blower attached to the propeller
shaft. Nose 17 is a design to determine the effect of
reducing the main diameter of the cowling by placing
bumps over the rocker boxes to house them. The
Nose 1
Figure 5. — Nose shapes of cowlings tested.
Nose 2
various forms are represented by profile lines in figure 4.
For convenience, the rear portion enclosing the electric
motor will be referred to as the “nacelle.” The por¬
tion forward of the exit opening will be referred to as
the “cowling.” The cowling may be considered to
consist of three parts: (1) Nose, (2) center section,
and (3) skirt. The center section of the cowling is
attached permanently to the engine cylinders (figs. 3(c)
and 3(d)). The same center section was used through¬
out all tests with the exception of the single test on the
complete cowling 17. The nose and skirt sections
were attached to the center section, care being taken
to form a continuous smooth line. A photograph of
each nose shape tested is reproduced in figure 5.
The original series comprised nose shapes 1, 2, 3,
and 4, all being of the same length and general con-
basic shape is shown in figure 4 and in figure 5. Nose
18 is a combination of a perforated disk and nose 2.
Nose 19 is a combination of a solid plate and nose 2.
The various shapes of skirt section tested are shown
in figure 4. Skirts 5, 9, and 10 closed up the rear open¬
ing to the cowling. Skirt 8 had flaps of 5-inch chord
and 6-inch span turned out in the positions shown in
figure 4.
Nacelles. — Nacelles 1 and 2, 44 and 50 inches in
diameter, respectively, were used in this investigation.
The leading contour of the nacelle formed the inner
surface for the cowling slot and is termed “inner cowl¬
ing.” Inner cowlings 2 and 3 were used with nacelle
1 ; inner cowlings 4, 5, and 6 were used with nacelle
2. These inner cowlings and the nacelles are shown
in figure 4.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
367
Baffles.— Baffles of conventional shape were used in
this investigation. (See figs. 3(c) and 3(d).) They
were in contact with the cylinder barrel fins from the
100° position to the 145° position (see fig. 6) for the
standard-baffle condition shown in table I. In order
these tests. Propeller B (Hamilton Standard drawing
lCl-0) has airfoil sections close to the propeller hub.
Propeller C (Navy plan form 5868-9) has the round
part of the shank carrying farther out on the blade and
fairing slowly into an airfoil section. Propeller Bx is
Nose 3
Nose 4
Nose 6 Figure 5.— Continued. Nose shapes of cowlings tested. Nose 7
to cover different degrees of baffling in this investiga¬
tion, the baffles were moved back % inch for a few tests.
The baffles were removed for several tests, as shown
in table I.
Propellers. — Two 10-foot diameter, 3-blade Hamilton
Standard adjustable propellers (fig. 7) were used for
the same as propeller B except that the distribution
of blade-angle setting beyond the 70-percent radius
has been changed. A more complete description of the
propellers is given in the associated report on pro¬
pellers (reference 8).
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
368
Nose 18
Figure 5.— Continued. Nose shapes of cowlings tested
Nose 19
FULL-SCALE TESTS OF
N. A. C. A. COWLINGS
369
Spinners. — Dimensioned drawings of the spinner
shapes and their positions with reference to the plane
of the propeller are given in figure 8. (See also fig. 9.)
Spinner 9 was the only spinner that admitted air
through the center.
Special devices. — Several special devices were
tested in order to gain some insight into their effects
on the normal arrangement.
1. Auxiliary airfoil: A circular airfoil of the section
shown in figure 4(a) was used in combination with
370
REPORT NO.
592— NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
nose 7. Auxiliary airfoil 1 was tried in two positions
as shown. Auxiliary airfoil 2 had the same chord
as airfoil 1, but the leading edge was turned down as
shown in the drawing. It was tried only in position 1.
2. In order to investigate the possibility of dis¬
charging the cooling air through the rear of the nacelle,
the special design shown in figure 4(b) was tested.
Unfortunately, the resistance through the nacelle was
too large to permit a sufficient range to be covered.
Pressure and temperature apparatus. — Static-pres¬
sure orifices were placed over the inner and outer
surfaces of the cowling to give a sufficient number of
measurements to determine the static pressure at any
point on these surfaces. Twelve pitot tubes and
twelve static-pressure tubes were placed between the
fins on a cylinder to measure the loss in energy as the
air flowed around the cylinder. Four pitot tubes and
four static-pressure tubes were placed across the exit
of the baffles to determine the energy in the air at
that place. Sixteen pitot tubes and eight static-pres-
sure tubes were placed in the exit of the skirt to measure
the air flow through the engine. Survey tubes were
placed at intervals outside the cowling surface to
determine the flow condition with different cowling
shapes. A survey was made of the air stream at six
locations along the axis of the nacelle with each pro¬
peller and with no propeller.
Thermocouples were placed at positions around the
cylinder corresponding to the positions of the pressure
measurements. Hot-wire anemometers were used in
the front and the rear of the cylinder to determine
the relative cooling obtained in each place.
f
No. 2
Figure 9. — Spinners.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
RESULTS
The top speed actually employed in the tunnel was
approximately 100 miles per hour. The V/nD values
were, however, extended to depict conditions up to
300 miles per hour at one-third the actual Reynolds
Number. The present paper is confined to a report
on the results of the aerodynamic properties of cowlings
at normal-flight speeds. Several of the tests were also
concerned with the cooling properties.
All propellers were actually tested throughout the
blade-angle range of 15° to 45° (reference 8). The
present report includes only propellers B and C at a
blade-angle setting of 25°. The tests were actually
extended over the complete range of Pc and it is en¬
tirely for convenience that the results of this paper are
confined to a representation of a normal cruising
condition. All conclusions in regard to the results are
definitely identical with those obtainable at any other
value of Pc in the cruising range. The conditions
obtained in the lower end of the speed range are pre¬
sented in a separate report (reference 9). The tests, in
general, comprised the following measurements:
Drag, or thrust, and the power supplied.
Pressure distribution over nose, skirt, and nacelles.
Pressures in front and rear of engine unit.
Velocities through baffles and skirt opening.
Temperatures of heated-cylinder barrel.
Table I summarizes the condensed results pertaining
to the experiments on cowlings under a cruising condi¬
tion and includes pertinent related information. The
subdivisions relate to specific variables. The main
division is on the basis of conductivity with secondary
divisions for the nacelles, spinners, and other special
devices.
Each unit was given a designation made up of five
numbers or letters separated by dashes. These num¬
bers refer to the parts of the unit shown in figure 4
and are, in order, nose— skirt — propeller — inner cowl¬
ing — spinner. Thus 7 — 2 — C — 3 — 7 represents a test
made on nose 7, skirt 2, propeller C, inner cowling 3,
and spinner 7. A missing part is represented by the
number 0. These designations are given in column 1
of table I. Column 2 is the pressure p{ in front of
the engine divided by the air-stream velocity head q.
Column 3 is the pressure in the rear of the engine pr
divided by q. Column 4 is the difference between
columns 2 and 3, or Ap/q. Column 5 gives the values
of the conventional drag coefficient CD=D/qF. Col¬
umn G gives the drag at q=25.Q> pounds per square
loot, which corresponds to a speed of 100 miles an hour
at standard conditions, or the thrust at a value of l/v7 Fc
of 1.8 at a q of 25.6 pounds per square foot. Column
7 is the net efficiency of the arrangement at the value
of lf\/Pc of 1.8. Column 8 presents the pump effi¬
ciency. Columns 9 and 10 give the index tempera¬
tures at the front and back, respectively, of the barrel
of the electrically heated cylinder. The index temper-
371
atures are the temperature differences between the
cylinder and the air stream.
FORCE MEASUREMENTS
The total drag for the test arrangement 7 — 2 — 0
3 — 0 for a range of q up to 28 pounds per square foot
is given in figure 10. In order to have a representative
picture in a particular case of the drag distribution of
each part of the set-up, the pressure distribution over
the whole unit is shown in figure 11(a). The values
plotted are the nondimensional pressures p/q measured
along the surface of the body. The recorded pressures
are plotted on normals to the surface at the point
where the orifice was located. Both positive and neg¬
ative values are plotted on the outside of the body, the
appropriate sign being indicated.
Using the same values, secondary plots (fig. 11) give
the graphical integration of the axial force with the
pressure plotted against the radius. The area under
the plots represents the pressure drag of the body.
The figures also give the individual contribution of
each part, the momentum in the exit slot being included.
Figure 10. — Sample drag curve for test arrangement 7—2 — 0—3—0.
The actual measured drag for the unit was 72.5
pounds and the value given by the pressure plot is 57
pounds. To the latter value should be added 10
pounds, or more, estimated for the skin friction. The
essential point in this comparison is not the closeness
of the agreement but the picture obtained of the rela¬
tive effect of the several parts of the set-up.
The same set-up was tested with propeller B operat¬
ing (7 — 2 — B — 3 — 0). The conventional curves of
propeller thrust coefficient CT, power coefficient CP,
and propulsive efficiency 77 are plotted against V/nD
in the usual manner (fig. 12(a)). Of more direct
concern in the present paper is, however, the curve of
net efficiency Vn plotted against the quantity l/\ZPc
(fig. 12 (b)), both quantities having been defined in the
earlier analysis of the problem. As previously men¬
tioned, the values of ??„ included in table 1 were taken
from such curves of rjn against 1 /y/Pc for a value of
1 /\ZP~C of 1.8.
372
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
PRESSURE DISTRIBUTION
As mentioned in the introduction, the drag of an
arrangement without the propeller operating is not a
safe criterion of performance. This section and table I
show how the pressures over the body change with
propellers operating in front of the body. Under the
cruising condition reported here the effect of the pro¬
cowling or, more specifically, may be traced back to the
nose section. Another cause of large losses may be
traced back to an inefficient skirt section. An indirect
effect of the nose manifests itself in a variation of the
static pressure on the frontal area of the engine, this
pressure being always somewhat less than the corre¬
sponding total head of the air stream. This pressure
-160
-120
-80
-40
0
40
r i i i i — i — i — i — i — | —
r a, 18.4 pounds draq
b, 22 ■■ ■■ .
c, 7.6 pounds thrust
d, 6.8 ~ - ......
—
Skier ex/
t -
J
Nacelle
V:
c
b
V
~a
r
H
L_J
f
J
Outside of skirt
Radius, inches
FKrURE 11.— Pressure distribution on the test arrangement 7— 2—0— 3—0 and the integrated drag from the pressure distribution.
poller is less marked than in the condition of climb or
take-off.
From the distribution of the static pressure over the
entire unit as given graphically in figure 11, an impres¬
sion of the relative importance of the various parts is
obtained. A study of a number of similar plots shows
that the pressure drag of the rear portion, or nacelle,
remains fairly constant, resulting in the important
conclusion that the cause of essential differences in the
drags of the several arrangements is to be found in the
on the front of the engine must be measured with con¬
siderable care in order to obtain reasonable accuracy
in the integrated pressure drag. An error of 0.05 q at
a value of q of 25.6 pounds per square foot corre¬
sponds to an error of 19 pounds in the pressure drag.
The pressures pf/q on the front of the engine, taken
as an average of several simultaneous measurements
over the area, are given in table I. The pressure
distribution over a number of individual cowlings is
given in figure 13. The pressure distribution over a
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
373
number of skirts tested in conjunction with nose 7
is given in figure 14. The effect of a propeller on the
pressure distribution on arrangement 7 — 2 — B — 3 — 0
is given in figure 15 for several air speeds. The greatest
value of such pressure plots lies in the possibility of
Attention will be called to the fact that care must be
taken to obtain the pressure distribution under the cor¬
rect conditions. Some noses, in particular nose 1, are
very critical in regard to the effect of the propeller
slipstream. This effect has been referred to in the in-
Fioure 12. — Sample curves. Arrangement 7 — 2— B — 3 — 0. Blade angle set 25° at 0.75/?.
qualitatively distinguishing between desirable and
undesirable flow characteristics. It is possible to
associate an efficient nose with a smooth distribution
of the static pressure. On such a basis one would
evidently select nose 2, 3, or 7.
troduction as an effect of the relative direction of the
local air flow with respect to the leading edge or con¬
tour of the nose. It is interesting to observe that nose
1, which is unusually inefficient at normal air speeds,
approaches a reasonable efficiency at low air speeds.
REPORT NO 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
374
Figure 13.— Pressure distribution over various cowling shapes.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
375
Skirt 6
r
Figure 14.— Pressure distribution over the various skirts for test arrangement 7— X— 0— 3— 0.
-L'.j
38348 — 38-
376
REPORT NO. 592 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Thus with a proper consideration of the effect of
Reynolds Number and the propeller slipstream, it is
concluded that the pressure distribution is an excellent
although somewhat indirect method for evolving an
aerodynamically efficient cowling design, the procedure
being to adjust the shape repeatedly until the smooth¬
est pressure distribution is reached in whatever range
may be desired. Cowling 7 was directly produced as
a result of this type of procedure, this cowling being
the least critical to changes in operating conditions,
combined with high efficiency. The high negative
pressure on the nose of the cowling is utilized in the new
nose-slot cowling (reference 10) to give a higher pressure
drop across the engine for cooling.
CONDUCTIVITY
The physical definition of the term “conductivity”
has already been given. Two measurements are needed
to determine experimentally this quantity K: the pres¬
sure drop A p/q across the resistance and the rate of air
flow Q. The value A pfq is obtained directly by a
system of pressure tubes placed over the front and the
rear areas of the engine unit, the averages being given
in table I. The rate of flow is determined by a number
of permanent installations for velocity surveys across
the exit opening, a total of 24 tubes, 16 impact and 8
static, being used. As previously mentioned, the
conductivity is obtained by the formula
Q_
FV
IAp
2
It is to be noted that, thus defined, the quantity K is
entirely a function of engine-baffle design. That this
assertion is strictly true was confirmed by tests of a
given baffle arrangement with a variety of different
noses and skirts, all resulting substantially in the same
value of K. Independence of the Reynolds Number
was similarly established by tests over the entire range
of air speeds. This independency of the Reynolds
Number is explained by the fact that the pressure loss
in the baffles consists primarily of the exit loss and is
therefore nearly proportional to the square of the
velocity.
Three values of conductivity are used in the present
investigation:
(1) K— 0.0424, representing the case of the baffles
fitting tightly against the cylinder
barrel.
(2) K= 0.0909, representing the case of the baffles
moved back % inch, giving a somewhat
diverging channel along the back of the
cylinder barrel.
(3) K= about 0.5, representing the case of an un¬
baffled engine, the pressure drop being
too small to be measured with sufficient
accuracy.
The accuracy in determining the values (1) and (2) by
the above-described method is within 1 percent.
These conductivities cover the useful range, as the
value of the conductivity for an actual engine with
commercial type of baffles of satisfactory design had
been determined in the preliminary test as RT=0.06.
Deeper fins and more cylinders in parallel, as used in
2-row radials, might increase this value to as much as
0.15.
In regard to the optimum conductivity of the engine-
baffle unit, it is to be observed that a minimum quantity
of air is necessary to carry away a given quantity of
heat. The maximum temperature difference between
the air and the cylinder is of the order of 400° F. By the
reduction of the quantity of cooling air, a condition is
soon reached in which the effect of the reduced tem¬
perature difference more than offsets other advantages.
A reasonable increase in the temperature of the cooling
air on passing through the baffles is of the order of 50°
to 60° F. The corresponding air quantity may be
considered the minimum and the related conductivity
the optimum.
The “apparent conductivity” of the skirt exit open¬
ings, defined as A2/F, is found to be large compared with
the conductivity of the engine. The pressure drop
through the skirt is therefore small in comparison with
the pressure across the engine, except for the narrowest
skirt 3. This condition is different for the unbaffled
engine. In such an engine the pressure drop is largely
used to create velocity in the exit opening. It may, in
consequence, be seen from table I that a value of very
nearly 1 q is available for cooling under ordinary con¬
ditions.
PUMP EFFICIENCY
It has been shown in the first part of the paper that
the pump efficiency is given by formula (3)
,=k(^T 1
Vp:
\qj GD-a
£>n
for the case of the propeller off. Similarly, formula (4)
is used for the power tests. The values of CDo and tj0,
which quantities relate to the closed basic contour indi¬
cated in figure 1 , were determined by tests of the actual
shape 19 — 5 — 0 — 3 — 0 as CDo=0.112, or a drag of 42
pounds at 100 miles per hour, and by tests of the shape
19 — 5 — C — 3 — 0 as rj0= 74.2 percent.
For propellers B and C the values of the constant C,
representing KF/SPC, in formula (4) at the standard
value of 1/jqr 0f 1.8 are 0.046 and 0.099 for the con¬
ductivities K of 0.0424 and 0.0909, respectively.
The experimentally determined pump efficiencies are
given in table I. These efficiencies are in strict accord¬
ance with the definition given in the introductory
analysis and in complete agreement with one adopted
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
377
in reference 11. The drag obtained on the closed basic
cowling shape (fig. 1) is to a certain extent arbitrary,
thus permitting efficiencies in excess of unity as may
be noted in a few cases. It must be realized that such a
definition permits efficiencies in excess of unity, ex¬
plainable by the fact that some duct arrangements
improve the flow to some extent, which condition might
Figure 16. — Pump efficiency against skirt exit area for several skirts.
be expected to occur on somewhat inefficient forms,
that is, forms with poor streamlining.
The table shows widely varying pump efficiencies
from almost zero to more than unity (i. e., 100 percent).
Some of the results are reproduced in figures 16, 17, and
IS. In figure 16 the pump efficiency is plotted against
therefore, does not necessarily attain the optimum
efficiency at each skirt size. This fact is particularly
true for the small and the large skirt openings. Notice
that skirt 2 yields efficiencies of from 50 to more than
80 percent for normal conductivities of baffled engines,
and of 100 percent for the unbaffled engine. As might
be expected, the pump efficiency is seen to increase
with increase in flow velocity through the exit opening,
indicating that the major loss is of the nature of mixing
or impact loss occurring along the nacelle.
Figure 17 is a cross plot of figure 16, the efficiency
being plotted against the conductivity, each curve repre¬
senting a given skirt. Note, in particular, that the
the area of the exit opening; each of the three curves
relate to a constant conductivity. Note that the peak
efficiencies increase with the conductivity and occur
at successively larger exit openings. It is to be noted
that the pump efficiency depends to a considerable
extent on the shape of opening and not only on its
cross-sectional area. The curve for each conductivity,
smaller skirt openings yield considerably higher effi¬
ciencies at the low conductivities corresponding to
standard type baffles. The dotted curve obtained on the
large nacelle 2 with a small skirt opening, shown in this
figure for comparison, gives an efficiency of from 80 to
90 percent in the same range of conductivity, indicat¬
ing definitely a beneficial influence from the increase
in nacelle diameter.
378
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 18 refers to the large nacelle, 2. Note that
the efficiencies exceed those from the tests of the small
nacelle, all lying in the range from 70 to 100 percent.
These tests were obtained with skirt 6, the exit opening
being varied by increasing or decreasing the actual
length of the skirt. As skirt 0 is cylindrical, the exit
area was varied without changing the external contour
of the body.
The effect of flaps on the pump efficiency is shown in
figure 19, in which the pump efficiency is plotted against
the flap angle in degrees. The steep slope of the curve
at small angles confirms the importance of careful stream¬
lining in order to attain the highest efficiencies. These
tests were obtained on skirt 8, which was successively
bent in the shapes indicated in the main drawing (fig.
4). It is of interest to note that the available pressure
drop is increased only very slightly by the flaps (table
ing figures 21(b-e) serve to illustrate the direction of
the flow lines in front of the engine and the magnitude
of the conductivity. The value of the conductivity
obtained from the location of the streamline outlining
o
the flow into the cowling is in expected agreement with
the calculated value; this particular streamline corre¬
sponds very nearly to the smoke line shown in figure
21(d). In figure 21(c) all the smoke flows outside,
while in 21(e) all the smoke flows definitely through
the cowling. Note the closeness of the smoke nozzle
to the axis. These figures also demonstrate the
instability of the flow around the nose of a cowling, as
the smoke stream oscillates alternately in and out of
the cowling.
COOLING
The photographic smoke-flow studies show a violent
large-grain turbulence in front of the engine. This
Figure 20. — Measured streamlines for test arrangement 7 — 2 — B, — 3—0.
I), the maximum increase amounting to less than 20 per¬
cent and associated with a decrease in pump efficiency.
STUDY OF FLOW LINES
In order to gain a quantitative insight into the con¬
dition of the flow around and into the cowling, the actual
flow lines were determined as shown in figure 20 (the
method used will be described in a later paper) and a
photographic study of smoke flow was carried out.
Figure 21 shows a group of smoke pictures taken with a
moving-picture camera. A study of these films in
slowr motion reveals several interesting details. There
seem to exist certain fairly well-defined main flows
almost stationary in character. The flow appears, on
the whole, extremely turbulent with disturbances of
large size. Figure 21(a) shows the flow' in front of the
engine. Notice the very disturbed flow'. The remain-
fact must be kept in mind when analyzing the results
of the cooling tests. These results are given in com¬
pact form in the main table I. The temperatures given
are the temperatures of the front and the back of the
cylinder barrel. Figure 22(a) is an example of the
actual distribution of the temperature around the
electrically heated cylinder, the front being indicated
by the 0°. This test refers to the standard baffle
arrangement shown in cross section in figure 6. The
temperatures plotted are the differences between the
cylinder temperature and that of the tunnel air stream.
The electric heat input was held constant throughout
all tests at 1 .75 kilowatts so that the index temperature
is a direct measure of the local heat transfer. All
heat-transfer tests are taken at a tunnel speed of 100
miles per hour.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
379
(a) Smoke flow in front of the cowling without the propeller.
(b) Smoke flow into the cowling without the propeller.
Figure 21.— Smoke flow around cowlings.
380
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
4
h
7 ^
(c) Smoke flow into the cowling outside the streamline with the propeller (d) Smoke flow into the cowling with the propeller operating; streamline.
operating.
Figure 21.— Continued. Smoke flow around cowlings.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
(e) Smoke flow into the cowling inside the streamline with the propeller
operating.
Figure 21. — Continued. Smoke flow around cowlings.
D 45 90 135 180
Front Hear
Angular position around cylinder, degrees
(a) Several cases with no propeller.
Angular position around cylinder, degrees
(b) Reference case with no propeller and with propeller B ; 1<= 0 0424.
Front Rear
Angular position around cylinder, degrees
(c) Condition corresponding to most efficient cooling; A'=0.0424.
Figure 22. — Temperature distribution around the electrically heated cylinder.
382
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
A reference point for the index temperatures tabu¬
lated in table 1 is obtained by comparing any given case
with the temperatures given for the test arrangement
7 — 2 — B — 3 — 0, which copies an actual power run of a
similar engine of 550 horsepower tested at the same
tunnel velocity of 100 miles per hour and using the
same external cowling arrangement. This engine
A p, lb. /sq.ft.
Figure 23. — Rear index temperature against A p for the various noses on skirt 2;
K= 0.0424.
showed a maximum cylinder temperature of 400° F.
above that of the air stream. The index temperature
of 73° shown in table I for this particular test repre¬
sents, therefore, exactly the same condition of cooling;
that is, a rear temperature of more than 73° may be
considered unsatisfactory in the same sense as a tem¬
perature in excess of 400° F. above that of the sur-
Figure 24. — Rear index temperature against A p for the various skirts for nose 7 with
no propeller; K= 0.0424.
roundings in the actual case. Other plots of tempera¬
ture distribution around the cylinder barrel are shown
in figures 22 (b) and (c). It is to be noted that the
condition constituting sufficient cooling on the Pratt
& Whitney Wasp SlHl-G might be too conservative.
It is entirely possible that a reference temperature of
80° F. or even of 90° F. might represent sufficient
cooling on improved designs.
Figures 23, 24, 25, and 2G illustrate the dependency
of the rear index temperature on the pressure drop
across the engine, plotted on logarithmic scales. The
slope of the line that seems to fit the experimental
results the closest is —0.31, or Ti=CAp~°-zl. Figure
23 shows results for the various nose shapes using skirt
2 and no propeller; figure 24, the results for various
Figure 25.— Rear index temperature against A p for the various spinners on noses 2
and 7 with skirt 2; A'=0.0424.
skirts in conjunction with nose 7; figure 25 gives the
results for a number of combinations of propellers and
spinners on noses 2 and 7 ; and figure 26 shows the
results for the conductivity 0.0909 both for the large
and the small nacelles. Two main conclusions may be
drawn from these results:
(1) That the rear index temperature for a given con¬
ductivity depends only on the pressure drop through
Figure 26.— Rear index temperature against A p for several arrangements; A'=0.0909.
the baffle. All points lie reasonably close to the aver¬
age line drawn in the figures.
(2) That the increased conductivity has a detri¬
mental effect on the heat transmission. It is seen by
comparing the results in figures 25 and 26 representing
the conductivities of 0.0424 and 0.0909, respectively,
that the temperature is increased from 78° F. to 102°
F. at a given pressure drop of A^=10 pounds per
square foot.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
383
Net efficiency , r/n . percent
Figure 27.— Rear index temperature against 17 „ for al! eases of 0.0424 conductivity with curves designating equal performance in respect to cooling and efficiency.
Small nacelle used.
38548—38-
26
384
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
In figures 27 and 28 the index temperature is plotted
against the net efficiency ijn, in figure 27 for the stand¬
ard conductivity K= 0.0424 and the small nacelle, and
in figure 28 for the large conductivity K— 0.0909 for
tests on both the small and large nacelles. These
charts give in a compact form the entire results of this
investigation. The cost of the cooling is represented
by the distance between the particular point rjn and
the ordinate representing the ideal efficiency at rj0=74.2
percent. The temperatures are seen to range from 54°
F. to more than 100° F. The curves drawn in the
figures arc considered to be curves of constant
performance. They are obtained by the following
reasoning: If overcooling exists in a certain test,
there is a possible and permissible gain in the net
efficiency, which can be realized by using a narrower
skirt. Assuming a constant pump efficiency there exist
the following relations:
The index temperature Tx— Ap-0-31 constant and the
work done r}0—r]=Ap 3/2 constant and thus, by elimina¬
tion of Ap, Tt= (??0— constant or Tt is nearly
proportional to the inverse of \/r]o~rln> Thus it is seen
that the change in Tt due to a regulation in the quantity
of cooling air can be predicted on the basis of the net
efficiency. A given increase in index temperature is
thus associated with a definite increase in net efficiency.
Although the rear cylinder temperatures seem to
depend in a very regular manner on the pressure drop
A p, the front temperature shows no such relationship.
It is rather remarkable that the front portion of the
cylinders cools, on the whole, just as well as the baffled
portion. The very unstable three-dimensional flow in
front of the cowling is obviously very beneficial to the
heat transmission. As the present investigation is
restricted primarily to the matter of cowling design,
only a few remarks will be made here. It is noted
(fig. 22(a)) that an unbaffled engine is overcooled on
the front and overheated on the rear, demonstrating
conclusively the technical value of the baffles. A
comparison of figures 22(b) and (c) shows the apparent
value of a spinner in improving the frontal heat trans¬
mission. A study of the main table I reveals several
cases of good front cooling. Spinner 3 appears to show
a very low front temperature.
In regard to the cost of the cooling on the front, it is
observed in table I that the drag of the basic cowling
shape is 42 pounds at 100 miles per hour and that the
drag of the better streamline form employing nose 8 is
only 32 pounds. It seems necessary to conclude that
the difference of 10 pounds represents the cost of the
comparatively poor aerodynamic shape of the nose of
the conventional type cowling, which, on the other
hand, reappears as a beneficial effect in regard to the
cooling of the front of the cylinders. It might be
expected that the reasonably large spinner might re¬
claim a certain fraction, at least, of the 10-pound drag
loss. The various spinners tested have been described
(fig. 9). It is quite interesting to observe that several of
these spinners show a large beneficial influence on the
front cooling, particularly the flat, spinners 1, 3, anti 0.
Table II shows the front temperatures obtained on
various spinners.
Figure 29 shows the pressure distribution obtained
on nose 7 in the presence of three typical spinners. In
this group the plot (b) for spinner 7 is of the most
interest, owing to the fact that this test represents the
most efficient arrangement obtained throughout the
entire series. (Cf. fig. 27.) The high net efficiency
and the good cooling are in this case definitely attribu¬
table to the spinner. The relatively small dimensions
of this spinner make jtossible the practical realization
of these gains.
<£ propeller
Figure 29.— The pressure distribution as affected by several spinners.
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
385
There is, finally, another problem that will be touched
upon. It concerns the matter of baffle design. The
present investigation confined itself to tests on a single
baffle as described. Pitot tubes installed between the
fins of the cylinder permitted the determination of the
energy loss along the flow path. Results obtained in
parallel with the temperature curves just presented
(in fig. 22) are given for the total pressures in figure 30.
Figure 30(a) shows these curves for the two lowest
conductivities. It may be seen in figure (3 that the
baffle covers about 45°, extending from 100° to 145°
for the tightly fitting baffle. It is interesting so
observe that only about one-third of the energy lost
takes place inside the baffle and two-thirds behind.
The baffle transposed rearward one-half inch and
forming a diverging channel appears to provide a more
efficient design, the exit loss being fairly small. The
next figure 30(b) shows several cases with baffles
removed. The low pressure in front of the cylinder
with nose 3 is rather noticeable. The standard baffle
is shown again in figure 30(c). Notice the slight
effect of the propeller. Figure 30(d) is of interest
as it refers to the test arrangement 7 — 2— C — 3—7,
which represents in every respect the best combination
discovered in the investigation.
Front Rear
Angular position around cylinder, degrees
Figure 30— Total pressure distribution around the cylinder.
386
REPORT NO. 592 -NATIONAL ADVISORY COMMITTI I I OK U KONAI TICS
GENERAL CONCLUSIONS
1. It has been found that the basic blunt-nose
cowling shape of an air-cooled engine has a drag
somewhat in excess of that of a more properly stream¬
line shape, such as an airship form. It was shown
that the blunt nose is the cause of an instability in the
air flow in front of the cowling that sets up a large-
scale turbulence. This turbulence accounts for the
remarkably good cooling on the front of the engine.
The mechanical cost of this particular cooling compares
favorably with the pressure cooling obtained on the
rear of the engine.
2. The pumping efficiency, the ratio of the internal
work done to the work expended by the corresponding
increase in drag, has been found to range from almost
zero to more than unity. The pump efficiency is
largely dependent on the flow velocity and the shape
of the exit passage.
3. The leading edge of the cowling should be given a
smooth, very rounded form, such as nose 7. The
diameter of the cowling inlet nose opening was found
to be of little significance, either in regard to drag or
in regard to cooling. As a general rule, the larger the
opening, the better, care being taken only to provide
a proper design of the nose contour. In this connection,
it is worth keeping in mind that the flow immediately
in front of the cowling is almost radial. A too straight
cowling gives rise to a condition of breakdown of the
flow at the front edge of the cowling. This effect was
demonstrated in the present investigation in tin1 case
of cowling 1.
4. It has been found that a smooth contour line for the
skirt design is a primary requirement. The rear
edge of the skirt should not project into the air stream.
The necessary exit opening should be obtained by a
retraction of the inner cowling. The design of the
inner cowling is less critical.
5. The most obvious method of varying the pressure
across the engine is to vary the area of the exit opening.
If this increase in area is accompanied by an outward
flare of the trailing edge as is accomplished by the
use of cowl flaps, a slightly greater increase in the pres¬
sure difference can be obtained than that resulting from
a simple increase in area.
6. It is obvious from theoretical considerations that
in a normal cruising condition tin* propeller causes only
a slight contraction of t he streamlines around the nacelle
and that therefore no important effects of any kind arc
to be expected. T his effect was umply verified by the
test results. The. propeller actually shows a blocking
effect that gives a slight decrease in cooling. Spinners
influence the stability of the flow around the front of
the cowling and do, in some cases, improve the over-all
performance of the combination. Spinner 7 on cowling
7 showed both an increase in net efficiency and improved
cooling. The condition at low air speed is discu»ed in
reference 9.
7. Tests performed on the combination with the
larger afterbody showed a consistent increase in per¬
formance, demonstrating the importance of a Mnooth
merging of the contour lines of the front and aftcrlmdx
and the value of a better exposure of the exit opening
of the unexpanded and stabler air stream.
S. The main result of the cooling problem studied in
this investigation is that a tightly baffled engine i«
definitely superior in regard to cooling efficiency The
results obtained at the minimum conductivity K
0.0424 are in every respect better than tliors* obtain'd
at the conductivity A 0.0909 or on an unbafflcd cn-
mr
gine. Another important result i- the observation that
the inherent large-scale turbulence occurring in front of
the cowling accounts for the good cooling on the ex¬
posed frontal area of the engine This effect should, of
course, be used to the fullest extent in the design of
baffles.
9. It is of interest to note that, although increased
conductivity of an engine i* beneficial to pump efficiency
the detrimental effect on cooling i*. much greater that
no compromise is possible. In other words, a tightly
bullied engine is superior in over-all performance in
spite of an inferior pumping efficiency. With h new
type of nose-slot cowling greater pump efficiency is ob¬
tained at low conductivities.
.
Langley Memorial Aeronautical Larokatouv,
National Advisory ('omxiiitie eor Akkonai m-
Langley Field, \ a., May IS, IUS6.
FI LL-SCALE TESTS OF N. A. C. A. COWLINGS
387
LIST OF SYMBOLS
j)f< pressure in front of the engine.
/>n pressure in rear of the engine.
S/>, pressure drop across the engine, Aj> pf —pT.
l), drag of the cowling-nacelle unit.
U0, drag of a smooth nacelle entirely enclosing the
engine.
q, dynamic pressure of the air stream,
p, density of the air.
b\ frontal area of the engine.
c D
Ld qF
qb'
quantity of the air flowing through the cowling.
1’, velocity of the air stream.
r)t pump efficiency, without propeller.
(if Uq) t
R, net force on the thrust balance with propeller on.
7’ R f l), propulsive thrust.
/’, power supplied to propeller.
RY , .
x)n j, • net eiliciency of propeller-nacelle unit.
S, propeller disk area.
p • -1,
... .• unit disk loading.
o.S l
1 .. pS
< r,
net propeller-nacelle eiliciency obtained on same
set-up as used for /V
QAp
ating.
.1, area of the free air stream entering the cowling.
A
r\r pump efficiency with propeller oper-
’’ Vn ' /
k-
-V'
V 7
k
A
b
comluctivitx of the engine
f V
\ 1
Q Ky{tr
p,r static pressure at the exit of the >lot.
1,. velocity in the exit of the slot.
Api, pressure drop through exit passage.
A2, area of exit of the slot
A/' Ayv-f Ap2, total pressure drop across cowling.
K2, apparent conductivity of the exit slot.
relation of conductivities of
engine and slot exit.
n, revolutions per second of the propeller.
If, diameter of the propeller.
Cn
T
uni)'’
thrust coefficient.
CP f>n qjh' power coefficient.
V
jp advance-diameter ratio of the propeller.
TV
v j, > propulsive efficiency.
T(, index temperature.
H , work done by the cooling air.
REFERENCES
1. Weick, Fred E.: Drag and Cooling with Various Forms of
Cowling for a “Whirlwind” Radial Air-Cooled Engine — I,
T. R. No. 313, N. A. C. A., 1929.
2. Weick, Fred E. : Drag and Cooling with Various Forms of
Cowling for a “Whirlwind” Radial Air-Cooled Engine — II.
T. R. No. 314, N. A. C. A., 1929.
3. Schey, Oscar W., and Biermami, Arnold E.: The Effect of
Cowling on Cylinder Temperatures and Performance of a
Wright J 5 Engine. T. It. No. 332, N. A. C. A., 1929.
4. McAvov, William H., Schey, Oscar W., and Young, Alfred
W.: The Effect on Airplane Performance of the Factors
that Must Be Considered in Applying Low-Drag Cowling
to Radial Engines. T. R. No. 414, N. A. C. A., 1932.
5. Theodorsen, Theodore: On the Theory of Wing Sections
w ith Particular Reference to the Lift Distribution. T. R.
No. 383, N. A. C. A., 1931.
6 Goldstein, Sydney: On the Vortex Theory of Screw Propel¬
lers. Proc. Roy. Soc. (London), Series A, vol. 123,
April 6, 1929, pp. 440-465.
7. Wrick, Fred E., and Wood, Donald IE: The Twenty-Foot
Propeller Research Tunnel of the National Advisory Com¬
mittee for Aeronautics. T. R. No. 300, N. A. C-. A., 1928.
8. Theodorsen, Theodore, Stickle, George W., and Brevoort,
M. J.: Characteristics of Six Propellers Including the
High-Speed Range. T. R. No. 594, N. A. C. A., 1937.
0 Theodorsen, Theodore, Brevoort, M. J , and Stickle, George
W.: Cooling of Airplane Engines at Low Air Speeds.
T. R. No. 593, N. A. C. A., 1937.
Ill Theodorsen, Theodore, Brevoort, M. J., Stickle, George W.,
and Gough, M. N.: Full-Scale Tests of a New Type
N, A. C A. Nose-Slot Cowling. T. R. No. 595, N. A.
C. A., 1937.
11, Hartshorn, A. S.: Wind Tunnel Investigation of the Cooling
of an Air-Jacketed Engine. R. <fc M. No. 1641, British
A. R. C., 1935.
388
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I.— CONDENSED EXPERIMENTAL RESULTS
1
2
3
4
5
6
7
8
9
10
1
Remarks
Designation of arrangement
Pf/q
prlq
(2-3)
A Plq
Co
(D/qF)
Drag in lb. at
? = 25.6 lb. per
sq. ft., or thrust
at 1/Vp7=1.8
and 5 = 25.6 lb.
per sq. ft.
1/ Vp7=1.8
Vp
Index tempera¬
tures
Nose
Skirt
Propeller
Inner cowling
Spinner
Front
Tf
Rear
Tr
\
NACELLE 1— ZERO
AIR
2— 5—0 —3—0 _
0. 1193
45. 0
Closed skirt.
7— 2—0 —3—0 ..
1. 00
-0. 274
1. 274
. 1365
51. 5
7 3—0 —3—0... _ _
1 . 00
—.071
1.071
. 1246
47.0
Closed by flat plate at front of
7— 6—0 —3—0- .
1. 00
-. 417
1. 417
. 1749
66. 0
t cylinders.
7— 7—0 —3—0 ..
1. 00
-.442
1.442
.215
92.5
7— 0—0 —3—0 .
1.00
— . 371
1. 371
. 1316
61. 0
j
STANDARD BAFFLES— CONDUCTIVITY 0.0424
0— 2—0 —3—0 _
1.004
-0. 295
1.299
1. 182
446. 0
0. 058
0— 2— C —3—0-
.910
-.230
1. 140
-0. 075
.068
1— 2—0 —3—0— .
1. 008
— . 062
1 . 070
.330
124. 5
.214
1— 2— B —3—0-..
. 982
-. 050
1 . 032
206. 0
. 589
.316
1— 2— C —3—0....
. 906
-. 059
. 965
211.0
. 605
. 320
2— 2—0 —3—0 _
.956
-.048
1.004
. 194
73.0
.517
81. 7
57. 1
2- 2— B —3— CL
. 926
.983
222. 0
.636
.421
2— 2— C —3—0 _
.883
-.057
.939
223.0
.640
.412
71.6
56. 2
2— 5—0 — 3— 0--
. 123
46. 4
Zero cooling air.
3— 2—0 —3—0 _
. 973
-.051
1. 024
. 196
74.0
.521
66. 0
57.0
3— 2— B —3—0..-
.877
-. 061
. 939
226. 0
.648
.445
3— 2— C —3—0 _ _
.853
-.062
. 915
227. 0
. 650
.438
59.8
60.8
4— 2—0 —3—0 _
.989
-. 039
1.027
. 1935
73.0
.539
•
4— 2— B —3—0 ...
1. 004
-. 032
1. 036
214. 0
. 612
. 375
4— 2— C —3—0 _
.894
-. 045
.944
218.0
.625
.363
5— 4—0 —2—0 . .
. 984
. 064
.920
. 1755
66. 4
.823
Conductivity 0.C69. Pre-
6— 2—0 — 3— 0.... .
.971
-. 058
1. 030
. 2027
76. 5
. 486
79.3
65.9
lim inary test.
6— 2— B —3—0...
. 885
-.061
. 945
224. 0
.642
.423
6— 2— C —3—0 . .
.868
-. 074
. 942
220. 0
.631
. 380
6— 3—0 —3—0- . .
. 962
.345
. 616
. 1603
60. 5
.417
81.8
68.8
6— 4—0 —2—0....
. 960
.047
.913
66. 4
.813
Do.
7— 2—0 —3—0 .
.983
-.046
1.030
. 1929
72. 5
.551
89. 5
70. 6
7— 2— B —3—0 . . .
.901
-.053
.954
223. 0
. 638
.410
88. 6
73.0
7— 2— C —3—0 _
.871
-.062
.933
223. 0
.640
.408
77.2
64.7
7— 2— B*— 3 — 0
.888
-.045
.934
226.0
. 646
.432
7— 3—0 —3-0 . .
.946
.358
. 588
. 1497
56. 5
.494
104. 6
76.5
7— 4—0 —2—0 _
. 952
. 067
.885
. 1772
67. 0
. 757
Do.
7— 6—0 —3—0....
. 975
— . 218
1. 194
. 2700
102.0
.349
82.0
59.0
7— 7—0 —3—0 ...
.967
-. 249
1. 215
.387
146. 0
. 205
71.3
50.7
7— 7— C —3—0 _
.871
-.312
1. 183
167. 0
.478
81.0
81.7
7 0—0 —3—0 _ .
.953
-. 261
1. 214
.237
89.5
.451
81. 5
60.0
FLAPS
7— 8—0 —3—0 _ .
0. 956
-0. 222
1. 179
0. 265
100. 0
0. 353
7— 8 — C —3—0 ...
.870
-. 264
1. 133
201.0
.336
7—8—0 —3—0. . .
.980
-. 233
1. 213
.307
116. 0
.289
fi-inch flare.
7— 8— C —3—0 .
.877
-. 293
1. 170
186. 0
.534
.280
Do.
7— 8-0 —3—0 ...
.972
-. 242
1. 214
. 372
140. 5
. 218
1-inch flare.
7— 8— C —3—0 ..
.874
-. 319
1. 193
170. 0
.486
. 235
Do.
7— 8—0 —3—0 ..
. 995
— . 246
1. 241
. 506
191. 0
. 149
2-inch flare.
7— 8— C —3—0 _
.872
-.289
1. 161
108. 0
.310
. 134
Do.
7— 8—0 —3—0 ...
. 980
-. 246
1. 225
. 583
220. 0
. 122
3-inch flare.
7— 8— C —3—0 _
.874
-.291
1. 165
73. 0
. 208
. 109
Do.
STREAMLINE SHAPE
8— 3—0 —2—0 _ _
0. 1007
38. 0
Zero cooling air.
8— 5—0 —2—0....
. 0861
32.5
Do.
9—2—0 —3—0.. ......
0. 959
-0. 058
1.017
. 1987
75.0
0. 497
73.0
64.0
9 — 2— B —3—0 _
.842
-.077
.919
228. 0
0. 653
.456
74.0
75.0
9— 2— C —3—0. _
.836
-.080
.916
224.0
.643
.408
68.0
69.0
NOSE TO FIT BLOWER
15— 2—0 —3—0 _ . _
0. 984
-0. 031
1.015
0. 1975
74.5
0.500
99. 0
60. 5
’
15- 2— C —3—0 _
.893
-.044
.937
219.0
.627
.364
95. 0
63.0
PERFORATED DISK
18— 2—0 —3—0
0. 793
-0. 074
0. 867
0. 1908
72. 0
0.429
18— 2— B 3—0
. 768
-.083
.851
223. 0
0. 640
. 354
18— 2— C —3—0 _
. 692
-.086
. 778
| -
229.0
. 655
.365
110.0
71.0
FLAT DISK
10— 2—0 —3—0 _
-0. 300
0. 1259
Zero cooling air.
19— 5—0 —3—0 _ _ _
. 1115
42. 0
Zero cooling air. (C/j„).
19— 5— B —3—0 _ _
254, 0
0. 728
Zero cooling air.
19— 5— C —3—0 _ _
L .
259 0
. 742
—
Zero cooling air. (rju)
FULL-SCALE TESTS OF N. A. C. A. COWLINGS
TABLE I.— CONDENSED EXPERIMENTAL RESULTS— Continued
389
Designation of arrangement
W3
a
0) O
■ — • o
0)
C/5
c
T? g* « a
'Jt t- 2
£ 03 Ph ” BO
P//9
Pr/?
4
5
6
7
8
9
10
Drag in lb. at
Index tempera¬
tures
(2-3)
AP/S
of
3,
9=25.6 lb. per
sq. ft., or thrust
at l/v'PL=i.8
and 9 = 25.6 lb.
per sq. ft.
*7n at
i/v'p7=i.s
Vv
Front
T,
Rear
Tr
Remarks
SPINNERS
. 2-
2-
2-
2-
2-
2-
2-
2-
2-
2-
2-
2-
2—
2-
2-
2-
2—
2—
2_
2—
2
2-
2-
2—
2-
2-
9 _
-0 —3—1 _
-C -3—1 _
-0 —3—1 _
-0 —3—2 _
-C —3—2 _
>0 —3—9 _
-0 —3—3 _
-C —3—3 _
-0 —3—1 _
B —3—1 _
■C —3—1 _
-0 —3—2 _
-B —3—2 _
-C —3—2 _
0 3- 3
B —3—3 _
■C —3—3 _
•C -3—3 _
•0 — 3— 2&3
B — 3— 2&3 -
•0 —3—6 _
B —3—6 _
■C —3—6 _
0 -3-7 _
•C -3-7 _
C —3—9 _
C —3—10 _
598
. 674
.437
. 707
. 723
. 743
. 895
. 832
. 481
. 673
.547
. 548
. 677
. 608
. 176
.028
.087
. 671
. 126
. 009
. 251
.431
.351
. 778
.744
. 199
. 606
-0. 085
-.071
-. 103
-.074
-. 073
-. 071
-. 062
-.071
-.088
-. 070
-.087
-.069
-.066
-.034
-.210
-. 178
-. 194
-.082
-.206
— . 177
-. 121
-. 106
-.117
-.070
-. 065
-. 145
-.080
0. 683
. 745
.540
.781
. 796
.814
.957
. 903
. 569
.743
.634
.617
.743
.692
.034
. 150
. 107
.753
.080
. 186
.375
.537
. 468
.848
.809
.344
.686
0. 1855
"Visii"
. 1975
. 1895
’. 1815
. 1815
. 1550
1510
. 1722
. 1935
70.0
215.0
69.5
74. 5
214.0
222.0
71.5
228. 0
68. 5
221.0
230. 0
68.5
222. 0
224. 0
58. 5
216.0
220.0
228.0
57. o
219.0
65.0
220. 0
224.0
73.0
231.0
231.0
230. 0
0. 321
0.617
.237
_ . -
.339
.612
.252
.637
.323
83.0
75.0
.504
84.0
56.0
.654
. 452
78.0
59. 0
_ _ _ _ _
. 256
72.5
66.0
. 634
. 272
59.0
62.0
.660
. 284
65.0
63. 0
. 291
.635
. 275
67.0
65. 0
.643
.268
62. 0
59.0
. 006
1 12. 0
158. 0
. 620
. 022
50. 0
78.0
.631
.015
68. 0
112.0
.652
.334
82.0
62.0
.024
87.0
128.0
. 628
.032
65.0
98. 0
. 159
69.5
74.0
. 630
. 161
55.0
63. 0
. 642
. 148
65.0
74.0
_
. 400
80.0
67. 0
. 681
.413
65. 0
54.0
.661
. 115
55.0
85.0
.658
.313
Position 1.
Do.
Position 2.
Dish pan.
Do.
Position 1.
Do.
Do.
Dishpan.
SPECIAL DEVICES— HONEYCOMB
3— 2—0 —3—0
3— 2 — C —3—0
7— 2—0 —3—0
7— 2— Bx— 3— 0
0. 864
-0. 049
0.913
0. 1908
72.0
0. 461
63.0
66.0
. 775
-.063
.838
239. 0
0. 684
.609
69. 0
73.0
.871
-.043
.914
. 1908
72.0
.464
64.0
65.0
.844
-.048
.892
.
232. 0
.664
.495
84.0
70.0
AUXILIARY AIRFOIL
7— 2—0 —3—0
7— 2— Bx— 3— 0
7— 2—0 —3—0
7- 2— Bx— 3— 0
7— 2—0 —3—0
7— 2— Bx— 3— 0
0. 961
.906
.965
-0. 036
-. 039
0. 997
. 945
0. 2200
83.0
228.0
0. 653
0. 386
. 475
—
.
No. 1 position 1.
Do.
-.038
1.003
. 2320
87.5
.351
86. 0
63. 0
No. 1 position 2.
.876
-.045
.921
225. 0
.646
.423
,82. 0
64.0
Do.
.977
-.028
1.005
.2040
77.0
.458
.
No. 2 position 1.
.905
-.038
.943
229. 0
. 657
.493
Do.
TAIL PUMP-CONDUCTIVITY 0.0250
19— 5—0 —3—0.
2— 5—0 —3—0.
2— 5— B —3—0.
0. 928
.903
1
0. 357
.281
0.571
.622
0. 1087
. 1272
41.0
48.0
242.0
0. 693
.685
.270
Zero cooling air.
NACELLE 1— BAFFLES BACK H INCH— CONDUCTIVITY 0.0909
7— 2—0 —3—0
0. 992
0 116
0. 876
0. 2000
75. 5
0.837
68.0
72.0
7— 2— Bx— 3— 0 _
.891
. 119
. 772
229. 0
0. 656
. 777
80.0
90. 0
7— 3—0 —3—0 _
.941
.588
.353
. 1510
57. 0
_
.480
89.0
98. 0
7— 6—0 —3—0 _
.999
-. 139
1. 138
. 2910
110.0
_ _ _ _ _ _
. 615
59.0
63. 0
7—7—0 —3—0 _ _ _
.987
-.206
1. 193
.4130
156. 0
.393
60. 0
63. 0
NACELLE 1— BAFFLES REMOVED— CONDUCTIVITY APPROXIMATELY 0.3-0.6
0— 0—0 —2—0.
1— 2—0 —2—0.
1— 2— C —2—0-
3— 2—0 —2—0
3— 2— C —2—0 .
7— 2—0 — 2— 0..
7— 2— C —2—0.
7— 3—0 —2—0-
7— 6—0 —2—0..
0. 958
.878
.909
. 747
1.015
. 808
.993
.999
0. 835
.816
.428
.320
.768
.676
.902
.447
0. 123
.052
.481
.427
.247
. 192
.091
.552
0. 399
. 1630
’.’2046’
’. i6l6
\ 1325
. 2400
150.5
61. 5
243. 0
77.0
219.0
61.0
237. 0
50.0
90. 5
0. 697
.628
’.’oso’
58.0
65. 0
38.5
42. 0
50. 0
53.0
76.0
44.0
89.0
113.0
87.0
95.0
100.0
115.0
146.0
72.0
BUMPED COWLING
17— 0—0 —2—0.
17-10—0 —2—0.
17— 10— C —2—0.
0.916
.865
0. 866
.800
0. 050
.065
0. 1259
47.5
250.0
46.5
255. 0
I
_
6. 716
. 1232
_ Nose closed off.
1
. 739
Do.
m
REPORT NO. 592— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I— CONDENSED EXPERIMENTAL RESULTS— Continued
1
2
3
4
5
6
7
8
9
10
Remarks
Designation of arrangement
Pflq
prlq
(2-3)
A p/q
Cd
<D/qF)
Drag in lb. at
g = 25.6 lb. per
sq. ft., or thrust
at 1/v/jPc=L8
and 5=25.6 lb.
per sq. ft.
rjn at
l/yPc = 1.8
Vp
Index tempera¬
tures
Nose
Skirt
Propeller
Inner cowling
Spinner
Front
Tf
Rear
Tr
NACELLE 2— STANDARD BAFFLES— CONDUCTIVITY 0.0424
19— 9 — 0 —6—0—
0. 1126
42. 5
Zero air.
7—7—0 —4—0. . . . .
0. 962
-0. 205
1. 167
. 2680
101.0
0. 339
80.0
53.0
7— 7 — B *—4—0— . . . .
.889
-.256
1. 145
208. 0
0. 595
.384
91.0
67.0
7— 7— C —4—0 .
.886
-.241
1. 127
205. 0
.587
.357
7— 6—0 —5—0 _ _
.967
.082
.885
. 1696
64.0
.602
59.0
87.0
1.7-inch opening.
7— 6 — Bi — 5 — 0 _
. 878
.075
.803
236. 0
. 677
. 508
98. 0
74. 0
7— 6—0 —5—0 _
.973
.026
.947
. 1762
66. 5
.597
83.0
57.0
2.5-inch opening.
7— 6— B,— 5— 0 . . .
.892
.023
.869
234.0
.671
. 522
100. 0
75.0
7— 6—0 —5—0
959
— . 029
988
. 1855
70.0
. 562
3.9-inch opening.
7— 6— B,— 5— 0 _ _
.881
-. 033
. 914
233. 0
. 668
.543
7— 0—0 —5—0 .
.963
— . 139
1. 102
.2070
78.0
. 510
7— 6—0 —6—0
. 982
. 028
954
. 1749
66. 0
. 617
.877
.024
.853
237.0
.679
. 574
ms-inch rear opening.
7— 6—0 —6—0
.993
. 147
. 846
. 1630
61.5
.635
jiU-inch rear opening.
7— 6— B ,—6—0
. 885
. 134
. 751
241. 0
. 692
.599
7— 8—0 —6—0
. 953
— . 282
1. 235
4480
169. 0
172
2-inch flare.
7— 8— B x— 6—0-
.872
— . 425
1. 297
156. 0
. 447
.230
Do.
7— 9—0 —6—0-
. 900
. 1193
45.0
7— 9— C —6—0—
.890
251. 0
.720
SPINNERS
7— 0— C —6—1.
0. 523
249. 0
0. 713
Position 1.
7— 9— C —6—1 _ ..
.312
241.0
.691
Position 3.
7— 9— C —6—1 _
. 257
237.0
. 679
Position 4.
NACELLE 2— BAFFLES BACK U INCH— CONDUCTIVITY 0.0909
7— 6—0 —5—0 .
0. 983
0. 428
0. 555
0. 1537
58. 0
0. 885
83.0
92.0
l!t-inch rear gap.
7— 6—0 —5—0 _
.979
. 191
. 788
. 1755
67. 0
. 990
77.0
84. n
2%-inch rear gap.
7— 6—0 —6—0- . . . .
.980
. 394
.586
. 1590
60. 0
.851
80.0
88.0
1 hi -inch rear gap.
7— 6—0 —6—0 _
.975
. 240
. 735
. 1735
. 919
67. O
72. 0
2-inch rear gap.
7— 6— Bx— 6— 0 _ _
.869
.241
.628
238. 0
0. 681
.804
89.0
97.0
Do.
7— 6—0 —6—0 _
.986
. 151
.835
. 1881
71.0
.900
66.0
73.0
2?t-inch rear gap.
TABLE II.— FRONT CYLINDER TEMPERATURES
OBTAINED WITH VARIOUS SPINNERS
Designation of
arrangement
Front
cylinder
tempera-
ature
Tf
(°F.)
Ratio of
front to rear
cylinder
temper¬
ature
Tr
Tr
Remarks
Nose
Skirt
Propeller
Inner cowling
Spinner
1— 2— C— 3— 9 .
83
1. 106
2— 2— 0—3— 3 _
84
1.50
Dishpan behind propeller.
2— 2— C— 3— 3 _
78
1. 323
Do.
7—2—0 —3—1 _
72.5
1.098
Position 1.
7— 2— B -3—1.. .
59
.952
Do.
7— 2— C— 3—1 _
65
1.033
Do.
7— 2— B— 3— 2 .
67
1.032
7— 2— C— 3— 2 _
62
1.05
7-2-0 —3—3 _
112
.709
7— 2— B— 3— 3 _
50
.642
7— 2— C-3— 3 . .
68
. 607
7— 2— C— 3— 3 _
82
1.322
Dishpan behind propeller.
7— 2— C— 3— 2 & 3...
7— 2— B— 3— 2 & 3...
65
. 663
7—2—0 —3—6 _
69.5
.939
7— 2— B— 3— 6 _
55
.873
7— 2— C— 3— 6 _
66
.892
7— 2— 0—3— 7 . .
80
1. 193
7— 2— C— 3— 7 _
65
1. 202
7— 2— C— 3— 9 _
55
.647
REPORT No. 593
COOLING OF AIRPLANE ENGINES AT LOW AIR SPEEDS
By Theodore Theodorsen, M. J. Brevoort, and George W. Stickle
SUMMARY
A comprehensive experimental study has been carried
out at full scale in the N. A. C. A. 20-foot wind tunnel,
the general purpose of which is to furnish information in
regard to the functioning of the power plant and propeller
unit under different conditions. This report deals par¬
ticularly with the problem of the cooling of an airplane
engine on the ground. The influence of different nose
forms, skirts, flaps, propellers, spinners, and special
blowers has been investigated. Among the more interesting
results are the demonstration of the comparative ineffi¬
ciency of adjustable skirt flaps, the detrimental effect of
small-diameter front openings of the cowling, and the very
beneficial effect of a carefully designed airfoil section near
the hub of the propeller. A small axial fan of simple con¬
struction was found to give efficient cooling on the ground.
INTRODUCTION
The problem of cooling an airplane engine on the j
ground obviously presents the greatest difficulty. The
velocity head in the slipstream is then a minimum.
The engine does not ordinarily develop its maximum
horsepower, but the quantity of heat to be disposed of
is not much reduced. A certain velocity head and a
corresponding pressure drop are generally required to
cool the engine satisfactorily. The problem then be¬
comes one of providing a certain pressure drop for cool¬
ing on the ground or at a minimum air speed; cooling
at higher speeds, of course, follows. Special devices,
such as flaps on the skirt or fans in front of the cowling,
are sometimes used to improve the cooling on the
ground.
It has been shown (reference 1) that the cooling for
the cruising condition is almost exclusively a function of
air speed, the effect of the propeller slipstream velocity
being of little importance. At low air speeds the situ¬
ation is different; the cooling is largely dependent on the
propeller effect. On the ground the cooling depends,
of course, entirely on the propeller. The subject of
primary interest in this paper is the study of the factors
affecting the cooling on the ground.
ANALYSIS OF THE PROBLEM
It was shown in reference 1 that the cooling of an
engine is a function of the pressure drop A p across the
cylinder bank. Most of the tests reported in this paper
were extended down to the minimum tunnel speed.
This minimum tunnel speed corresponds to the effect
of the local propeller slipstream on the closed-circuit
tunnel and is approximately 20 miles per hour, low
enough to permit an extrapolation of results to the
condition of zero air speed.
At very low air speeds the effect of the slipstream
dominates the situation, the propeller functioning as a
low-pressure blower. For the condition of zero air
speed, the quantity /\pfn2 has been chosen as the char¬
acteristic function, this quantity being independent of
the revolution speed of the propeller. The square root
of this quantity is plotted against the advance-diameter
ratio VfnD. Plots of this type conveniently picture the
relationship between the available pressure and the
air speed at any combinations of the other variables
and show' directly the primary results of the present
investigation .
In order to apply the results for the condition of zero
air speed, there need be known only the revolution
speed n of the propeller at any particular angle of
attack. For this purpose it is very convenient to plot
the pressure function A pjn2 against the nondimensional
powder coefficient CP at zero air speed, defined as
^ P _2*Q
p pnilT on2 IT
where P is the power and Q the torque of the pro¬
peller. A curve of this type is illustrated in figure 1
391
392
REPORT NO. 593— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 2.— The X. A. C. A. fan installed on the engine.
for a particular propeller over the entire range of blade-
angle settings. The ordinate used is actually the square
root of the pressure function, or^A pin, and the abscissa
is similarly -y/Cp. At a given power and propeller
diameter the revolution speed is known at each blade
angle and, in consequence, also the value of Ap. The
selection of the blade angle producing the highest pres¬
sure drop Ap is identical with the selection of the point
on the curve having the greatest slope for a straight
line drawn from the point to the origin. It is found,
in general, that this condition corresponds to that of the
maximum speed of the engine and a resulting minimum
propeller blade-angle setting. In order to represent the
degree of transmissibility of the baffles, a quantity K,
designated “conductivity,” has been defined in reference
1 as
where Q is the quantity of the air passing through the
baffles per second.
F, the cross section of the nacelle as a reference
area.
q, the velocity head,
and V, the velocity of the air stream.
COOLING OF AIRPLANE ENGINES AT LOW AIR SPEEDS
893
DESCRIPTION OF EQUIPMENT
This investigation was conducted in the N. A. C. A.
20-foot tunnel, which, with its equipment, is described
in detail in reference 2. The general arrangement of
the test model is shown in figure 2. Detailed descrip¬
tion of the particular equipment used is given in refer¬
ence 3. Figure 3 (a) shows the various nose cowlings
and skirts employed in the present investigation, to¬
gether with other equipment used. Figure 3 (b) [
shows an experimental blower used in conjunction
with nose 15 especially designed to house it. Figure
3 (c) shows an axial fan of simple construction here¬
inafter referred to as the “N. A. C. A. fan.” Figure
3 (d) shows a circular flat disk 24 inches in diame¬
ter, which was attached to the front of the propeller
in some of the following tests and is referred to as
“spinner 6.” Figure 3 (e) shows a normal type of
spinner which was actually an integral part of the
experimental blower shown in figure 3 (b) but which
was sometimes used separately and designated “spin¬
ner 10.” Figure 4 is a photograph of the four pro¬
pellers with the designations employed in this report.
The following table is given for reference from the
associated propeller report (reference 3). A photo¬
graph of the experimental blower is shown in figure
5; the N. A. C. A. fan may be seen just behind the
propeller in figure 2.
Figure 4.— Propellers tested.
PROPELLER DATA
Propeller
designa¬
tion
Drawing
Num¬
ber of
blades
Diameter
(feet)
Type
Remarks
Airfoil
section
A
Hamilton-Standard 6101-0 _
3
10.06
Controllable
Clark Y.
Do.
Do.
B
Hamilton-Standard 1C1-0. . _ _
3
10. 04
10. 04
Adjustable _
_ do _
. - - - -
Bx
Hamilton-Standard 1C1-0 (modified). .
3
Pitch decreased from the 70 percent
Navy plan form 5868-9 _ - ... _
radius to the tip.
C
3
10. 02
_ do
Do.
Do.
R. A. F.-6.
13
Navy plan form 5868-9 .. _ _ _
2
10.00
do
E
Navy plan form 3790.. _ _
3
9.04
do
1
RESULTS
Figures 6, 7, 8, and 9 show the basic results of the
investigation. Code numbers appear showing different
arrangements. For example, arrangement 6-2-B-3-0
indicates that nose 6, skirt 2, propeller B, inner cowling
3, and no spinner were used. The ordinate used is
Va p/n and the abscissa is the quantity V/nD, as pre¬
scribed in the preceding analysis. The range presented
is actually the entire range of flight speed and it is
noted that the slipstream effect gradually diminishes as
the speed is increased. The curves asymptotically
approach straight lines through the origin.
The series given in figure 6 shows, in particular, the
effect of the blade-angle setting, the propellers B,
Bx, C, D, and E being used on the most neutral cowlings
composed of noses G or 7 and skirt 2. It is noticed that
propeller B, or Bx, which has a good airfoil section near
Figure 5. — Wright blower with propeller C and spinner 10.
394
REPORT NO. 593— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
V_
nD
Figure 6.— Dependency of ijApIn on V/nD for several propellers at various blade angles.
the hub, is superior to the almost identical propeller
C with a round hub section. The three-blade propeller
C, and the two-blade propeller D, having identical
blade sections, give available pressure drops almost
proportional to the number of blades.
The next series (fig. 7) gives the effect of the various
noses tested, the propellers used being restricted to B
and C at blade angles of 25° and 35°. The result of
most immediate interest is the apparent inferior cooling
properties of the noses 3 and 9, the available pressure
drop A p being of the order of one-half or less of those
obtained on the normal designs. It is further noticed
that nose 4, which is characterized by a very flat nose
section pointing radially inward, shows without excep¬
tion the highest available pressure at the ground point.
Noses 6 and 7, which are among the best at cruising
condition (reference 1), appear, however, to be fairly
close to the maximum.
COOLING OF AIRPLANE ENGINES AT LOW ATR SPEEDS
nD
nD
(a) Propeller B set 25°. (b) Propeller B set 35°.
(c) Propeller C set 25°. (d) Propeller C set 35°.
Figure 7.— Dependency of -jAp/n on V/nD for several nose shapes on different propeller arrangements; skirt 2.
Figure 8 reproduces the experimental results in re¬
gard to the much-discussed problem relating to the use
of cowling flaps. The flaps used were of normal de¬
sign, 5 inches long, and were given successive increases
in flap angle corresponding to flares of 1 , 2, and 3
inches at the rear end. The results show that the gain
in available pressure is in the order of 15 percent as
compared with the unflared skirt. This result is inter¬
esting insofar as it shows the performance of normal
short flaps to produce a suction at the slot. In con¬
trast, it is seen that skirts 7 and 8 represent a decided
gain over the narrower skirt 2, this latter gain being in
the order of 50 percent. Similar results are available
for other propellers and blade angles and show sub¬
stantial agreement.
Figure 8.— Dependency of y/Ap/n on V/nD for several skirts with nose 7 and pro¬
peller C set 25° at 0.75 R.
396
REPORT NO. 593— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 9 shows the results of a related investigation
on the effect of fans or blowers, presented for comparison
in conjunction with some other typical cases. The
most interesting result is the remarkable effectiveness
of the very simple N. A. C. A. fan. The Wright blower
is seen to be very inefficient, the pressure function re¬
maining below 0.2, and is inferior to the propeller B alone.
Improved cooling on the ground is generally attained
at some loss of efficiency at high air speeds. This loss
is evident from the associated net-efficiency curves of
figure 9. It is noticed that nose 7 with spinner 10, which
gives poor cooling on the ground, shows the highest
efficiency in flight conditions; whereas the N. A. C. A.
fan, being superior for cooling, shows the lowest net
efficiency.
The following table shows the pressure constants for
the various propeller noses and skirts for the condition
of cooling on the ground.
VALUES OF PRESSURE CONSTANT
n VA P
n
AT nD=0
Blade angle
(clegs.)
Propeller B
Propeller B
Propellei
C
Propeller D
Propeller E
Remarks
15
20
25
35
15
25
30
35
40
45
15
20
25 | 35
45
15
35
10
20
30
40
N ose
1
Skirt
2
0. 193
O. 201
0. 114 0. 160
2
2
. 180
. 212!
. 128
. 149
3
2
. 150
. 202
. 146
. 108
. 129
4
2
.214
. 170
. 166
6
2
0. 160
0. 183
. 188
0. 121
0. 136
_
. 160
0. 184
0. 104
0. 127
0. 142
0. 127
0. 148
0. 195
0. 205
2
. 190
. 198
0. 170
0. 202
0. 204
0.210
0. 218
0. 195
. 152
9
2
. 128
.100
0. 200
7
8
. 199
8
. 195
14-inch flare.
8
. 201
1-inch flare.
8
.214
2-inch flare.
8
.208
3-inch flare.
15
2
0. 150
15
2
.195
Spinner 10 and Wright
blower.
N. A. C. A. fan.
15
2
_
. 243
2
.183
Spinner 10.
Figure 9.— Dependency of V Ap/n on V/nD and of 7 on 1 /%! Pc for propeller C
set 25° at 0.75 R with different test units.
Figure 10 shows the pressure functionyA^/A on the
ground for the five propellers. As explained in the pre¬
vious analysis, the slope of a line drawn from any parti¬
cular point on this curve to the origin is proportional to
the square root of the available pressure A p, the maxi¬
mum slope giving the greatest available pressure on the
ground. It is seen that this point, at which the highest
pressure occurs in most cases, corresponds to a blade
angle of less than 15°. Assuming a 550-horsepower
engine with a 10-foot controllable propeller, the mini¬
mum blade angle permissible to prevent excess speed is
about 19°, which corresponds to 1,460 r. p. m. of the
propeller. The reason for the more effective action of
the propellers occurring at low pitch settings lies in
the fact that the propeller loading is concentrated more
toward the hub. The practical conclusion is that, in
order to obtain maximum cooling on the ground, the
propeller should be given a minimum blade-angle set¬
ting corresponding to maximum engine speed.
Thus far the discussion has dealt entirely with the
pressure drop and the factors affecting it. Results of
some related tests of temperature measurements that
were conducted at the same time will now be presented.
It has previously been found (reference 1) that an
available pressure drop of 10 pounds per square foot
across the engine, if properly used, will provide suffi¬
cient cooling in accordance with present-day practice.
It was found that a very definite relation between the
rear temperature and the pressure drop exists; the
front temperature was shown to depend on several
COOLING OF AIRPLANE ENGINES AT LOW AIR SPEEDS
397
<0
cl
C
-b
|G, w
<3 K
./
Blade angle, 40°
i
3/ad
e an
qle,
25°
Blad
e ar
igle.
25°
30°
3JJo
^40° \
I
20°
A
45°
15°
IS
o /
~ 5
cl
/
/
h
c
— T
/
/
V
§
/
Ql
to
>
/
A.
7 -
t)
/
/
V
Cl
/
/
/
'
7
/
/
£
/
1
550
/
/
4
(o
to
/
/
_
1
i
/
/
/
1
1
/
/
1
(a)
1
1
0>)
6/
ade
ang
/e, 2
5°^
~4d
20 \
t
3/adi
s an
qle ,
45°
o ^ —
15°
/
/
/
i
CL
l5d
v_ 7 — 7
/
/
/
V
to
/
2
CL
L
/
/
/
0-
/
Q)
to
>
/
t
£
/
/
/
V
0
—
/
1
a
to
_
"7
/
£
- 0)
— r~
1
i
(c)
/
1
(d)
to
to
./
.2
.3
"V Cp
.4
.5
.6
(a) Arrangement 6-2-B-3-0.
(c) Arrangement G-2-C-3-0.
(e) Arrangement 6-2-E-3-0.
(b) Arrangement 7-2-B,-3-0.
(cl) Arrangement 6-2-D-3-0.
0
other factors. In the present paper, the temperature
distribution around the circumference of a cylinder is
shown in more detail. The particular cylinder on which
the measurements were made contained an electric
heater, the output of which was kept constant at
1.75 kilowatts, the temperature thus being a direct
Figure 10.— Dependency of Ap/n on VCV for V/nD= 0 at differ¬
ent blade-angle settings at 0.757?.
measure of the heat transmission. This tem¬
perature is referred to as an “index temperature.”
Figure 11 shows selected examples of the
temperature distribution around a heated cyl¬
inder at various air speeds and for different
arrangements. For the cases shown in figure
11 it is necessary to realize that the high tem¬
peratures shown at the lowest air speeds are
somewhat misleading, being directly a conse¬
quence of the very low revolution speeds of
the propeller in this condition. Comparison
with results in reference 1 of the available
pressure on the ground and at low speeds indicates
that the extrapolated values of the temperatures at
zero air speed would not be much in excess of those
obtained at the lowest air speed . The revolution speeds
employed in the tests were roughly of the order of
one-half of those on conventional installations since
Index temperaiure,
398
REPORT NO. 593— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(a) Arrangement 7-2-0-3-0; A'=0.0424. (d) Arrangement 15-2-C-3-10 (Wright blower); A'=0.0424.
(b) Arrangement 7-2-B-3-0; A' =0.0424. (e) High and low speed for two arrangements; K = 0.0900.
(c) Arrangement 7-2-B-3-6; jRT=0.0424. (f) Baffles removed from arrangement of three nose shapes; /f=0.3 to 0.6.
Figure 11.— Distribution of index temperature around the cylinder for various arrangements.
Index temperaiure.
Index, temperaiure, °F. 5 Rear index iemperature,
COOLING OF AIRPLANE ENGINES AT LOW AIR SPEEDS
399
(b) Arrangement 7-2-B-3-0; A' =0.0424. (a) Arrangement 7-2-0-3-0; A'=0.0424.
(d) Arrangement 15-2-C-3-10 (Wright blower); 1^=0.0424. (e) Arrangement 7- 2-B-3-0; K— 0.0424.
(e) High and low speed for two arrangements; A'=0.0909.
Figure 13.— Dependency of index temperature on A p for various arrangements.
400
REPORT NO. 593— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
only about one-eighth of the power was used. As a
result, the ground cooling pressure amounted to about
one-quarter of actual values and the coefficients of heat
transmission to approximately 4-0-3, or about two-
thirds of the values at the proper propeller speed. As
a consequence the temperatures measured are about 50
percent in excess of the values that would be obtained
for the same heat output at normal propeller speeds.
The first four sets of curves of figure 11 are for the
standard baffling, K= 0.0424, all taken on the small
nacelle. In figure 1 1 (a) is shown a case of propeller
off; the three curves show three different tunnel speeds.
In figure 11 (b) is shown a case with propeller B and
in figure 11 (c) a flat spinner has been added. Note
the very beneficial effect of the spinner on the front
temperatures. In figure 11 (d) the results are given
for a special test series on a Wright experimental blower.
The next figure, 11 (e), shows the temperature distri¬
bution obtained with a larger gap between the cylinder
and the baffles; I\ = 0.0909 at two air speeds and with
both nacelles. Note the large increase in the rear tem¬
peratures. Figure 11 (f) shows the distribution for
minimum air speed for the case of baffles removed;
/v = 0.3 to 0.6.
Figure 12 shows the relationship between the rear
temperature and the pressure drop across the cylinder
bank as resulting exclusively from the change in the air
speed. The slopes of the resultant curves are some¬
what inconsistent, lying apparently between —0.2
and —0.3.
Figure 13 is given to indicate the exponents of the
temperature-pressure relationship at various angular
positions around the cylinder. It is apparent that the
frontal temperature is very independent of the pressure
drop. Figure 13 (e) shows a particularly irregular
result; the heat transmission on the front actually
increasing at low tunnel speeds, especially at the 45°
position, probably indicating a peculiar flow condition.
GENERAL CONCLUSIONS
1 . A blade section of proper airfoil shape near the
hub is found to be effective in producing increased
cooling on the ground, being far superior to the con¬
ventional round shank. The N. A. C. A. fan of very
simple construction gave the highest observed available
pressure; it appears, however, that this result could be
equaled by improving the design of the airfoil section
near the hub.
2. Adjustable skirt flaps were found to increase the
pressure drop in the order of 15 percent. Flaps are not
recommended except for very loosely baffled or unbaf¬
fled engines.
3. The design of the nose of a cowling is of some
influence in regard to the cooling at the ground point.
Noses with a small frontal opening were found to be
inferior and are not recommended. A nose design
with a radial inward bend of the leading edge (nose 4)
was found to be superior to, but only slightly better
than, the normal designs (nose 7) recommended for
cruising conditions.
4. The charts given in the paper for a number of
conventional propellers indicate the most efficient
blade-angle setting for obtaining the best cooling at the
ground point. The angle is apparently a function
only of the permissible maximum engine speed, which
was found to correspond to a blade angle of about 20°.
5. No very general conclusion is possible in regard to
the temperature distribution. The beneficial influence
of a tight baffling has been demonstrated. A flat plate,
or spinner, in front of the propeller hub has been
demonstrated to improve very effectively the cooling on
the front. The apparently inconsistent results often
obtained on the cooling of the front of the cylinder seem
to indicate that several unknown factors are involved
and leave a field for future study.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., June 2, 1936.
REFERENCES
1. Theodorsen, Theodore, Brevoort, M. J., and Stickle, George
W.: Full-Scale Tests of N. A. C. A. Cowlings. T. R. No.
592, N. A. C. A., 1937.
2. Weick, Fred E., and Wood, Donald H.: The Twenty-Foot
Propeller Research Tunnel of the National Advisory Com¬
mittee for Aernautics. T. R. No. 300, N. A. C. A., 1928.
3. Theodorsen, Theodore, Stickle, George W., and Brevoort,
M. J.: Characteristics of Six Propellers Including the
High-Speed Range. T. R. No. 594, N. A. C. A., 1937.
REPORT No. 594
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
By Theodore Theodorsen, George W. Stickle, and M. J. Brevoort
SUMMARY
This investigation is part of an extensive experimental
study that has been carried out at full scale in the N. A.
C. A. 20-foot tunnel, the purpose of which has been to
furnish information in regard to the functioning of the
propeller-cowling-nacelle unit under all conditions of
take-off, climbing, and normal flight. This report pre¬
sents the results of tests of six propellers in the normal and
high-speed flight range and also includes a study of the
take-off characteristics. The range of the advance-
diameter ratio has been extended far beyond that of earlier
full-scale experiments at the Laboratory , blade-angle set¬
tings up to 4'5° being included, which are equivalent to air
speeds of more than 300 miles per hour for propellers of
normal size and revolution speed. All the propellers were
tested in conjunction with a standard nacelle unit equipped
with half a dozen representative N. A. C. A. cowlings.
The results show very striking differences in the aerody¬
namic qualities of the various propellers, particularly in
the high-speed range. Also of interest is the fact that the
conventional propeller is shown to reach its peak efficiency
in a range of 200 to 350 miles per hour and at a blade angle
of approximately 35°. The inadequacy of using the pro¬
pulsive efficiency unconditionally as a figure of merit is
shown. This efficiency, defined in conventional manner,
is found actually to exceed unity in certain cases, owing to
the fad that certain cowlings show a decreased drag in the
propeller slipstream. The adoption of some standard
nacelle unit is therefore recommended as a basis for the com¬
parative testing of propellers. The experimental results
are presented in convenient charts. Charts for practical
use in selecting propeller diameters and charts for choosing
the optimum blade-angle setting in the take-off range are
given in an appendix.
INTRODUCTION
The reported investigation is part of a comprehensive
study of cowling-nacelle-propeller combinations (refer¬
ences 1 and 2). The tests were conducted in the
N. A. C. A. 20-foot tunnel (reference 3) of full-size
commercial propellers over the full range of blade angles
up to 45° and over the full range of tunnel speeds up to
about 100 miles per hour. Recent rapid increase in
the speed of airplanes has produced a need for tests
extending to large values of the advance-diameter ratio
V/nD. To the knowledge of the authors this is the
first time that the effect of the cowling form on the
propeller has been systematically investigated and that
a series of full-scale propellers has been tested up to
45° blade angle.
It has been mentioned elsewhere (reference 1) that
P
the quantity Pc-= (where P is the power supplied
to the propeller shaft, S the disk area, V the velocity,
and q the velocity head of the air stream) represents
the contraction of the propeller slipstream. It will be
referred to as the “unit disk loading” or “disk-loading
coefficient.”
The great convenience of using the quantity Pc in
comparing the results of tests of various propellers is
realized. The ideal efficiency is directly a function of
Pc. For a given horsepower and propeller size, Pc is
proportional to the inverse of the third power of the air
speed. For this reason the various diagrams are based
on l/yPc rather than on p , the abscissa thus being
proportional to the air speed. The various efficiencies
have in several cases been plotted against this quantity.
For practical purposes of choosing propeller diameters
for given values of the other variables, it is perfectly
possible to include curves of constant V/nD and blade-
angle setting. All practical values may, however, be
obtained directly from the contour charts given in the
appendix, which are based on the experimental results
of this investigation.
Equal values of Pc actually correspond to similar
flow conditions through the propeller disk and around
the nacelle. A test to simulate a speed of 300 miles per
hour may thus be run at 100 miles per hour tunnel speed
with the value of Pc adjusted to give the identical slip¬
stream contraction. This value is obtained by reduc¬
ing the thrust to 1/9 or the power supplied to the shaft
to 1/27 of the actual values at 300 miles per hour. The
test is thus actually conducted at a scale or Reynolds
Number of 1/3 of the full-scale values. Experience
shows, however, that no particular Reynolds Number
401
402
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
effect is expected in this range since the tests are con¬
ducted far beyond the usual model range. On the
other hand, the reported tests were all conducted at
tip speeds far below sound velocity and the results may
ing largely on the relative dimensions of the propeller
and the nacelle.
Since the same nacelle has been used throughout the
entire test series, it is certain that the combination
giving the highest net efficiency under any specified
condition is superior to any other combination. The
net efficiency may be considered as containing the pro¬
pulsive efficiency together with the efficiency of the
cowling-nacelle.
Figure 1.— Test model with nose 18 and propeller B mounted on the balance frame
in the 20-foot wind tunnel.
be considered free from any effects of the compress¬
ibility of the air.
As will lie evident front the test results, the propulsive
efficiency alone as defined in the usual manner is not a
dependable criterion of the efficiency of the propeller
tested in conjunction with a nacelle but is cpiite de¬
pendent on the particular nacelle or body used behind
the propeller. This efficiency is therefore significant
only if the various propellers are tested on the identical
nacelle. For this reason a quantity termed the “net
efficiency,” which relates to the entire propeller-nacelle
unit, has been used throughout this report. It is de¬
fined as
_RV
Vn p
where R is the net forward thrust of the entire unit as
measured on the thrust scale. This quantity is in
itself a perfectly arbitrary reference number, depend¬
Figure 2.— Propellers used in the investigation.
DESCRIPTION OF TESTS
Figure 1 is a photograph of the installation in the
20-foot tunnel used for this investigation. Figure 2
shows the propellers used, the complete details of which
are shown in figure 3 and in the following table.
PROPELLERS
Propeller
desig¬
nation
Drawing
Number
of
blades
Diam¬
eter
Type
Remarks
Airfoil sec¬
tion
A
Hamilton-Standard 6101-0 _ _ _
3
Feet
10. 06
Controllable. . .
Clark Y.
B
Hamilton-Standard 1C 1-0 _ __ _ _ _
3
10.04
Adjustable
Blade sent ion same as A except, near huh
Do.
Bx
Hamilton-Standard 1C1-0 (modified).. _
3
10. 0-4
_ do _
Blade angle decreased from the 70-percent radius
to the tip (fig. 3).
Do.
C
Navy plan form 5868-9 _ . _. _
3
10.02
_ do _ _
Do.
D
Navy plan form 5868-9 _ .. _ _
2
10.00
_ do . .
Same as C except 2 blades..
Do
E
Navy plan form 3790. _ _ _ _ _
3
9. 04
. do _
R. A. F. 6.
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
403
2.6
2.4
2.2
2.0
id
1.6
1.4
1.2
1.0
.8
.6
.4
.2
O
(a) Propellers A, B, and Bj. (b) Propellers C and D. (e) Propeller E.
Figure 3.— Blade-form curves for the propellers tested. D, diameter; 6, blade width; h, blade thickness; P. pitch; /?=/>/ 2, radius at tip; r, radius.
<£_ Propeller £ Cylinders
The drawing in figure 4 shows in detail the na¬
celle unit with the particular noses and skirts used
in the propeller tests. Power to the propeller was
furnished by a variable-speed electric motor en¬
closed in the nacelle unit. The propellers wTere
tested up to and including a blade angle of 45° at
0.7 5R and at tunnel speeds up to more than 100
miles per hour.
>5)1 5)
404
REPORT XO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TEST RESULTS
The propulsive efficiency p is defined
Figures 5 to 22 show the results of the experimental
investigation of six commercial propellers tested in
conjunction with a total of six different cowling shapes.1
Each figure includes the variation with \r/nD of the
conventional coefficients CT, CP, and the propulsive
efficiency v, all usually given at several blade-angle
settings. The coefficients CT and CP are defined as
follows:
CT =
T
prtD*
CP=
P
pn^D5
where p is air density and D the propeller diameter.
1 Owing to special interest in particular propellers, the faired values of Ct, Cp, rj, and
C.s' for propellers B and C with nose 6 and for propeller Bx with nose 7 are presented
in tables I. II, and III. It is of interest to note that the values of Ct and Cp at low
values of V/nD for the blade angles near 20° and 25° at 0.7 5R do not fair with the
values from the other blade angles as well as might be expected. These values check,
however, with values from other tests of the same propellers with different test
set-ups, indicating an instability of flow for low values of VlnD in this region of
blade-angle setting.
TV
v=-p-
where T— R-\-D} R being the reading on the thrust
scale under test conditions and D the drag for the
corresponding air speed of the nacelle unit measured
with the propeller off.
The net efficiency has been given in several cases.
The net efficiency is simply defined as
RV
and is a sort of over-all efficiency of the engine-nacelle-
propeller unit. This efficiency is plotted against
the quantity 1 jy/ Pc, where Pc is the propeller unit disk
loading.
The following table is a key to the numbers of the
figures in which are plotted the data of the various
combinations tested.
KEY TABLE TO FIGURE NUMBERS
The original results are given in figures 5 to 22.
Figures 23 to 27 give the efficiency envelopes of each
of the propellers for five different noses. Figures 28
and 29 give a comparison of propellers B and C with
separate efficiency envelopes for each of the noses
tested. The drag for the various noses tested is given
in reference 1 . The net efficiencies are given in
figures 30 to 35, and the particular results for pro¬
pellers B and C in regard to net efficiencies are fur¬
ther given in figures 36 and 37. All the results
are strictly comparable in showing the effect of pro¬
pellers and noses since the same skirt, the same con¬
ductivity 2 * * of the engine, and, as a consequence, the
same quantity of cooling air were used in all the tests.
Figure 38 shows the net efficiency with no cooling air
as obtained with nose 19 and skirt 5.
2 In order to represent the degree of transmissibility of the baffles, a quantity K,
designated “conductivity,” has been defined in reference 1 as
frVf
where
Q is the volume of the air passing through the baffles per second.
F, the cross section of the nacelle as a reference area.
g, the velocity head.
V, the velocity of the air stream.
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
405
Figure 5.— Curves of Ct, Cp, and r) against V/nD for nose 1, propeller B.
406
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 6.— Curves of Ct, Cp, and -q against V/nD for nose 1, propeller C.
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
407
38548 — 38
■27
408
REPORT NO. 594 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 8. — Curves of Ct, Cp, and rj against V/nD for nose 2, propeller C.
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
409
Figure 9.— Curves of Ct. Cp, and t ; against V/nD for nose 3, propeller B.
38
36
34
32
30
28
26
24
22
.20
JQ
.16
14
12
.10
08
06
04
02
0
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
l.O
.8
T1
.6
.4
.2
0
Figure 10,— Curves of Cr, Cp, and tj against VjnD for nose 3, propeller C.
,3d
.36
34
32
30
28
26
24
22
20
IQ
,16
!4
,12
JO
08
06
04
02
0
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
411
B/ade ang/e ai 0.75 R ,
25° 30 ° 33°
CP o - b - *q _
CT + - (7 a
n a - o - <j
V/nD
Figure ll.— Curves of Ct, Cp, and r; against V/nD for nose 4, propeller B.
412
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
Figure 12. — Curves of Cr, Cp, and q against V'/n/J for nose 4, propeller C.
413
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
V/nD
Figure 14. Curves of Ct, Cr, and tj against VjnD for nose 6, propeller A.
,J3
36
.34
,32
.30
28
,26
.24
.22
.20
.18
.16
.14
.12
JO
08
06
04
02
0
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 16.— Curves of CY, Cp, and 77 against V/nD for nose 6, propeller B
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
415
385 48 — 58 - 28
416
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 18. — Curves of CY. CV, and n against \'/nL) for nose G, propeller D.
41
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
Figure 19.— Curves of Cr, CV, and ij against t 'I a I) for uose 6, propeller E
418
REPORT NO. 594 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
419
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
420
REPORT NO. 594 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
421
Figure 23. — Propulsive-efficiency envelopes against V/nD for propellers B and C on
nose 2.
Figure 24.— Propulsive-efficiency envelopes against V/nD for propellers B and C on
nose 3.
DISCUSSION OF RESULTS
It should be noticed that the propulsive efficiency in
figure 5 is greater than 100 percent. The high value of
this efficiency is caused by a certain peculiarity in the
characteristics of nose 1, which lias been pointed out
in an earlier report (reference 1). It was shown in
reference 1 that the drag of this particular nose de¬
creased substantially with an increase in slipstream
velocity owing to the fact that the local angle of attack
at the leading edge of the cowling was sufficiently
decreased to prevent a marked breakdown that occurred
with the propeller off. This effect, which is quite
contrary to the expectations of the theory, renders the
practical use of the propulsive efficiency rather ques¬
tionable. In other words, whenever some critical flow
conditions exist that may be favorably affected by the
propeller slipstream, it is perfectly possible to obtain
efficiencies close to or in excess of unity. High ef¬
ficiencies reported from time to time may easily be
explained on this basis. There are, therefore, only two
alternatives. One is to adopt a standardized cowling-
nacelle shape. Nose 7, described in reference 1, is
particularly recommended for this purpose as being
unusually neutral to the local flow condition at the
nose. The other alternative is to avoid the use of the
propulsive efficiency altogether by adopting some other
figure of merit relating to the entire cowling-nacelle-
V/n D
Figure 25. — Propulsive-efficiency envelopes against 1 'jnD for propellers A, B.audC
on nose 4.
0 2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
V/nD
Figure 26.— Propulsive-efficiency envelopes against V/nD for propellers A, B, C, D, E on nose 6.
422
REPORT NO. 594 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
V/nD
Figure 27.— Propulsive-efficiency envelopes against V/nD for propellers B, Bx, and C on nose 7.
— —
_ =_4
~ — =3
—
_ ~v_z:
- =
—
A
lose
2
■■
SI
4 -
C2
—
"
1-
J .2 .4 .6 .8 1.0 1.2 /.4 1.6 f.8 2.0 2.2 2.4
V/nD
Figure 29.— Propulsive-efficiency envelopes against V/nD for noses 2, 3, 4, 6, and 7 with propeller C.
propeller unit. The quantity defined as net efficiency
has been used for this purpose. In the present report
both these characteristics have been given.
The propulsive efficiencies given in figures 26 and 27
for i lie most neutral cowlings 6 and 7 show that propeller
Bx is definitely superior to the others, exceeding the
least efficient propeller by 4 to 6 percent. Figure 28
shows the results for propeller B in conjunction with
live different cowlings. It will be seen that cowling 6
is superior, exceeding cowling 3 by 1 percent and
cowling 7 by about 2 percent. Figure 29 gives the re¬
sults of tests of propeller C with the five different noses.
In this case noses 3 and 2 exceed the others in efficiency
by about 5 percent. The highest of all efficiencies
obtained is 91 percent for propeller Bx with nose 7.,;
3 If a propeller is opera! ing at (if) speeds near the velocity of sound, I hese efficiencies
will, of course, be somewhat reduced by compressibility losses. The compressibility
losses may bp minimized by using thin propeller tip sections at or near the ideal angle
of attack. (See reference 4.) Karlier experiments at the Laboratory (reference 5)
have shown that sound velocity may be approached within 10 percent with no loss
in efficiency.
423
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
Figure 30.- Net-efficiency envelopes against l f\j Pc for propellers B and C
on nose 1.
.8
6
.4
n„
o
-.2
~T~
0*“
-
x
rropeh
'er
-B
-c
—
' N|
—
- D
' >
-L
\
X
-
X
s
\
X.
v '*
SkSy.
\
.8 1.0 1.2 L4 1.6 18 2.0 2.2 2.4 26 2.6 3.0 3.2
vm
Figure 34. Net-efficiency envelopes against 1 l%jPr for propellers B, r, I ), and Ii on
nose 6.
Figure 31.- Net-efficiency envelopes against 1 fy/Pt (or propellers B and C
on nose 2.
.8
.6
.4
'In
.2
0
-2
Figure 35.— Net-efficiency envelopes against l/\/ Pc for propellers B, B*, and C on
nose 7.
~
1
TT
2r
opet/er
- B
- R
s
—
-c
r N
\
U
X
_
N
8 i.o 18 1.41.6 1.6 6.0 22 2.4 2.6 2.6 3.0 32
l/Wc
.8
.6
.4
In
2
0
-.2
Figure 32. — Net -efficiency envelopes against lj-Jpc for propellers B and <
on nose 3.
1/ifPc
Figure 36.— Net-efficiency envelopes against 1/V-Pc for noses 1, 2, 3, 4, 6, and 7 with
propeller B.
3 y —
Figure 33.— Net-efficiency envelopes against 1 14 Pc for propellers A, B, C,
and E on nose 4.
Figure 37. Net-efficiency envelopes against U'-yJ Pc for noses 1, 2,3. 4, 6, and 7 with
propeller C.
424
REPORT NO. 594 — NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
Similarly, comparing net efficiencies for the most
complete cases, cowlings 6 and 7, as given in figures 34
and 35, respectively, it is again, seen that propeller Bx
is superior over most of the range. Notice also the
marked improvement in the net efficiency of propeller
Bx as compared with that of its original form, B. Fig¬
ure 3G for propeller B shows the superiority of noses
3 and 6 with 7 next. Since nose 3 gives poor cooling
at low air speed, it should not be considered on an equal
basis. Similar results for propeller C are shown in figure
37. This propeller is again less efficient than propeller
B. Notice in both figures the very inferior efficiency of
nose 1 . Figure 38 has been included to show the cost
of the cooling air as obtained by the standard skirt 2.
Figure 38. — Curves of net efficiency against 1 f^Pc for propellers B and C set 25° at 0.75 R; on nose 19, skirt 5, without cooling air; and on nose 2, skirt 2, with normal cooling air.
425
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
In figures 39 to 42 the propulsive efficiency rj has been
plotted against 1 /t]pc for propellers B, Bx, C, and D.
The envelopes for each of the five propellers are shown
in figure 43. If the definition of Pc is recalled, it may
be noted that with a fixed horsepower and a fixed pro¬
peller diameter the abscissa may be considered to repre¬
sent the air speed. With a 550-horsepower engine and
a 10-foot propeller, the abscissa happens to give the
air speed in units of almost exactly 100 miles per hour.
The propulsive efficiencies arc compared at, say, 250
miles per hour. They are: Propeller Bx, 90.9 percent;
B, 89.4 percent; the two-blade propeller D, 87.4 per¬
cent; and propeller C, 84.9 percent, or a range of 6
percent. At lower speeds the differences are still of
concern although less marked. It is of interest to note
that the peak efficiencies of all propellers tested is
found at a blade angle of approximately 35°.
The chart (fig. 43) is of value in demonstrating the
fact that the present commonly used power plant of
550 horsepower in combination with a 10-foot propeller
could be used to best advantage in the speed range
220 to 300 miles per hour. A 1,000-liorsepower engine
used on the same size propeller could be used to great¬
est advantage at about 25 percent higher speeds or in
the range of 270 to 370 miles per hour. In order to
make full use of a 1,000-horsepower engine at a speed
0 L .4 .8 12 16 2.0 2.4 28 3.2 3.6 4.0 4.4
Vl/Pc
Figure 43. — Propulsive-efficiency envelopes against 1 f\j Pc for propellers A, B, E
C, and D.
of 200 miles per hour, an impracticably large propeller
diameter is required.
It also is of interest to note that the two-blade pro¬
peller D, employing the same blades as the three-blade
propeller C, reaches a considerably greater peak effi¬
ciency. If 550 horsepower are used with both pro¬
pellers, it is seen that the propulsive efficiencies at the
speed of 250 miles per hour are, respectively, 87.4 and
84.9. This is a consequence of the fact that the com¬
monly used propeller sections are altogether too wide.
It was found that at the condition of peak efficiency of
the propeller, the actual or effective angle of attack
amounts to only about 4° to 5°. It can be shown that
a narrower blade with a correspondingly higher effec¬
tive angle would be aerodynamically more efficient
Vibration and flutter and other considerations, how¬
ever, prevent the practical use of such a blade.
Propellers B, C, and D all are designed with a con¬
stant blade angle for a setting of 12° at 0.75/?. Pro¬
peller Bx has a constant blade angle from 0.60/? out¬
ward for a setting of 30° at 0.75/?. (See fig. 3(a).)
Figure 44. — Power and torque characteristics of an actual engine used as an example.
In fact, propeller Bx is identical to propeller B except
for this change in blade-angle distribution. The gain
of almost 2 percent in efficiency observed in figure 43
demonstrates the importance of employing a design
blade angle adjusted to the proper flight condition.
Notice also that this gain is not obtained at the expense
of decreased efficiency in the lower speed range. Pro¬
peller Bx happens to be superior to all the propellers
tested over the entire practical High t. range.
The results of the tests of propellers B and C in con¬
junction with six different cowlings (figs. 36 and 37)
illustrate the importance of the effect of the cowling.
Considering the somewhat fictitious case of the to])
speed attainable with the present nacelle alone, it is
observed in figure 36 that the comparative top speeds
range from 267 miles per hour for nose 1 to 295 miles
per hour for nose 3. For propeller C (fig. 37) the com¬
parative range is 262 miles to 288 miles. Although the
differences between the cowlings of reasonable design
are fairly small, the inferiority of a design resembling
nose 1 should be kept in mind, this nose being the cause
of a speed reduction of almost 10 percent.
TAKE-OFF CHARACTERISTICS
The propeller characteristics at low air speeds may
be obtained from the basic test results given in figures
5 to 22. In order to make full use of this information
426
REPOET NO.
594-
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
O 50 _ IOO 150 200
V, m.p.h.
Figure 45. — Optimum blade angle and thrust in the take-off range, engine speed
2,000 revolutions per minute, with a 3:2 gear reduction ratio.
in calculating the take-off distance for a given set of
conditions, however, it is necessary to present the data
in a more direct manner. The optimum blade-angle
setting corresponding to the maximum available thrust
at any particular air speed is of particular interest.
The actual differences in the take-off characteristics
will be directly demonstrated by the use of a particular
example using engine characteristics as given in figure
44 corresponding to those actually obtained on a 550-
horsepower engine. The engine speeds chosen are:
2,000 revolutions per minute and 2,200 revolutions per
minute, both with a 3:2 gear reduction ratio; and
1,800 revolutions per minute with direct drive.
Figure 47.— Optimum blade angle and thrust in the take-off range, engine speed
1,800 revolutions per minute with direct drive.
The resulting blade-angle settings and thrusts in
the take-off range obtained from charts in the appendix
are presented in figures 45, 46, and 47. It is noticed
in working through one of these examples that no par¬
ticular optimum setting is reached; the maximum
permissible engine speed is the limiting condition.
Notice that propeller C is very superior to B or Bx in
regard to take-off, particularly in the lowest speed
range.4 The thrust of the two-blade propeller D is
further seen to amount to a little more than two-thirds
of that of the corresponding three-blade propeller C.
Propeller Bx is noticed to be slightly inferior to propeller
' This comparison is valid when propellers of a constant diameter are being com¬
pared, as would be the case when the propeller diameter is the limiting design factor.
Given a free choice of diameters, the comparisons must be made with a view to the
high-speed performance, necessitating an individual study of each case.
Figure 46. -Optimum blade angle and thrust in the take-off range, engine speed
2,200 revolutions per minute with a 3:2 gear reduction ratio.
427
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
B at speeds less than about 100 miles per hour. Notice
the inferior thrust values of the 9-foot propeller E.
Absorbing the same horsepower, this propeller is rela¬
tively overloaded and should not be directly compared.
The beneficial influence of increasing the propeller
speed may be observed by comparing the results from
the three figures.
The results are, of course, strictly true only for the
relative dimensions of the propeller and nacelle used in
these particular experiments, a larger propeller thus
calling for a larger nacelle, and vice versa. It is, how¬
ever, known that the propulsive efficiency will be af¬
fected very little by this variation in relative dimen¬
sions. The results may, therefore, he considered valid
also for the case of different relative dimensions of the
propeller in regard to the nacelle.
As these propellers are fairly representative of com¬
monly used types, it is possible by some exercise of
judgment to obtain a fairly reasonable estimate of the
take-off characteristics also of any other propellers.
GENERAL CONCLUSIONS
1. Peak efficiency of the propellers tested occurs at
a blade-angle setting of approximately 35°. The
difference in peak efficiency varies as much as C percent,
demonstrating the value of selecting a good design,
particularly in the high-speed range.
2. The peak propulsive efficiency of the conven¬
tionally dimensional units of 9- to 12-foot propellers
on 500- to 1,000-horsepower engines has been found to
lie in the range of 200 to 350 miles per hour, showing
the beneficial influence of higher air speeds on the pro¬
peller.
3. A two-blade propeller of the kind tested was
found to be superior in efficiency (in the high-speed
range) to a three-blade propeller using identical
blades, the peak efficiency exceeding that of the three-
blade propeller by about 2 percent.
4. A propeller equipped with a controllable hub
shows an almost negligible decrease in efficiency as
compared with the identical propeller with a standard
hub. The difference is of the order of % percent,
which is close to the limit of test accuracy.
5. In regard to the take-off characteristics, the
maximum permissible revolution speed is in all cases
found to be the most favorable. The three-blade
propeller is superior to the two-blade propeller using
the same horsepower, which is to be expected.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., June 4, 1986.
LIST OF SYMBOLS
V,
velocity of air stream.
n,
revolutions per unit time of the
propeller.
D,
diameter of propeller.
V
advance-diameter ratio of the pro-
nl)'
peller.
P,
power supplied to propeller shaft.
s,
disk area of propeller.
T
velocity head of air stream, }{> p 1 A
P-P
c gSV’
unit disk loading or disk-loading coeffi-
cient.
p,
air density.
R,
net forward thrust of the entire unit
as measured on the thrust scale.
RV . .
Vn j ) '
not efficiency.
r\
X)
1
ii
thrust.
D.
drag of the nacelle unit for the
corresponding air speed measured
with the propeller off.
T
Ct=—
1 hrust coefficient.
pwLr
-l— — y3/pS
V ~PC V 2 P
n _ A
P prvjy
power coefficient.
p Q
torque coefficient.
TV
v=-p->
propulsive efficiency.
Q,
Qc=
i
h,
b,
r,
R,
6,
T>
Q
P/A
C -
Vo,
5 /pZ6
V /w’
torque of propeller,
torque coefficient.
thickness of blade section of propeller,
width of blade section of propeller,
radius to any blade section of propeller,
radius of propeller.
propeller blade-angle setting at 0.75 R.
geometric pitch of propeller.
speec 1 -power coeffi cient.
net propeller-nacelle efficiency with no
cooling air.
APPENDIX
CHARTS FOR SELECTING PROPELLER DIAMETERS
The characteristics of a propeller are given as a
relation of three and only three variables; these vari¬
ables may be given as CT, CP, V/nD. For geometri¬
cally similar propellers these quantities remain con¬
stant. Any other three independent variables may
be selected, and the combination of Cs, V/nD, and 17
is chosen because of certain advantages. Since only
three quantities are involved, it is obviously possible
to give a complete representation of the characteristics
in a single contour chart. Inserting values of the
efficiency 77 against Cs as ordinates and V/nD as
abscissas for various blade-angle settings, connecting
points of equal efficiencies and points representing
given blade angles, gives a contour -map containing all
results. This type of chart is primarily useful in
selecting the diameter of a propeller. It is tacitly
assumed that the type of propeller has already been
chosen and that charts are available. It is interesting
to observe that the contour lines map a smoothly
shaped peak; no crowding of the lines occurs. In the
selection of a propeller diameter this type of chart
makes it possible to judge the effect of changes by
observing how the representative point moves with
respect to the efficiency peak.
Charts I give the results for the three-blade pro¬
peller B, the modified version Bx, C, and the two-blade
propeller D. The charts are applicable to controllable
propellers allowing for 1/2 percent decrease in effi¬
ciency by a slight increase in the diameter.
PROCEDURE FOR THE USE OF CONTOUR CHARTS FOR SELECTING
PROPELLER DIAMETERS
Given: Horsepower P, revolutions per second n,
air speed V, and density p.
Calculate:
(1) For a controllable-pitch propeller, select the
point of maximum efficiency at this value of Cs. (The
efficiency envelope is shown by a curve on the chart.)
Bead oil' angle setting and V/nD, the latter giving the
value of D }
Examples are shown on the particular charts.
(2) For a fixed-pitch propeller the selection of the
blade-angle setting is a matter of compromise. It is
necessary to choose a blade angle that shows peak
efficiency at a somewhat smaller value of Cs than the
one calculated for the flight condition. The choice
depends on how much efficiency is to be sacrificed at
the high-speed condition in order to improve the take-
oil'. It is therefore necessary to resort to the simultan¬
eous use of charts giving the take-off characteristics.
1 Notice that the blade-angle setting in the charts is the true setting at the operating
condition. The results presented are free from compressibility effects and twist of
blades due to air loads and the effect of the centrifugal force. The blade twist can be
estimated and allowed for.
428
CHARTS FOR THE TAKE-OFF CONDITION
In the determination of the diameter of a propeller,
consideration must be given also to the condition of
take-off. It is desirable to know the thrust in order to
calculate the take-off distance. For the controllable-
pitch propeller, the determination of the minimum
blade-angle setting is of interest. For the fixed-pitch
propeller, the setting is a matter of balancing the per¬
formance at high speed against that at take-off. It will
probably be necessary to study two or three blade-angle
settings in order to arrive at a specific result. Charts
for determining the take-off thrust, based on the results
of this investigation, are given in charts II as supple¬
ments to charts I already described. These charts,
which have been developed along similar lines, show
contour curves of constant thrust and constant blade-
angle setting against the coordinates V/nD and 1 /tJQc=
'pW
\
Q
the latter quantity representing a torque
coefficient; the actual engine torque Q is, as usual,
considered to be a constant. Results are given in
charts II.
PROCEDURE FOR THE USE OF CHARTS ON TAKE-OFF
CHARACTERISTICS
(1) Controllable-pitcli propeller.
Given: Engine torque Q, propeller diameter D ,
revolutions per second n, and air speed V.
Calculate l/y^c.and V/nD.
Read off from the chart CT[CQ~~ TD/Q and the blade
angle. For constant 11 the whole range of air speed is
given by a straight line through this point and the origin.
Blot thrust and blade angle against air speed (as in fig.
45, etc.).
(2) Fixed-pitch propeller
Calculate 1 / A Qc and V/nD.
Make a choice of blade angle and read from the chart
the related values of CT/CQ and 1 /-yjQc. Plot thrust
against air speed for this blade angle. If the resulting
take-off thrust is found to be inadequate, choose a lower
blade angle and repeat the procedure; or vice versa.
REFERENCES
1. Theodorsen, Theodore, Brevoort, M. J., and Stickle, George
W.: Full-scale Tests of N. A. C. A. Cowlings. T. R. No.
592, N. A. C. A., 1937.
2. Theodorsen, Theodore, Brevoort, M. J., and Stickle, George
W.: Cooling of Airplane Engines at Low Air Speeds. T. R.
No. 593, N. A. C. A., 1937.
3. Weick, Fred E., and Wood, Donald II.: The Twenty-Foot
Propeller Research Tunnel of the National Advisory
Committee for Aeronautics. T. R. No. 300, N. A. C. A.,
1928.
4. Theodorsen, Theodore: On the Theory of Wing Sections with
Particular Reference to the Lift Distribution. T. R. No.
383, N. A. C. A., 1931.
5. Wood, Donald H.: Full-Scale Tests of Metal Propellers at
High Tip Speeds. T. R. No. 375, N. A. C. A., 1931.
429
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
Chart I (a). — Characteristics of three-blade propeller B. Hamilton-Standard 1C1-0. Example (shown by circle) — Given: P=S50 horsepower; n— 24
revolutions per second; V= 200 miles per hour. Result: /3=27°; i?=0.877; D = 10.68 feet.
0 .4 .0 1.2 /.6 2.0 2.4
V/nD
Chart I (b). — Characteristics of three-blade propeller B,. Hamilton-Standard 1C1-0 (modified). Example (shown by circle) Given: P 550
horsepower; «=24 revolutions per second; H=200 miles per hour. Result: 0=29°; tj=0.883; Z) = 10.44 feet.
430
REPORT NO. 594- NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
('hart I (C).— Characteristics of three-blade propeller C. Navy plan form 5868-9. Example (shown by circle)— Given: P=550 horsepower; n=24
revolutions per second; V=200 miles per hour. Result: 0=28.3°; ??=0.855; /> = 10. J 8 feet.
Chart I (d).— Characteristics of two-blade propeller D. Navy plan form 5868-9. Example (shown by circle)— Given: P= 550 horsepower; n = 24
revolutions per second; F=200 miles per hour. Result: 0=25°; =0.865; £>=]!. 50 feet.
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
431
Chart II (a). — Take-off characteristics for three-blade propeller B. Hamilton-Standard 1C1-0.
Chart II (b).— Take-off characteristics for three-blade propeller B*. Hamilton-Standard 1C1-0 (modified).
REPORT NO. 594 NATIONAL
ADVISORY COMMITTEE FOR AERONAUTICS
("hart II (c) . — Take-off characteristics for three-blade propeller C. Navy plan form 5868-9.
V_
nD
i A/q~c
Chart II (d).— Take-off characteristics for two-blade propeller D. Navy plan form 5S6S-9
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
TABLE T.— FAIRED VALUES FOR NOSE 6, PROPELLER B
VI nD
Set 15° at 0.75 R
Set 20° at 0.75 R
Set 25° at 0.75 R
Set 30° at 0.75/1*
- 1
Ct
Cp
V
Ct
Cp
V
C.
Ct
Cp
c.
Ct
Cp
C
0
0. 1230
0. 0529
0
0
0. 1323
0. 1140
0
0
0. 1529
0. 1563
0
0
0. 1598
0. 2074
0
0
.05
. 1191
. 0529
.113
.09
. 1299
. 1078
. 060
.08
. 1492
. 1522
.049
.07
. 1582
. 2051
. 039
. 07
. 10
.1150
. 0529
.217
. 18
. 1288
. 1009
. 128
. 16
. 1477
. 1510
.098
. 15
. 1566
. 2030
.077
. 14
. 15
. 1101
. 0527
.314
. 27
. 1272
. 0948
. 201
.24
. 1459
. 1494
. 146
. 22
. 1550
. 2007
. 1 16
. 21
.20
. 1048
. 0522
.402
.36
. 1253
. 0897
. 280
.32
. 1442
. 1474
. 196
. 29
. 1535
. 1982
. 155
. 28
. 25
.0988
.0516
.479
.45
. 1231
. 0851
. 362
.41
. 1427
. 1451
. 246
.37
. 1519
. 1959
. 194
.35
.00
. 0920
. 0505
. 546
.54
.1201
.0812
. 445
.50
. 14)1
. 1425
. 298
.44
. 1502
. 1933
. 233
.42
.35
. 0849
. 0187
. 610
.04
. 1 169
.0782
. 523
.58
. 1395
. 1397
.350
.52
. 1487
. 1908
.273
.49
.40
.0770
. 0403
. 005
. 74
. 1120
. 0760
. 590
.67
. 1380
. 1363
. 405
.59
. 1470
. 1881
.312
. 56
.45
. 0087
.0432
.715
.84
. 105.3
.0741
.640
. 76
. 1365
. 1326
.463
.68
. 1454
. 1853
. 353
.63
.50
. 0002
. 0398
. 756
.95
. 0982
.0719
. 684
. 85
. 1350
. 1285
.525
.76
. 1440
. 1824
. 395
. 70
.55
. 051 2
. 0358
. 780
1.07
. 0907
. 0691
. 722
.94
. 1322
. 1238
.588
.84
. 1423
. 1794
. 436
. 78
.00
.0417
.0313
.800
1. 20
.0827
.0657
. 755
1.03
. 1272
. 1187
.644
.92
. 1408
. 1761
.480
.85
.05
. 0320
. 0230
.800
1.35
. 0743
.0015
.785
1. 13
. 1202
. 1 133
.690
1.01
. 1391
. 1721
. 525
. 92
.70
. 0223
.0201
.777
1.53
. 0056
. 0567
.810
1.24
.1125
. 1082
. 728
1.09
. 1377
. 1686
.572
1. 00
. 76
. 0124
. 0131
.710
1.79
. 0565
. 0510
.830
1.36
. 1044
. 1028
. 762
1. 18
. 1357
. 1643
. 620
1. 08
.80
. 0010
.0017
. 272
2.34
.0472
. 0446
.846
1.49
. 0960
. 0970
.791
1.28
. 1326
. 1594
.665
1. 16
. 85
_
. 0377
. 0376
. 852
1.64
. 0870
.0910
.812
1.37
. 1 275
. 1537
. 705
i.24 ;
90
. 0282
. 0300
.846
1.81
.0788
. 0847
.837
1. 48
. 1207
. 1466
. 740
1.32
95
.0182
.0215
.805
2. 05
. 0688
. 0775
.845
1.67
. 1135
. 1400
.770
1.41
1.00
_
. 0080
. 0125
. 640
2.42
. 0595
. 0695
.856
1. 71
. 1060
. 1324
.800
1.50 |
1 0"'
0018
. 0020
3. 65
. 0500
. 0600
.874
1.84
. 0980
. 1250
.823
1 . 59
1 10
. 0400
. 0502
.876
2. 00
.0896
. 1171
.841
1.69
1. 15
. 0297
. 0392
.871
2. 20
.0810
. 1085
.859
1.80
i 1 20
. 0189
. 0275
.825
2. 46
.0719
. 0990
.870
1 . 90
1 1 2f>
.0080
. 0145
. 745
2. 91
. 0624
. 0880
. 885
2. 03
1.30
-.0028
. 0015
3. 62
. 0527
. 0769
.891
2. 17
1 35
. 0430
. 0650
. 893
2.33
] 10
. 0327
. 0514
. 890
2.54
1 4 5
. 0225
. 0380
. 858
2. 79
1 50
.0124
.0231
. 806
3. 18
1 55
.0020
. 0080
.387
4. 07
1 on
I or,
1 70
1 75
1 sn
1 85
i on
l 9t5
2 00
2 05
1 2 10
f
2 1 5
, 2 20
j 2 25
1
2 20
2 35
2 40
2 45
1
2 50
1 2 55
2 00
434
REPORT NO. 594 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I.— FAIRED VALUES FOR NOSE 6, PROPELLER B— Continued
Set 35°
at 0.75 R
Set 40°
at 0.757?
Set 45°
at 0.75 R
Ct
Cp
n
C,
Ct
Cp
V
c.
Ct
Cp
n
c.
0
0. 1635
0. 2695
0
0
0. 1643
0. 3324
0
0
0. 1576
0. 3868
0
0
. 05
. 1629
. 2662
.031
.07
. 1640
.3291
.025
.06
. 1581
.3842
.021
.06
10
. 1617
. 2631
.062
. 13
. 1637
.3260
.050
. 13
. 1585
.3817
. 042
. 12
. 15
. 1606
. 2600
. 093
. 20
. 1633
. 3228
.076
. 19
. 1589
. 3792
. 063
. 18
. 20
. 1593
. 2567
. 124
. 26
. 1628
.3197
. 102
. 25
. 1592
. 3767
.085
.24
. 25
. 1583
. 2535
. 156
.33
. 1624
.3164
. 128
.32
. 1596
. 3742
. 106
.30
.30
. 1570
. 2501
. 188
.40
. 1618
. 3132
. 155
.38
. 1599
.3717
. 129
. 37
.35
. 1557
. 2467
. 221
. 46
. 1613
.3100
. 182
.44
. 1602
. 3693
. 152
.43
.40
. 1543
.2432
.254
.53
. 1607
. 3067
. 210
.51
. 1605
. 3667
. 175
. 49
. 45
. 1530
. 2396
. 288
. 60
. 1600
. 3033
.238
. 57
. 1608
. 3640
. 199
. 55
. 50
. 1517
. 2360
.322
. 67
. 1593
. 3000
. 266
. 64
. 1607
.3614
.222
. 61
.55
. 1502
. 2323
. 356
.74
. 1585
. 2963
. 294
. 70
. 1605
. 3586
. 246
. 68
. 60
. 1490
. 2285
. 391
.81
. 1577
. 2927
.323
. 77
. 1601
. 3557
. 270
. 74
.65
. 1475
. 2245
.427
.88
. 1566
. 2890
. 352
. 83
. 1596
. 3527
. 294
. 80
. 70
. 1462
. 2205
.464
.95
. 1554
. 2853
.381
. 90
. 1588
.3499
.318
. 86
.75
. 1445
. 2165
.500
1.02
. 1542
. 2813
.412
.97
. 1577
. 3466
.341
. 93
.80
. 1427
. 2121
. 538
1.09
. 1527
. 2770
.441
1.03
. 1565
. 3434
. 365
.99
.85
. 1405
. 2078
.575
1. 17
. 1510
. 2730
. 470
1. 10
. 1550
. 3400
. 388
1.05
.90
. 1375
. 2028
. 610
1. 24
. 1492
. 2683
. 500
1. 17
. 1538
. 3362
.411
1.12
.95
. 1345
. 1982
.645
1.31
. 1470
. 2634
. 530
1.25
. 1522
. 3324
.435
1. 19
1. 00
. 1317
. 1940
. 678
1.39
. 1445
. 2580
. 560
1.31
. 1507
. 3277
. 460
1. 25
1.05
. 1290
. 1895
. 715
1.47
. 1418
. 2530
.589
1.38
. 1490
.3232
. 484
1.32
1. 10
. 1255
. 1841
. 750
1. 54
. 1392
. 2490
.615
1.45
. 1475
.3183
. 510
1.38
1. 15
. 1202
. 1777
.779
1. 62
. 1372
. 2455
.643
1.52
. 1460
.3135
. 536
1.45
1. 20
. 1140
. 1700
.804
1.71
. 1355
. 2428
. 670
1.59
. 1443
.3088
. 560
1. 52
1. 25
. 1067
. 1624
.820
1. 80
. 1340
. 2100
. 698
1. 66
. 1428
. 3052
. 585
1. 59
1.30
. 0993
. 1533
. 842
1.89
. 1324
. 2360
.730
1.74
. 1412
.3015
.610
1. 65
1.35
. 0913
. 1440
. 855
1. 99
. 1300
. 2310
. 760
1.81
. 1398
. 2990
.631
1. 72
1.40
.0830
. 1340
.867
2. 09
. 1267
. 2255
. 796
1.89
. 1385
. 2964
. 655
1. 79
1. 45
. 0750
1240
.876
2. 20
. 1215
. 2185
. 805
1. 96
. 1371
. 2948
.675
1. 85
1. 50
. 0658
.1117
.884
2. 32
. 1157
. 2103
.825
2. 05
. 1360
. 2925
. 698
I. 92
1.55
. 0570
. 0990
.893
2.46
. 1090
. 2010
.841
2. 13
. 1348
. 2904
. 720
1. 98
1.60
.0478
. 0850
. 900
2. 62
. 1020
. 1910
. 855
2.23
. 1339
. 2878
. 745
2.05
1.65
. 0385
.0712
.892
2.80
. 0940
. 1790
. 866
2. 32
. 1324
. 2845
. 767
2. 12
1 70
. 0288
. 0558
.876
3.03
. 0858
. 1670
.873
2.42
. 1303
. 2805
. 790
2. 20
1.75
. 0195
. 0400
.853
3. 33
.0770
. 1540
.875
2.54
. 1270
. 2760
.805
2. 27
1.80
. 0100
. 0237
. 760
3.80
. 0685
. 1400
.881
2.66
. 1220
. 2690
.816
2. 34
1.85
. 0007
. 0078
. 166
4.88
. 0595
. 1240
.888
2.81
. 1160
. 2590
.829
2.42
1.90
. 0500
. 1080
.880
2.96
. 1095
. 2480
.839
2.51
1. 95
.0410
.0915
.874
3. 14
. 1030
. 2353
.855
2. 60
2. 00
0320
0745
K60
3 35
0950
9990
2.05
. C230
.0575
.810
3.63
. 0876
. 2080
.863
2. 80
2. 10
.0147
.0400
. 771
4.00
.0800
. 1920
.874
2. 92
2. 15
. 0058
.0220
.566
4. 61
.0714
. 1750
.877
3.05
2. 20
— . 0025
.0038
6.70
0632
1 ^RO
.880
3. 18
2.25
0550
1400
2. 30
0470
1230
2. 35
0387
1 050
867
2.40
0305
0870
R49
2. 45
0??K
.0688
0505
812
2.50
7)1 50
2. 55
0070
0320
4 81
2. 60
-.0005
.0140
6. 10
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
435
TABLE II.— FAIRED VALUES FOR NOSE 7, PROPELLER Bx
\ 7 71 D
Set 15° at 0.75 ft
Set 25° at 0.75ft
Set 30° at 0.75ft
Ct
Cp
V
C,
Ct
Cp
V
C. ,
Ct
Cp
V
C,
0
.05
. 10
. 15
.20
.25
.30
.35
.40
.45
.50
.55
. 60
.65
.70
.75
.80
.85
.00
.05
1.00
1.05
1. 10
1. 15
1.20
1 25
0. 1167
. 1131
. 1088
. 1043
.0990
.0931
. 0868
.0797
.0720
,0640
.0555
.0467
.0378
.0281
.0181
.0087
-.0041
0. 0480
. 0483
.0485
. 0485
. 0482
.0478
.0468
. 0452
.0430
. 0405
.0375
. 0338
. 0293
. 0240
.0180
.0125
.0021
0
.117
.224
.323
.411
.487
.556
.617
.670
.711
.740
.760
.775
.761
. 705
.522
0
.09
.18
.27
.37
46
.55
.65
.75
.85
.96
1.08
1.21
1.37
1.56
1.80
2. 75
0. 1240
. 1259
. 1275
. 1289
. 1298
. 1304
. 1307
. 1305
. 1300
. 1285
. 1259
. 1222
.1170
. 1102
. 1030
. 0954
.0873
. 0795
.0710
. 0620
. 0530
. 0433
. 0330
. 0225
.0118
. 0005
0. 1388
. 1375
. 1360
. 1340
. 1322
. 1298
. 1270
. 1240
. 1200
.1155
.1100
. 1060
. 1022
. 0993
.0960
. 0921
.0877
. 0825
.0761
.0692
. 0614
.0525
.0425
.0320
.0195
.0065
0
.046
.094
. 144
. 196
.251
.308
.368
.433
.501
. 572
.634
.687
.722
.752
. 777
. 796
.819
.840
. 850
. 863
.865
.854
.808
.727
.096
0
.07
. 15
.22
.30
.38
.45
.53
.61
.69
.78
.86
.95
1.03
1. 12
1.21
1.30
1.40
1.51
1.62
1.75
1.89
2. 07
2.29
2.64
3. 42
0. 1381
. 1380
. 1378
. 1373
. 1370
. 1365
. 1359
. 1350
. 1340
. 1330
. 1315
. 1305
. 1295
.1289
. 1277
. 1258
. 1222
. 1170
.1105
. 1040
.0960
.0879
.0797
.0713
.0630
. 0540
. 0447
. 0348
. 0250
.0150
. 0050
-.0050
0. 1828
. 1802
. 1778
. 1751
. 1728
.1705
. 1681
.1660
. 1638
. 1620
. 1596
. 1570
. 1535
. 1487
. 1440
. 1390
.1343
. 1292
. 1244)
. 1187
. 1130
. 1070
. 1008
. 0937
.0850
.0750
. 0645
.0522
.0400
.0273
.0150
.0018
0
.038
.078
. 118
. 159
.200
.242
.284
328
.369
.412
. 457
. 506
.564
. 620
.679
.728
.770
.802
.832
. 850
. 862
.870
. 875
.889
.900
.901
.900
. 875
.797
.500
0
.07
. 14
.21
.28
.36
.43
.50
.58
.65
.72
.80
.87
.95
1.03
1. 11
1. 19
1.28
1.37
1.46
1.55
1. 64
1.74
1.85
1.96
2. 10
2.25
2. 43
2.66
2.98
3.47
5. 50
- -
- -
—
1.30
1.35
1.40
1.45
1.50
1. 55
- . -
- -
—
1.
1.75
1 . Ov
- -
- -
" -
•LIU
L. 61)
. iX)
2. 45
- -
£t. UU
ji. UU
430
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE II— FAIRED VALUES FOR NOSE 7, PROPELLER Bx— Continued
VI vD
Set 35°
at 0.75/7
Set 40°
at 0.75 R
Set 45°
at 0.75 1{
Ct
CP
V
C ,
Ct
Cp
V
C,
Ct
Cp
V
c.
0
0. 1515
0. 2468
0
0
0. 1492
0. 2970
0
0
0. 1456
0. 3490
0
0
.05
. 1508
. 2440
.031
.07
1490
. 2930
.025
.06
. 1460
.3480
.021
.06
. 10
. 1500
.2410
. 062
. 13
. 1484
. 2890
.051
. 13
. 1462
. 3465
.042
. 12
. 15
. 1490
.2381
.094
.20
. 1480
.2850
.078
. 19
. 1465
. 3450
.064
. 19
. 20
. 1480
.2351
. 126
.27
. 1473
.2810
. 105
.26
. 1468
. 3435
.086
.25
. 25
. 1470
. 2292
. 160
.34
. 1470
. 2773
.133
.32
. 1470
. 3420
. 107
.31
.30
. 1460
. 2263
. 194
.41
.1463
. 2734
. 161
.39
. 1470
. 3405
. 129
. 37
. 35
1448
. 2233
. 227
.47
. 1457
. 2695
. 189
.46
. 1470
. 3385
. 152
.44
.40
. 1435
. 2202
. 260
. 54
. 1450
. 2658
.217
.52
. 1470
. 3370
. 175
.50
.45
. 1123
.2170
.295
. 61
. 1443
. 2625
.248
.59
. 1470
. 3350
. 197
.56
. 50
. 1410
.2140
.330
. 68
. 1435
. 2590
. 278
.66
. 1470
. 3330
221
. 62
. 55
. 1397
.2105
.365
.75
. 1429
. 2560
.307
.72
. 1470
. 3308
. 244
. 69
.00
. 1382
.2074
. 400
.82
. 1420
.2530
.337
.79
. 1468
.3283
. 268
. 75
.65
. 1365
.2040
.435
.89
. 1410
.2500
.367
.86
. 1464
. 3255
.292
.81
.70
. 1348
. 2004
.470
.97
. 1400
. 2472
.397
.93
. 1460
.3220
.318
.88
.75
. 1333
. 1972
.507
1.04
. 1390
. 2445
.427
1.00
. 1455
. 3185
. 343
.94
.80
. 1325
. 1944
545
1. 11
. 1380
. 2420
. 456
1.06
. 1448
.3148
. 368
1.01
.85
. 1325
. 1920
.586
1. 18
. 1368
. 2400
.485
1. 13
. 1440
. 3110
.394
1.07
. 90
. 1330
. 1897
. 630
1. 26
. 1353
.2378
. 512
1.20
. 1429
. 3075
.418
1. 14
. 95
. 1325
. 1855
. 679
1.33
. 1338
. 2356
.545
1.27
. 1415
. 3043
.441
1. 21
1.00
. 1315
. 1800
.730
1.41
. 1328
. 2335
. 569
1.34
. 1401
. 3013
. 465
1.28
1.05
. 1293
. 1800
.754
1.48
. 1325
.2317
.601
1.41
. 1384
. 2985
. 487
1.34
1. 10
. 1250
. 1740
.791
1.56
. 1331
. 2300
. 637
1.48
. 1370
. 2960
. 510
1.40
1. 15
. 1181
1670
. 813
1.64
. 1334
.2282
.671
1. 55
. 1358
. 2938
. 532
1.47
1.20
.1110
. 1600
.833
1.73
. 1335
. 2258
.710
1.62
. 1350
. 2918
. 555
1.53
1.25
. 1033
. 1525
.846
1.82
. 1330
.2215
. 750
1.69
. 1343
. 2901
. 578
1. 60
1.30
. 0955
. 1445
.853
1.92
. 1310
. 2163
. 787
1. 77
. 1340
. 2889
. 603
1 . 67
1.35
. 0870
. 1360
.864
2.01
. 1270
. 2105
.815
1.84
. 1343
.2880
. 629
1.73
1.40
.0785
. 1260
.872
2. 12
. 1213
. 2044
.830
1.92
. 1349
. 2875
. 655
1.80
1.45
. 0698
. 1147
.881
2. 24
. 1150
. 1976
.844
2. 00
. 1359
. 2870
. 686
1.87
1. 50
. 0610
. 1023
.895
2. 36
. 1086
. 1900
.857
2.08
. 1365
. 2858
.717
1.93
1.55
. 0520
. 0890
. 905
2.51
. 1018
. 1820
. 866
2. 18
. 1365
. 2830
. 747
2.00
1. 60
. 0428
.0745
.918
2. 69
. 0940
. 1730
.870
2.28
. 1353
. 2783
.777
2. 07
1. 65
. 0333
. 0600
. 915
2. 89
. 0864
. 1620
.880
2. 38
. 1324
.2723
.801
2. 14
1.70
. 0230
. 0450
. 869
3. 16
. 0785
. 1500
.890
2. 48
. 1280
. 26.50
.821
2.22
1. 75
.0135
. 0290
.814
3. 56
. 0700
. 1367
.896
2. 60
. 1225
.2575
.832
2.30
1. 80
. 0040
. 0123
. 585
4.33
. 0620
. 1225
.911
2. 74
. 1167
.2495
.842
2. 38
1 . 85
05xo
1^80
1.90
0440
0930
900
3 05
1030
2289
1.95
. 0350
. 0782
.873
3. 24
. 0950
. 2150
.862
2. 66
2. 00
. 0260
0030
X25
X
087^
2010
865
2. 05
. 0170
. 0465
749
3 xx
0700
1853
2. 10
. 0078
0270
. 607
4 32
0713
1700
2. 15
— . 0013
. 0060
5. 99
0632
1 535
3 1 x
2. 20
0554
lxxn
883
3. 27
3 44
2. 25
0470
1 205
87Q
2. 30
0393
1 040
a to
X A9
2. 35
0310
n§7n
836
3 82
2. 40
0231
0605
.797
735
2. 45
01,50
0500
4 45
2. 50
0070
0295
. 593
5 05
2. 55
-.'0010
! 0095
6. 48
437
CHARACTERISTICS OF SIX PROPELLERS INCLUDING THE HIGH-SPEED RANGE
TABLE III.— FAIRED VALUES FOR NOSE 6, PROPELLER C
Set 15° at 0.75/?
Set 20° at 0.75 R
Set 25° at 0.75 R
Set 30° at 0.75 R
VlnD
Cr
o
V
C.
Ct
‘ c> 1
V
a
Cr
Cp
V
Cr
Cp
V
c.
0
.05
. 10
. 15
.20
. 25
.30
.35
.40
.45
.50
.55
.60
.65
.70
. 75
.60
.65
.90
.95
1.00
1.05
1 10
- H
0. 1322
. 1280
. 1224
. 1165
. 1101
. 1036
. 0968
. 0899
.0826
. 0752
. 0674
. 0587
. 0495
.0391
. 0288
.0183
.0080
-.0020
0. 0584
.0582
. 0578
.0572
. 0564
. 0555
.0543
. 0530
. 0514
. 0492
.0461
.0419
. 0370
.0314
.0252
.0182
. 0106
. 0025
0
. 110
. 212
.306
.391
.467
. 535
. 593
.643
.688
. 732
.770
.802
.810
.800
. 755
. 604
0
.09
. 18
. 27
.36
.45
.54
.63
.72
.82
.93
1.04
1. 16
1.30
1.46
1.67
1. 99
2. 82
0. 1514
. 1492
. 1465
. 1433
. 1397
. 1352
. 1306
. 1252
. 1 193
. 1129
. 1060
. 0985
. 0905
.0818
. 0729
. 0635
.0542
.0447
. 0350
. 0254
0. 0856
. 0857
. 0858 1
. 0857
. 0853
. 0848
.0840
.0831
.0819
.0804
.0786
0764
. 0732
.0691
. 0643
.0586
. 0523
. 0455
.0380
.0298
0
.087
. 170
.251
.328
. 399
.467
.528
.583
. 632
.675
.710
.743
. 770
. 793
.812
.829
.835
.828
.810
0
.08
. 16
.25
.33
.41
.49
.58
.66
. 75
.83
.92
1.01
1. 11
1.21
1.32
1.44
1.58
1.73
1.92
0. 1469
. 1486
. 1499
. 1510
. 1520
. 1529
. 1534
. 1538
. 1538
. 1.529
. 1505
. 1452
.1378
. 1297
. 1212
. 1126
. 1037
. 0943
.0849
.0757
0. 1742
. 1668
. 1610
. 1556
1505
. 146.)
. 1414
. 1373
. 1338
. 1307
. 1282
. 1258
. 1230
. 1194
.1155
. 1110
. 1062
. 1003
.0940
.0808
0
.045
.093
. 146
.208
.262
.325
.392
.460
.527
.587
.635
.073
.705
. 735
.752
. 788
.800
.8)3
.829
0
.07
. 14
. 22
.29
. 37
.44
.52
.60
.68
. 76
.84
.91
.99
1.08
l. 16
1.25
1.34
1.45
1.55
0
. 1709
. 1692
. 1678
. 1662
. 1648
. 1635
. 1622
. 1610
. 1599
. 1588
. 1578
. 1570
. 1562
. 1554
. 1532
. 1454
. 1369
. 1286
. 1201
0
. 2201
.2173
. 2144
. 21 14
.2083
. 2050
.2017
. 1982
. 1947
. 1910
. 1974
. 1840 1
. 1804
. 1761
. 1708
. 1649
. 1589
. 1528
. 1461
. 1397
0
. 039
. 078
. 117
. 157
. 198
. 240
282
! 325
.370
.414
. 465
.512
. 563
.617
.673
. 705
. 733
. 760
. 781
.800
.815
. 830
0
.07
. 14
. 20
. 27
.34
.41
.48
.55
.62
. 70
• 7"
.84
.92
. 99
1.07
1. 15
1.23
1.31
1.39
1.48
1.57
1.67
.0153
. 0200
. 765
2.20
. 0662
.0788
.840
1. 67
.1117
.0013
. 0090
.510
2.69
. 0557
. 0693
.844
1. 79
.1031
. 1329
. 1256
.0454
.0580
. 852
1.94
. 0948
.0480
. 839
2. 11
. 0862
. 1175
. 844
1. 77
1 90
.0250
. 0364
.825
2. 33
0770
. 1090
. 848
.849
.851
1.87
1 25
. 0150
. 0240
.781
2. 64
. 0679
. 1000
1 . 98
2. 11
2. 26
.0047
.0118
. 518
3. 16
. 0577
. 088 1
.0472
. 0752
. 845
i 1 . oO
. 0365
. 0612
. 835
2. 45
. 0265
. 0470
. 818
2. 6 1
2.98
.0159
. 0327
. 730
1.55
. 0068
-.0047
.0184
.0040
.572
3. 45
4.83
1.60
1.65
1.70
| !-75
L85
1.90
1.95
2.00
2. 05
2. 10
2. 15
2.20
_
—
- -
- . —
—
—
—
—
... •-
2. 25
2. 30
_
—
.
—
2. 40
2.45
2. 50
. .
- . .
—
_
- - -
—
- -
.
.
—
—
—
—
—
—
“ — —
_ _ _
_ _ _
2. 55
2.60
2, 65
. .
. .
—
—
—
f . .
—
- -
—
.
.
438
REPORT NO. 594— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE III.— FAIRED VALUES FOR NOSE 6, PROPELLER C— Continued
Set 35° at 0.75 #
I
Set 40°
at 0.75#
Set 45°
at 0.75#
VI nD
Ct
Cp
V
C.
Ct
Cp
V
C.
CT
Cp
V
c.
0
0
0
0
0
0
0
0
0
0
0
0
0
.05
. 1770
. 2728
.033
.06
. 1725
.3324
.026
.06
. 1663
.3937
.021
.06
. 10
. 1757
. 2699
.065
. 13
. 1730
.3320
.052
. 12
. 1670
.3925
.043
. 12
. 15
. 1723
.2665
.097
.20
. 1733
.3313
.079
. 19
.1677
.3911
.064
. 18
.20
. 1702
. 2630
. 130
.26
. 1737
. 3302
.105
.25
. 1682
.3900
.086
.24
.25
. 1680
. 2592
. 162
.33
. 1738
.3288
.132
.31
. 1687
.3886
. 109
.30
.30
. 1659
. 2552
. 195
.39
. 1739
.3270
. 160
.38
. 1692
.3871
. 131
.36
.35
. 1638
.2510
.228
.46
. 1738
.3249
.187
.44
. 1697
.3857
. 154
.42
.40
. 1618
.2467
.262
.53
. 1737
.3226
.215
.50
. 1700
.3840
. 177
.48
.45
. 1600
. 2422
.297
.60
. 1733
.3199
.244
.57
. 1702
. 3824
. 200
.55
.50
. 1582
.2377
.335
.67
. 1728
.3170
.273
.63
. 1704
.3806
.224
.61
.55
. 1566
.2330
.370
.74
. 1720
.3138
.302
.69
. 1705
. 3788
.247
.67
.60
. 1550
.2283
. 407
.81
. 1710
.3102
.330
.76
. 1704
.3767
. 271
.73
.65
. 1538
. 2245
445
.88
. 1699
.3066
.360
.82
. 1702
.3743
.295
.79
.70
. 1527
.2220
.480
.95
. 1684
.3027
.388
.89
. 1700
.3720
.320
.85
.75
. 1517
. 2206
.516
1.02
. 1663
. 2988
.417
.96
. 1694
.3690
.344
.92
.80
. 1508
.2186
.552
1.09
. 1641
. 2945
.445
1.02
. 1687
. 3660
.369
.98
.85
. 1501
.2154
.593
1. 16
. 1619
.2898
.477
1.09
. 1678
.3625
.393
1.04
.90
. 1488
.2110
.635
1.23
.1598
.2847
.505
1. 16
. 1666
.3587
.418
1. 10
.95
. 1471
. 2062
. 680
1.30
. 1578
.2799
.536
1. 23
. 1650
.3544
.442
1. 17
1.00
. 1442
.2015
. 715
1.38
. 1560
.2755
.568
1.30
. 1631
.3498
.467
1.24
1.05
. 1393
. 1968
.743
1.45
.1545
. 2712
. 599
1.37
. 1609
.3446
.490
1.30
1. 10
. 1340
. 1915
.770
1.53
. 1531
.2672
.631
1.43
. 1585
. 3390
.514
1.37
1. 15
. 1279
. 1858
.791
1.61
. 1520
. 2632
.665
1.50
1503
.3333
. 540
1.43
1. 20
. 1210
. 1795
.810
1.69
. 1511
. 2595
.699
1.57
. 1542
. 3280
.564
1.50
1.25
. 1131
. 1723
.821
1.78
. 1497
.2530
.730
1.64
. 1522
. 3236
.589
1.57
1.30
. 1048
. 1644
.828
1.87
. 1472
.2519
.761
1.71
. 1503
.3199
.611
1.63
1.35
. 0962
. 1550
.837
1.96
. 1427
. 2470
. 780
1.79
. 1488
.3168
.633
1.70
1.40
. 0875
. 1453
.843
2.06
. 1372
.2409
.797
1.86
. 1476
. 3142
.657
1. 77
1. 45
.0788
. 1345
.848
2. 17
. 1310
. 2340
.811
1.94
. 1170
.3127
.681
1.83
1.50
.0700
. 1236
.850
2.28
. 1240
2262
.822
2. 02
. 1468
.3110
.708
1.90
1.55
.0611
. 1110
.853
2.41
. 1160
.2170
.829
2. 10
. 1460
.3088
.732
1.96
1.60
.0521
.0984
.848
2. 54
. 1078
.2065
.835
2. 19
. 1445
.3054
.756
2.03
1.65
. 0430
.0843
.842
2.71
.0988
. 1950
.836
2.29
. 1413
. 3010
.775
2. 10
1.70
. 0340
.0693
.835
2.90
.0900
. 1825
.838
2. 39
. 1370
.2950
. 790
2. 17
1.75
. 0243
.0531
.800
3. 15
.0810
. 1690
.839
2. 49
. 1318
.2880
.800
2. 25
1.80
. 0145
. 0365
.715
3. 49
.0720
. 1540
.840
2 62
. 1255
.2800
.806
2. 33
1.85
. 0048
.0200
.444
4. 05
.0630
. 1385
.841
2. 75
. 1191
.2720
.810
2. 40
1.90
-.0051
.0031
6.03
.0540
. 1230
.835
2.90
. 1125
. 2636
.811
2, 48
1.95
. 0450
. 1070
820
3 05
1056
2536
812
2 56
2.00
. 0360
. 0900
800
3 24
0086
J2427
813
2 66
2.05
. 0265
. 0720
754
3 48
0910
. 2293
K14
2 76
2. 10
. 0175
.0545
675
3 76
0830
. 2135
816
2 86
2. 15
.0083
.0365
.489
4 16
0746
1961
818
2 98
2.20
-.0008
. 0190
4 86
0663
1780
819
3 10
2.25
-.0100
.0010
8.96
0580
1 595
820
3 25
2.30
0500
1410
816
3 40
2. 35
0412
1220
795
3 58
2. 40
0330
1040
762
3 77
2. 45
0242
0855
694
4 00
2.50
0160
0670
597
4 26
2.55
0073
0485
.383
4 67
2.60
- 0010
0300
5 24
2.65
-.0095
.0120
6. 42
REPORT No. 595
FULL-SCALE TESTS OF A NEW TYPE N. A. C. A. NOSE-SLOT COWLING
By' Theodore Theodorsen, M. J. Brevoort, George W. Stickle, and M. N. Gough
SUMMARY
An extended experimental study has been made in regard
to the various refinements in the design of engine cowlings
as related to the propeller-nacelle unit as a whole, under
conditions corresponding to take-off, climb, and normal
flight. The tests were all conducted at full scale in the 20-
foot wind tunnel. This report presents the results of a
novel type of engine cowling, characterized by the fact that
the exit opening discharging the cooling air is not, as usual,
located behind the engine but at the foremost extremity or
nose of the cowling. This type of cowling is inherently
capable of producing two to three times the pressure head
obtainable with the normal type of cowling because the
exit opening is located in a field of considerable negative
pressure. Thus identical conditions of cooling can be
obtained, at correspondingly lower air speeds. In gen-
Flight tests of a temporary installation showed promising
results.
<£_ Propeller <£ Cylinders
' Perforated plate
Figure 2.— Drawing showing the principle of operation of the nose-slot cowling. The upper half of the drawing shows the practical application; the lower half shows the
arrangement of the test installation with nose 10-54.
INTRODUCTION
It has been shown in the report on conventional cowl¬
ings (reference 1) that the available pressure head across
the engine is very nearly ecpial to 1 g and that only in
very extreme cases, as by the use of skirt flaps, may this
38548—38 - 29
value be exceeded by about 20 percent. The pressure-
distribution tests reported in the same reference show
that a negative pressure of several times the velocity
head is available near the nose of the cowling. (See fig.
1 .) Since cases may be expected to occur in which a
439
440
REPORT NO. 595— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
large pressure drop is desired, a special type of cowling
was designed to have the exit opening at or very near
the front portion of the cowling in order to make use of
this available pressure drop. At first thought, this
arrangement might be expected to be inefficient as a
fairly large disturbance in the entire boundary layer is
normally expected. Peculiarly enough the contrary
seemed to be the case, the very first design showing a
very high efficiency. The air enters the cowling in the
central front opening in the usual manner, passes
through the engine baffles, and is then returned across
Figure 3. — The test installation in the 20-foot wind tunnel.
the top of the cylinders, guided into the nose ring, and
discharged through the slot.
DESCRIPTION OF TEST ARRANGEMENT
Figure 2 gives a general idea of the test arrangement;
the engine resistance was replaced by a perforated plate
just behind the nose ring, as shown in the lower half of
the figure. This plate contained several hundred
1-inch holes, any number of which could be closed as
desired, thus representing engines of a wide variety of
conductivities. Figure 3 is a photograph of the instal¬
lation with the original nose, which is designated 1 ()-)£,
the first numeral giving the number of the nose and the
second numeral giving the exit opening in inches, as
some of these noses were tested with two sizes of exit
opening. Figure 4 (a) is a photograph of nose 1 0— K ;
figures 4 (b) and 4 (c) show two more designs, 11-1 and
12-1, tested successively. A total of nine cowlings of
(a) Nose 10 -XA.
(c) Nose 12-1.
Figure 4.— Photographs of noses tested.
441
FULL-SCALE TESTS OF A NEW TYPE N. A. C. A.
NOSE-SLOT CO WI,I NG
(his type were tested, all of which are shown with the
proper designations in the scale drawing (fig. 5). All
the cowling nose rings were given the same major di¬
tests were conducted in connection with these tests
as the requisite information was available from
reference 1 .
Figure 5. — Drawings of the nine nose cowlings tested.
mensions; all were fitted to the same perforated disk
comprising the test resistance. The conductivity of
this perforated disk could be changed at will between
the limits of 0 to 0.09, thus simulating the complete
range of actual installations. No heat-transmission
The tests were performed at both high and low air
speeds, the low speeds for the purpose of obtaining the
cooling from the propeller slipstream alone. The tests
were conducted as usual, with the propeller both on and
off for the sake of completeness.
442
REPORT NO. 595— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
DEFINITION OF PARAMETERS USED
The various terms used in the paper will be defined
and briefly discussed. These terms are taken from the
report on conventional cowlings (reference 1).
(1) Pump efficiency, defined as
QAp
Vr (D-D0)V
where Q is the quantity of air per second which is forced
through the resistance.
A p, the associated pressure drop across the same
resistance.
D, the observed drag of the cowling-nacelle unit.
D0, the drag of a body of identical major dimen¬
sions but with the cooling channels closed
and the outline faired into a streamline
contour.
V, the air speed.
It may thus be seen that QAp is the useful work done
per second and that ( D-D0)\ r is the work expended.
It will be realized from the following that the pump
efficiency is a very precise measure of the aerodynamic
quality of the design. For the case of the power run,
or the propeller on, the pump efficiency is given by the
formula
(A p/qY't PCS
n’~ m-v KF
where the quantities K, F, Pc , S, 7?0, and 77 will be de¬
fined under the next headings.
(2) Conductivity, defined as
K__ A/F __ Q
■yjAplll jApfaFV
where F is the maximum cross-sectional area of the
nacelle. This quantity gives the inverse of the resist¬
ance of the engine to the air flow and is nondimensional.
The apparent conductivity of the exit opening may
similarly be represented by a value K2 which is simply
the ratio of the area of the exit opening to that of the
maximum cross section of the nacelle, or
It has been shown in reference 1 that the following
relation exists in regard to the flow through the cowling:
A P
q \FVj L K2
where A P is equal to the total head of the air entering
the cowling minus the static pressure in the region of
the exit opening. The former pressure is always
found to be very nearly equal to the total head of the
air stream. This equation will be referred to as “the
equation of flow regulation.”
(3) Propeller load factor or disk-loading coefficient,
defined as
Pc
p
qSV
where P is the power supplied to the propeller shaft,
and S is the disk area of the propeller. This quantity
is in the first order proportional to the contraction of
the propeller slipstream (reference 1). Equal values
of Pc thus essentially represent geometrically identical
flow pictures. In the analysis of the results obtained
for various propellers a certain simplicity is achieved
in comparing such results at a fixed value of Pc.
(4) Net efficiency, defined as
RV
Vn p
in the case of the power runs, where R is the thrust of
the unit as given by the thrust scale. The net efficiency
obtained with the cooling air shut off and the outline
faired into a carefully streamline contour is needed
to determine the pump efficiency for the case of pro¬
peller on and is designated 170.
(5) In reference 2 the quantity Ap/n2 was chosen as
a characteristic function to represent the cooling prop¬
erties of any particular combination of engine cowling
and propeller at the condition of zero air speed, repre¬
senting the case of cooling airplane engines on the
ground. The square root of the foregoing quantity, or
■\jAp/n, obtained from experimental data, is given as a
function of the advance-diameter ratio V/nD. It is
realized that the propeller at zero air speed acts very
much the same as any other blower in regard to the
pressure produced for cooling. The quantity Ap/n 2 or
■y/Ap/n is therefore very nearly a constant for a given
propeller at a given blade-angle setting and is inde¬
pendent of the revolution speed of the propeller. It is
referred to in the following discussion as the “pressure
constant.” The speed of the propeller may be con¬
sidered known from the results of a previous investiga¬
tion (reference 3).
TEST RESULTS
The test results are shown in condensed form in
table I. Column 1 gives the designation of the cowling
nose corresponding to those given in figure 5. Column
2 shows the propeller used, the zero standing for pro¬
peller off and the Bx and C, for the purpose of the present
paper, representing two normal 10-foot propellers
(reference 3). The main difference between Bx and C
is that Bx has a well-shaped airfoil section extending
down close to the hub, whereas C has a round shank.
Column 3 shows the apparent conductivity of the exit
opening. Column 4 is the conductivity of the test
resistance or “engine.” Columns 5, 6, and 7 show the
pressures (in terms of q) with respect to the test resist-
FULL-SCALE TESTS OF A NEW TYPE N. A. C. A. NOSE-SLOT COWLING
443
ance. Column 5 gives values of pf) the pressures in
front of, and column 6 gives values of pr, the pressures
in the rear of the resistance; column 7 gives values of
A p, the pressure difference across the resistance. Col¬
umn 8 gives the drag in usual coefficient form CD.
Column 9 is given, for convenience, to illustrate the
approximate forces involved by giving the drag at 100
miles per hour or, more exactly, at a q of 25.6 pounds
per square foot for the drag run; i. e., the forward net
Figure 6.— Dependency of pump efficiency on conductivity.
thrust at the same tunnel speed and at a fixed disk
loading for the propeller runs. Column 10 gives the
net efficiency t]n for the propeller runs, and column 11
the pump efficiency yp as defined in the preceding
section.
In figure 6 the pump efficiency has been plotted
against the conductivity for various noses. It was
the very successful result on the original nose 1 0— }4
that prompted the study of several other designs, which
were later tested. Noses 10, 12, and 16 all tend to
reach a 100-percent efficiency at conductivities beyond
0.07 and 0.08. Nose 10 actually exceeds 100-percent
pump efficiency even at the low conductivity 0.03.
The I’eason for the relatively large efficiences obtained
with this type of cowling lies in the fact that the ve¬
locities in the exit opening more nearly equal those of
the external air stream. The beneficial effect of large
exit velocities on the pump efficiency has been conclu¬
sively demonstrated in reference 1. The reason for
the larger exit velocities is due to the fact that a much
larger pressure difference is available and that part of
this difference may be used in the exit opening, leaving
at least the usual pressure drop for cooling.
The noses showing a very low efficiency in figure 6
were designed primarily with the intention of obtain¬
ing a large available pressure drop at zero air speed.
On the whole, the design was found to be critical, a
minor change in the external contour sufficing to drop
the efficiency from near 100 percent to a small quantity.
It was found that a projecting edge at the slot, such as
embodied in cowlings 12, 13, or 14 in figure 5, was very
detrimental to the efficiency. It was also noted that
the highest efficiency was obtained by locating the
outlet in a converging-flow field, as for nose 10, in
contrast to the low efficiency obtaining by locating the
outlet back of the maximum velocity, as for nose 11.
As is evident from the introduction, the main reason
for designing and testing the new nose-slot cowling is
the large pressure available for cooling. Figure 7 is a
plot of the results in table I giving the available pres¬
sure against the engine conductivity, K. It is seen
that the available pressure difference created by this
type of cowling lies in the region of 2 q and in a few
cases even exceeds 2.5 q. The decrease in available
pressure with increased conductivity is caused by the
fairly small size of the apparent exit conductivities,
ft may be observed from the equation of flow regula¬
tion previously given that a small value of K-> means
that a large part of the pressure difference created by
the cowling is used to produce velocity head in the exit
opening and the remaining pressure A p available for
cooling is correspondingly reduced. If the pressure
available for cooling A p is added to the velocity head in
the slot, it is found that the total, which is A/fi is of a
nearly constant magnitude for any given cowling.
The values K2 have been inserted for the various noses
shown in figure 7. It has been shown in reference 1
that 7v=0.05 may be considered as the normal value
of the conductivity of a well-baffled single-row radial
engine. The average available pressure of the nose
cowling at this conductivity is seen to approximate 1 q
and to reach a maximum of about Ifi q with nose 16-1 .
A comparison of the available pressure drops and effi¬
ciencies at any desired conductivity with those obtained
Figure 7 —Available pressure differences across the engine plotted against
conductivity.
on the regular cowlings (reference 1) shows that the
nose-slot cowlings for most conditions are superior;
hence, at an available pressure drop across the engine
of about 1 q, the efficiencies on some of the nose-slot,
cowlings approach 100 percent, while in the normal
type they were of the order of 60 to 80 percent.
No attempt was made during the present investiga¬
tion to test nose-slot cowlings with large exit conduc¬
tivities. Such cowlings should provide a larger pres-
•s-d-jj^j -bs/’q/p, ‘ a/'d_ v
444
REPORT NO. 595— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 8. — Pressure constants -y/Ap/n against VjnD for the several noses tested.
FULL-SCALE TESTS OF A NEW TYPE N. A. C. A. NOSE-SLOT COWLING
445
In order that the practical value of the information
Figures. — Original cowling installation on the Curtiss BFC-1 airplane. oil the 116W type ol cowling might be demonstrated,
needed only at low speed, the matter of some efficiency 1 ~~ ~j
loss is not important. It is perfectly possible to provide
means for changing the exit opening during flights. . ,
Figure 11.— The Curtiss BFC-1 airplane equipped with the nose-slot cowling.
Figure 10.— Close-up of the original cowling on the Curtiss BFC-1 airplane
The experimental results in regard to the pressure
drop available for cooling with the propeller slipstrean
the following flight tests were made with a preliminary
cowling installation on the Curtiss BFC-1 airplane.
The Curtiss BFC-1 airplane (fig. 9) has a Wright
SGR-1510 twin-row, 14-cylinder, geared engine, com¬
pletely equipped with pressure baffles and a wide-chord
ring cowling (fig. 10). A selective thermocouple in¬
stallation allowed the determination of temperature for
28 positions on the heads and bases of the 14 cylinders.
In this condition a level flight was made for reference
purposes at maximum allowable continuous power for
a sufficient length of time to allow all temperatures
; to stabilize. Complete data identifying the flight were
recorded.
The new N. A. C. A. nose-slot cowling was then
installed as shown in figure 11. This photograph does
not show the external oil cooler, as in figure 1, as it
had been removed just before the picture was taken.
The installation used nose 16-1 (fig. 5) and was arranged
as shown in the upper part of figure 2, except for the
fact that the internal dividing wall was located between
the heads and the cylinder barrel and below the spark
plugs. The wall extended back to the second row.
The flow is approximately as indicated by arrows in
the upper part of figure 2. Close-up photographs of
the design are shown in figure 12.
sure drop for cooling, probably at some expense of
pump efficiency. Since the largest pressure drop is
at zero air speed are given in figure 8 for noses 10, 11,
12, 13, 14, and 16. These results will be more fully
understood bv a study of reference 2, which shows the
'' pressure constant at zero air speed for various normal
and special arrangements. Noses 10, 12, and 16 are
seen to give very low pressure constants at the ground
point. Nose 11 compares favorably with the best
results previously obtained on normal cowlings. Noses
; 13 and 14 also give large available pressures on the
! ground. It is noticed, in general, that the noses giving
high available pressures on the ground are not efficient
in the flight condition, and vice versa.
PRELIMINARY FLIGHT TESTS OF THE NEW TYPE
N. A. C. A. COWLING ON BFC-1 AIRPLANE
446
REPORT NO. 595— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Another change consisted in reversing the pressure
baffles on the cylinder heads to suit the reversed flow
direction; the baffles on the barrel were redesigned to
fit the new installation. Three thermocouples on
front cylinders were moved from the rear to the front
spark-plug bosses. It should be noted that the loca¬
tion of the exhaust manifold (see fig. 10) could not be
flight reproducing the conditions of the one with the
original cowling was made. From this flight the follow¬
ing comparison was obtained.
At the same density altitude and with the same power
but with a free-air temperature lower by 13° C., the
indicated air speed was, within the accuracy of meas¬
urement, the same. The oil, both in and out, was 6° C.
Figure 12. — Close-ups of the nose-slot cowling installed on a Curtiss BFC-1 airplane.
changed for these tests and that therefore it was
entirely enclosed within the new cowling.
The operation on the ground of the engine with the
new nose-slot cowling indicated the absence of exces¬
sive heating, which would have prevented flight tests.
There was some evidence of unusual local heating,
mainly of the rubber connections on the intake mani¬
fold. It is appreciated that the completely new
arrangement might cause some change in local heating
of parts not designed for the type of air flow provided
bv this cowling. No evidence of overheating ap¬
peared. After a cautious take-off and climb, a level
cooler; the cylinder bases consistently averaged 30° C.
cooler; the heads, 35° 0. hotter, there being little
difference between the front and rear plugs; and the
magneto, 30° C. cooler. No difficulties were experi¬
enced. The handling characteristics of the airplane,
the visibility, the local cockpit heating, and the engine-
operating conditions appeared unchanged. Another
flight verified the results.
An inspection immediately after the engine was
stopped on the ground revealed nothing amiss; the
engine accessory or auxiliary compartment and the
cowling aft of the cylinders was exceptionally cool. It
FULL-SCALE TESTS OF A NEW TYPE N. A. C. A. NOSE-SLOT COWLING
447
was interesting to observe that, as expected, the nose
of the cowling was the hottest point.
In view of the fact that the air used to cool the
heads contains also the accumulated heat obtained from
the exhaust manifold, the results obtained indicate very
promising possibilities for considerably improved cool¬
ing when the baffling and manifold locations are de¬
signed specifically for this type cowling. Possible
speed gains are also indicated when the external cowl¬
ing lines may be incorporated in a new design rather
than adapted to an already existing afterbody shape.
GENERAL CONCLUSIONS
1. It has been found that the new type nose-slot
cowling produces pressure differences of 2 to 2.5 times
the velocity head of the air stream, as compared with 1 ve¬
locity head for the normal cowling. This fact is impor¬
tant as regards cooling in climb and at low air speeds.
2. A well-designed nose-slot cowling shows pump effi¬
ciencies close to 100 percent, owing to the fact that a
smaller fraction of the total available pressure head is
needed in the resistance, thus leaving a larger velocity
head in the exit opening and reducing the impact or
mixing losses that take place as the low-energy cooling
air re-enters the main air stream.
3. Nose-slot cowlings designed for high efficiency at
normal speed were found to be slightly inferior to normal
cowlings in regard to cooling in the propeller slipstream.
A specially designed nose-slot cowling for improving the
cooling on the ground was found to be inefficient at normal-
flight speeds in comparison with normal cowlings. A two-
slot design, in which one slot may be closed at will, may
therefore be recommended for cases in which good cooling
from the propeller slipstream is particularly important.
4. The nose-slot cowling is critical in regard to design.
It has been found that the exit opening should be
located so as to permit the low-energy air to join the
main air stream in a convergent-flow field, that is, ahead
of the point of maximum velocity. High efficiency is ob¬
tained only by exercising great care in the detail design.
5. Preliminary flight tests gave promising results.
Langley Memorial Aeronautical Laboratory,
National Advisory- Committee for Aeronautics,
Langley Field, Va., June 5, 1936.
REFERENCES
1. Theodorsen, Theodore, Brevoort, M. J., and Stickle, George
W.: Full-Scale Tests of N. A. C. A. Cowlings. T. R. No.
592, N. A. C. A., 1937.
2. Theodorsen, Theodore, Brevoort, M. J., and Stickle, George
W.: Cooling of Airplane Engines at Low Air Speeds. T. R.
No. 593, N. A. C. A., 1937.
3. Theodorsen, Theodore, Stickle, George W., and Brevoort, M.
J.: Characteristics of Six Propellers Including the High-
Speed Range. T. R. No. 594, N. A. C. A., 1937.
TABLE I.— CONDENSED TEST RESULTS
1
2 1
3
4
5
6
7
8
9
10
11 I
Nose
Pro¬
peller
Ki
IC
Pf
g
Pr
g
Ap
g
Drag in
pounds at
9 = 25.6
pounds/
square
foot, or
thrust at
1/ v>,=
1.8 and
9 = 25.6
pounds/
square
foot
Vn
10 -a
0
0. 0000
0. 922
-1.250
2. 170
0. 1287
48.6
0. 000
IU-1'2
0
. 00248
. 904
-1.083
1.986
. 1330
50.2
.318
io-34
0
. 00497
.904
-.955
1.860
. 1388
52.4
. 457
io-y,
0
. 00981
. 929
-. 756
1.683
. 1499
56. 6
.552
10-34
0
. 0200
.926
-. 388
1.313
. 1573
59.4
.652
10-34
0
.0304
.918
-.216
1. 135
. 1475
55.7
1.013
10-34
B
. 0292
.881
-. 153
1.034
250
0. 716
1.278
io-32
c
.0291
.854
-. 190
1.043
247
.708
.998
10-1
0
.0000
.911
-1.313
2. 223
. 1372
51.8
.000
10-1
0
. 00267
.930
-1.209
2. 140
. 1433
54. 1
.260
10-1
0
. 00527
. 923
-1. 117
2. 040
. 1510
57.0
.386
10-1
0
. 01034
.927
-1.010
1.938
. 1671
63. 1
.500
10-1
0
.01862
.926
-. 966
1.894
. 1965
74.2
.568
10-1
0
. 0238
.925
-1.058
1.983
.209
78.9
.680
10-1
0
.0278
.928
-1. 166
2. 095
. 205
77.6
.899
10-1
B
.0270
.891
-1. 101
1.992
236. 0
.676
1. 243
10-1
B
. 0236
.887
-.955
1.840
239. 0
. 685
1. 117
10-1
B
. 01034
.901
-.907
1.808
242.0
.693
.555
11-1
0
.0000
.925
-1.009
1.935
.299
113.0
.000
11-1
B*
.0000
.913
-1.306
2. 220
200. 0
. 573
.000
11-1
0
. 00484
.918
-.849
1. 768
.342
129.0
.0493
11-1
0
. 00979
.934
-.731
1.665
.381
144.0
. 0780
11-1
0
. 0267
.943
-. 593
1.536
.416
157.0
. 0865
11-1
Bx
.0214
. 923
-.800
1.723
166.0
.476
. 197
11-1
Bx
. 0462
.918
-. 172
1.090
180.0
. 516
.252
11-1
0
.0438
.950
-.114
1.064
.318
120.0
.233
12-1
0
.0000
.933
-. 794
1.725
. 1245
47.0
.600
12-1
B* i
.0000
.920
-.561
1.482
244.0
.698
• COO
12-1
0
. 00493
.914
-.681
1.594
. 1345
50.8
.426
12-1
0
. 00998
.910
-.595
1. 504
. 1427
53.9
.584
12-1
0
. 0222
.914
-.386
1.301
. 1557
58.8
.739
12-1
Bx !
.0213
.920
-. 175
1.095
243. 0
.696
.574
12-1
0
.0427
.932
-.017
.948
. 1589
60.0
.827
12-1
0
. 0647
.939
. 261
.679
. 1520
57.4
.890
12-1
Bx !
.0424
.915
. 137
.779
242.0
.693
.645
12-1
0
.0839
.933
.397
.536
. 1475
55.7
.908 1
j
12A-1
Bx
)
.0419
.920
-.613
1.531
150.5
.431
.276
12A-1
0
i .066
.0419
.957
-.373
1.330
.580
219.0
.137
12A-1
C
1
.0413
.863
-.569
1. 433
147.0
.42
.240
13-1
0
.0281
.938
-.446
1.384
.575
217.0
.699
13-1
Bx
.0287
.913
-.767
1.679
143.0
.41
.203
u-U
0
.0000
.948
-1.038
1.983
.527
199.0
.000
n-%
Bx
.0000
.44
.600 1
14-54
Bx
.054
112.0
32
14-54
0
.0201
.955
-.563
1.519
.651
246.0
.070
14-54
0
.625
236. 0
14-54
Bx
105.0
. 30
16-1
0
.0000
.921
-1.809
2. 730
.1324
50.0
o
o
o
16-1
Bx
.0000
.897
-1.750
2. 645
244.0
.700
.000
16-1
Bx
.01950
.894
-1.030
1.923
219.0
.627
.490
16-1
0
.01965
.903
-.946
1.848
.263
99.5
_
. 325
16-1
0
. U/U
.0388
.918
-.488
1.408
.263
99.5
.427
16-1
Bx
.0390
.893
-.499
1.391
216.0
. 62C
.568
16-1
Bx
.0790
.888
.061
.826
226.0
.648
.683
16-1
0
.0711
.908
-.049
.958
. 1967
74.3
.782
16-34
0
.0000
.890
-1.621
2. 513
. 1290
48.7
.000
16-34
Bx
. 01904
.878
-.668
1.547
234.0
.671
.557
16-34
0
.035
. 01920
.903
-.712
1.614
. 1872
70.7
_ _ _
.518
16-34
0
. 0390
.907
. 095
1. 00(
. 1671
63.4
. 688
16-34
Bx
.0383
.875
-.082
1
.955
1
235.0
.673
.561
1
38548 — 38
■30
REPORT No. 596
COOLING TESTS OF A SINGLE-ROW RADIAL ENGINE WITH SEVERAL
N. A. C. A. COWLINGS
By M. J.
Bkevoort, George \V. Stickle, and
Herman- II. Ellerbrock, J\
SUMMARY
EQUIPMENT AND TESTS
The cooling of a single-row radial air-cooled engine
using several cowling arrangements has been studied in the
N. A. C. A. 20-foot wind tunnel. The results show the
effect of the propeller and several cowling arrangements on
cooling for various values of the indicated horsepower in
the climb condition. A table giving comparative perform¬
ance of the various cowling arrangements is presented.
The dependence of temperature on indicated horsepower
and pressure drop across the baffles is shown by charts.
Other charts show the limiting indicated horsepower
against the pressure drop across the engine and the heat
dissipated at various values of the indicated horsepower.
INTRODUCTION
A study was made to determine the cooling charac¬
teristics and performance of a typical radial air-cooled
engine, using several cowling arrangements. The tests
were made in the N. A. C. A. 20-foot wind tunnel,
which has a maximum speed of 110 miles per hour.
With such a maximum speed the tests arc obviously
confined to the condition of climb. From practical
considerations such a range is ideal because, except
under very special operating conditions, the problem of
cooling is most important during climb. It follows,
then, that all conclusions concerning aerodynamic
characteristics and efficiency drawn from these tests
relate to the condition of climb alone. In tests cover¬
ing the complete range of take-off, climb, and cruising
conditions for several cowlings (references 1 and 2), it
was shown that certain cowlings which appear acro-
dynamically good in climb are poor in the cruising
condition.
The results show, for a particular engine, the relation¬
ship existing between the cooling and the developed
horsepower and the pressure drop across the baffles.
It is obvious that the results are, in detail, applicable
only to this engine. In the discussion of the results,
however, the chief emphasis is laid on general considera¬
tions and on the mechanism of cooling. It is believed
that, although the details are interesting, the more
important aspect of the investigation is the contribution
to a clearer picture of the mechanism of cooling.
The engine was mounted in the N. A. C. A. 20-foot
wind tunnel (reference 3) as shown in figure 1. The
engine is a 9-cylinder radial R-1340 SlIU-G Pratt &
Whitney Wasp. The over-all diameter is 5lT6 inches.
It, is rated at 550 horsepower at 2,200 r. p. m. and at
8,000 feet altitude. It has a 3:2 reduction gear, a
compression ratio of G, and is ecpiipped with a, geared
(a) Rare engine.
(b) With cowling.
Figure 1.— Engine and nacelle set-ups.
centrifugal supercharger that operates at 12 times
engine speed. The bore of the cylinders is 5.75 inches
and the stroke is 5.75 inches.
The two propellers used are shown in figure 2.
Propeller A is a Hamilton Standard controllable
propeller of blade form No. 6101—0 and propeller B is
a Hamilton Standard adjustable propeller of blade
form No. 1(M 0.
449
450
REPORT NO. 596— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 3 is a profile drawing of the engine and nacelle
with the various noses, skirts, and inner cowlings used
in this study.
Controllable (A). Adjustable (B).
Figure 2. — Propellers used.
Figure 4 shows the arrangement of baffles on the
head and barrel of the cylinder. Note that these
baffles are not tightly fitting in the sense that they touch
23 on cylinder 3. The remaining thermocouples were
located on cylinder 3. Cylinders are numbered counter¬
clockwise, cylinder 1 being at the top.
Air temperatures in front of and behind the engine,
oil-in and oil-out temperatures, and carburetor-air
temperatures were measured by shielded resistance
thermometers. The oil was cooled by a water radiator
located inside the nacelle.
The drop in pressure across the engine was measured
by pitot-static tubes located in front of and behind
the cylinders. The quantity of air passing through
the baffles was measured by pitot-static tubes located
in the skirt exit.
The engine power was controlled by varying the
manifold pressure. The manifold pressure, engine
speed, and air temperature gave the horsepower from
a calibration furnished by the manufacturer. The
fuel consumption was measured and frequent checks
were made on the exhaust-gas analysis from each
cylinder.
The routine of an individual test was as follows:
The engine speed, the horsepower, and the tunnel
speed were adjusted to the desired values. Sufficient
£ Pr ope/Zer £ Engine
the fin tips but that they are comparatively close-fitting
baffles.
The temperature of the engine was measured by 24
thermocouples connected to a recording pyrometer.
The thermocouples were penned to the head and spot-
welded to the barrel of the cylinder. The thermocouple
locations on cylinder 3 are shown by figure 5. Thermo¬
couples 1 to 9 were located on cylinders 1 to 9, respec¬
tively, at the position indicated for thermocouple 3 in
figure 5. Thermocouples 10, 11, 12, and 13 were
located on cylinders 1, 3, 5, and 7 at the position
shown for thermocouple 1 1 . Thermocouple 24 was
located on cylinder 8 at the position of thermocouple
time was allowed for all temperatures to become
stabilized. All temperatures and pressures were then
recorded. This procedure was repeated for various
values of engine speed, indicated horsepower, and
tunnel speed. Each cowling arrangment wras tested
in this manner. Ranges of engine speeds from 1,600
to 2,000 r. p. m., power from 300 to 550 horsepower,
and air speeds from 80 to 110 miles per hour were
covered. Drag tests with propeller off were made.
LIST OF SYMBOLS
Q, quantity of cooling air passing through the
engine per second.
COOLING TESTS OF A SINGLE-ROW RADIAL ENGINE WITH SEVERAL N. A. C. A. COWLINGS 451
Ap, pressure drop across the baffle.
K=
conductivity of the engine.
F, cross-sectional area of the engine.
p, mass density of the air.
A, area of the free air stream entering the
engine.
dynamic pressure of the free air stream.
p f, pressure in front of the cylinder.
pr, pressure in rear of the cylinder.
V, velocity of the free air stream.
P
qSV’
propeller disk loading coefficient.
P, power supplied to the propeller.
S, disk area of the propeller.
n, revolutions per second of the propeller.
D, diameter of the propeller.
AT, difference between the temperature of a
particular point on the cylinder and that
of the inlet cooling air.
ANALYSIS OF THE PROBLEM
The useful work done in cooling the engine is QAp,
and Q is proportional to V Ap . The power to cool can
then be written as proportional to (Ap)3 2. It has been
shown in reference 1 that
Power to cool
y 2KF(Ap)m
Vp
K=
The value /i = 0.06 was constant throughout the in¬
vestigation. It depends entirely upon the finning and
the baffling of the cylinders. The pressure drop Ap is a
function of the air-stream velocity and of the cowling
and baffle design. It is obvious from the foregoing
equation that the selection of the minimum values of
K and Ap which will provide adequate cooling is very
desirable from the standpoint of aerodynamic efficiency.
Reference 1 has shown that it is practically impossi¬
ble to develop a Ap of more than 1.3 q for this general
type of cowling. Such a high value, moreover, is
attained at very low efficiency.
The problem, then, is to determine under what con¬
ditions and how efficiently the modern engine can be
cooled with various pressure drops. This study of the
climb condition answers a part of that question.
In such a study it is extremely important that only
the quantity under consideration be permitted to vary,
all other factors remaining constant. This condition
is particularly difficult when the tests are made on an
actual engine, where variations in air-fuel ratio, car,
buretor-air temperature, oil temperature, oil pressure-
Air f/ow
Y
(a) Barrel.
Air flow
(b) Lower head.
and mechanical condition of the engine must be elim¬
inated as far as possible. Tests have shown (reference
4) that a variation of 1.0 in the air-fuel ratio will result
in a change of approximately 20° F. in the cylinder
temperature. The maximum variation from cylinder
452
REPORT NO. 596— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 5. — Thermocouple locations on cylinder 3.
causes to a minimum. The air-fuel ratio was checked
by exhaust-gas analysis and the fuel consumption was
maintained constant at 0.57 lb./b. hp.-hr. by the use of
a fuel flow meter. The variations of air-fuel ratio from
cylinder to cylinder are characteristic of the engine and
check the cylinder-to-cy Under temperature variation
reasonably well. Any variation due to carburetor-air
temperature or over-all air-fuel ratio affects all cylinders
and causes discrepancies resulting in a scattering of the
points. This type of variation was relatively small.
Isolated cases of temperatures that appear to be in
error by as much as 40° F. will be found but, in general,
the temperatures are accurate to ± 10° F.
column 7 gives the pressure in rear of the cylinders
divided by the dynamic pressure; column 8 is the
difference between columns 6 and 7, or the pressure drop,
in percentage of g, across the baffles. Column 9 is the
actual pressure drop across the baffles in pounds per
square foot at a dynamic pressure of 25.6 pounds per
square foot, which corresponds to 100 miles per hour
under standard conditions. Column 10 gives the tem¬
perature in front of the cylinder, an average of thermo¬
couples 10 through 13; column 11 gives the temperature
in the rear of the cylinder, an average of thermocouples
1 through 9. Throughout the report, all temperatures
are given as the difference between the temperature at
to cylinder was 0.8 of a ratio, which should result in a
temperature variation of 16° F. The carburetor-air
temperature never varied more than 24° F. for a single
cowling test nor more than 58° F. for all the tests.
Such variations will, according to unpublished test
results, cause temperature variations of 3°F. and 8° F.,
respectively. The oil temperature and pressure were
maintained relatively constant and the spark plugs
and mechanical condition of the engine were checked
at frequent intervals.
It is believed that the careful control of these vari¬
ables reduced the variation in results due to undesired
RESULTS
Table I is presented as a short resume of the results
for all the cowlings for a particular horsepower, engine
speed, and air speed. Column 1 gives the number of
the nose; column 2 gives the number of the skirt;
column 3 gives the number of the inner cowling. These
three numbers are used, in the same order, to designate
the complete cowling. Column 4 gives the measured
drag of the engine and nacelle at a dynamic pressure of
25.6 pounds per square foot. Column 5 gives the
propeller designation. Column 6 gives the pressure in
front of the cylinders divided by the dynamic pressure;
Rear
Front
453
COOLING TESTS OF A SINGLE-ROW RADIAL ENGINE WITH SEVERAL N. A. C. A. COWLINGS
a particular point on the cylinder and that of the inlet
cooling air. Column 12 gives the net thrust of the
engine-propeller-nacelle unit at a value of l/-v/P^ = 1.12
and a velocity of 100 miles per hour.
TABLE I
[100 m. p. h.; 425 i. hp.; 1,800 r. p. in.; 380 b. hp.]
1
2
3
4
5
6
7
S
9
10
11
12
Nose
Skirt
Inner cowling
SO d-
t- Cn xn
Propeller
<1 i ^
t/i
S— 1
.
-O **"'*
a,
<
Tempera¬
ture dif¬
ference
S 'I £d
w 9 -
s— *-< a;
.C — ' c 3 JR
-*-3 ' '
^ O ~ JD
%
C "p
C
A" °
Rear
(°F.)
1
1
1
152. 4
Off
1.00
-0. 252
1.252
32.0
1
1
1
A
0. 782
-. 508
1.290
32. 1
273
239
931
1
2
1
117. 1
Oil
. 990
-.091
1.081
27.7
1
2
1
A
. 770
-.083
.853
21. 1
293
279
963
1
3
1
100. 8
Oil
. 975
.091
.884
22.6
1
3
1
A
.849
. 227
.622
15.2
292
296
979
2
3
1
53.5
Off
.977
. 159
.818
21.3
2
3
1
A
.824
.271
. 553
13. 7
275
313
950
2
2
1
69.0
Off
.978
-.068
1. 046
26. 5
2
2
1
A
. 752
-. 114
.866
21.0
265
291
925
2
1
1
110.9
Off
. 972
-. 280
1.252
31.4
2
1
1
A
. 725
-.512
1.237
29. 7
265
267
897
3
1
1
no. 5
Off
.868
—.299
1. 167
29.8
3
1
1
A
.560
-.514
1.074
26.0
257
275
916
3
2
1
68. 0
Off
.903
-. 099
1.002
25. 7
3
2
1
A
.628
-. 137
. 765
18.8
286
309
942
3
3
1
55.2
Off
.920
. 141
.779
20.3
3
3
1
A
.671
. 186
.485
11.8
315
357
937
4
3
1
56.0
Off
.984
. 162
.822
21.4
4
3
1
A
.808
. 247
.561
13.7
304
320
947
4
1
1
111.0
Off
1.000
-.273
1. 273
32. 1
4
1
1
A
.852
-. 519
1.371
32. 9
274
268
875
3
1
2
121.5
Off
.913
-.268
1. 181
30.5
3
1
2
A
.628
-.464
1.092
26.8
266
274
906
2
1
2
119.0
Off
.955
-.284
1.239
32.0
2
1
2
A
.726
-. 491
1.217
29. 7
265
290
00
00
4-
1
1
2
150.0
Off
.949
-.288
1. 237
31.2
1
1
2
A
.808
-.480
1.288
32.3
266
241
916
4
1
2
119. 2
Off
.945
-. 281
1. 226
31.5
4
1
_ 2
A
.836
-. 481
1.317
33.2
263
260
870
4
0
2
73.0
Off
.950
-.042
.992
25. 5
4
2
2
A
.810
-. 042
.852
20.4
292
296
907
The dependence of the temperature upon the pressure
drop is quite apparent. It can also be seen that large
pressure drops are very costly in drag. It is evident
that, for cases of propeller on, the pressure in front of
the cylinder is decreased and that in the rear is exag¬
gerated; that is, a negative pressure behind the cylinder
with propeller off becomes more negative with propeller
on and a positive pressure becomes more positive. It
is well to remember that this effect of the slipstream is
of importance only in the low-speed range; it becomes
negligible under cruising conditions. Further, except
in a few arrangements using skirt 1, which lias a wide
opening, Ap/q is actually higher without the propeller
operating. Another point of interest is that the maxi¬
mum value of Ap/q is approximately 1.3 in spite of the
high power put into the slipstream.
The net thrust of the engine-propeller-nacelle unit as
given in column 12 shows that nose 1 gives the greatest
net thrust. It can be seen that this same nose gave
the highest drag with the propeller off (column 4).
This seemingly contradictory result is caused by the
critical flow over the leading edge of nose 1 and is con¬
sistent with the results of references 1 and 2. Atten¬
tion is called to the fact that nose 1 is again inferior in
the high-speed range (reference 1). This result brings
out the importance of testing cowlings at the operating
condition under which best operation is desired.
Table I introduces the type of result derived from
the tests. The plan of presentation of the results will
be to show by charts the interdependence of the various
quantities as the engine power, the air speed, etc., are
varied .
Figure 6 shows plots of /A p/n against V/nD for the
10-foot-diameter propeller used. Plots of this type con¬
veniently picture the relationship between the available
pressure, the air speed, and the propeller speed. These
results are not directly comparable with those presented
in reference 2. The present tests were made using a
controllable propeller, the blade-angle setting varying
throughout the range of V/nD; whereas the tests of
references 1 and 2 were made using an adjustable pro-
./
O
.2
K
ah/
0
.3
.2
./
O
1
/Vose
/
Cowling 4-3
-2
—
d
A7
?-/
3
4 -
'"3-5
-/
Skirt
3
—
—
Co
wiir
1-2
-/
<5
7-
4-2
-2
<*
3
-2-
■/
__ _
---
^ > —
2
-2-!
AA
-/ rf
2
Co
whr
lg '
4-1
-/
-X.
’’7
A
l-l
-/-
TL
-/-
/
_
--
---
3-i
Sk
irt
/
J .2 .3 .4 5 .6 .7 .8
V/nD
Figure 6.— Variation of the pressure constant -y Sp/n with \r/nD and cowling
arrangements.
peller, the setting remaining constant throughout the
range of V/nD. Figure 7 shows plots of A Ap,/n against
V/nD for the various arrangements, with a dashed line
showing the case of propeller off'. Such a line is known
to pass through the origin and to have a slope of aA p DJV
so that it can be precisely drawn. It is of interest
to show the little-realized fact that a propeller with a
large hub and a round blade section near the hub often
decreases instead of increasing the Ap obtained without
the propeller. One exception is noted, the arrangement
4-1-1, shown in figure 7 (d). Propellers with a good
airfoil section near the hub, such as propeller B in
figure 7 (d), give an increase in Ap.
Figure 8 shows the temperature difference plotted
against the indicated horsepower. The points deter¬
mining a given line are for a constant Ap. Tlie scatter¬
ing of the points can be explained by small variations
454
REPORT NO. 596— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
in Ap. The conditions under which the tests were run
are indicated. Although the range is not sufficient to
define the slope precisely, lines drawn with a slope of
0.37 are quite consistent with the data. This result is
all the more convincing when one considers that the
points are taken for several engine speeds. Further,
performance to be able to correct for variations in
horsepower. The determination of such a slope makes
this possible.
Cross plots (fig. 9) of the curves of figure 8, in which
the indicated horsepower is plotted against Ap for three
temperature differences, give three curves that show
V/nD
(a) Nose 1. (h) Nose 2. (e) Nose 3. (d) Nose 4.
Figvre 7 —Comparison of the available pressure drop for the conditions of propeller olY and propeller on.
this slope is of the same magnitude as that found by the limiting indicated horsepower permissible at various
Schey and Pinkel (reference 5) from flight tests on a values of A p. These curves show the advantage, with
Pratt & Whitney 1535 supercharged engine. It is limited power, of allowing as high a cylinder tempera-
recognized that this slope is a function of the baffling, ture as possible.
the cylinder finning, and the mechanism of cooling; The slope found in figure 8 is used in figure 10, m
consequently, it can be used only for the arrangement which the temperature difference divided by the inch-
tested. It is necessary, however, in studying cowling cated horsepower to the 0.37 power is plotted against
COOLING TESTS OF A SINGLE-ROW RADIAL ENGINE WITH SEVERAL N. A. C. A. COWLINGS 455
2A p. The value 2Ap is used instead of Ap for conven¬
ience in plotting. These curves show reasonable slopes
for the dependence of cooling on Ap. The slope may
vary from —0.4 to 0, —0.4 resulting from a completely
turbulent boundary layer on fins of narrow width.
The minimum slope will result when the cooling does
not depend upon the velocity flow. Intermediate
values of the slope correspond to longer fins (reference
6) and laminar flow in the boundary layer. Thus,
when part of the cooling is accomplished by other
means than a directed velocity flow' of air over the fins,
the slope will be less than was expected. This result
is particularly true of the front of the cylinder, where
there is no directed velocity. The only reason for the
Figure 12 show's the dependence of AT on Ap for
several positions on the cylinder at a constant horse¬
power. The results are shown for both the adjustable
and the controllable propellers. The temperatures in
the rear show the same dependence on Ap as in the
previous charts. The temperatures on the front show
a lack of dependence on A p that cannot be explained.
It has been showui, in the analysis of the problem,
y/ 2 KF(A')
that the powder required to cool is
^P
It has
been calculated for the tests of cowlings 2,3, and 4 and
is shown in figure 13 plotted against the temperature
difference. This chart serves to emphasize the w'ell-
known fact that a small reduction in temperature is
accomplished at a large expenditure of power to cool.
Cowling
Approxi¬
mate air
speed,
m. p. h.
Pressure
drop across
cylinder
Ap, lb./sq.
ft.
1-2-1
80
21.1
1-3-1
100
14.2
1-1-2
110
31.8
Figure 8.— The effect of indicated horsepower on the cylinder temperature difference. Fuel consumption, 0.57 pound per brake horsepower-hour.
existence of a slope is the fact that both turbulence and
Ap are functions of the air-stream velocity. It has been
shown (reference 1) that the cooling in the front of the
cylinder is accomplished by such large-scale turbulence.
The consistently lower slopes found for the thermo¬
couples on the front than on the rear of the cylinder in
this study confirm this result.
Figure 11 show's plots similar to those of figure 10 for
noses 2, 3, and 4. Here again it is noted that the
curves for the thermocouples on the front of the cylinder
have lower slopes. The wide scattering of the points
in some cases for the front thermocouples can possibly
be explained as follow's: Ap can be varied in two ways,
by varying the air-stream velocity and, as a result, the
turbulence, or by varying the skirt exit. When Ap is
simultaneously varied by both means, it is quite likely
to cause considerable scattering.
tooo
C
%600
0
§400
300
Ti
Jb
%200
I 150
IOO
/
>
—
-
— ?
AT - 350°
.. _ :
" 300° »
- */
"
25 C
r
:
0
00 30 50 too 20 30
A p, /b./sq. ft.
Figure 9.— The effect of Ap on the limiting horsepower at several constant tempera¬
ture differences. Average of thermocouples 1 to 9.
It becomes all the more striking wdien it is remembered
that large expenditures of powrer are, in general, made
at relatively low' efficiencies. If it is assumed that a rea-
REPORT NO. 596— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
sonable operating temperature involves a temperature
difference of 300° F., then it is evident (fig. 13) that
the cost in power to cool is from 1 to 1.5 percent of the
indicated horsepower.
As a rule, the heat dissipated is not directly discussed
in such an analysis. Measurements were made, how¬
ever, that allow a rough determination of the heat
dissipated both to the cooling air and to the oil cooler.
Figure 14 shows the amount of heat dissipated to the
cooling air for several arrangements, and figure 15
shows the amount dissipated to the oil cooler. The
percentage of the indicated horsepower dissipated
varies from 40 to 75. It will be noted that the per¬
centage of heat dissipated is relatively higher at lower
indica ted horsepower.
I 7 " 1
o Cowling 2-3- / + Cowling 3-2-1 v Cowling 2- !~2
a » 2-2-1 v » 4-3-1 ^ " 4-1-2
DISCUSSION
In the presentation of the results, considerable
emphasis has been placed on the fact that the tempera¬
tures on the front of the cylinder do not, in general,
COOLING TESTS OF A SINGLE-ROW RADIAL ENGINE WITH SEVERAL N. A. C. A. COWLINGS 45"
depend on Ap but upon large-scale turbulence. Such
emphasis is justified by the general misconception that,
if the required Ap is developed, the cooling problem
has been solved. It is, however, quite possible to
develop a desired Ap that will cool the baffled part of
the cylinder satisfactorily yet be so deficient in large-
scale turbulence on the front of the cylinder that little
500
400
300
200
. 150
U-4
G 100
<1
400
300
200
150
100.
1 - 1 ' 1 1 |
1
_ ^ / r> r-\ /o _ /I PP
e =
AI
-v
i
1
aI
1
(
<0
-
M
°
/-
-3
■ o
A
Ah.
0
o
.
/
o
0
S
£
V
o
47
K -
_
r
7
rr
_
Q) L
A
_
Cb
15
0
A J _
S/opt
D — —
O.c
39
A
_ O-
A
c
3
10-
Ask
1
“1
3 A
> C
i i i
diusti
yb
/e
b
;e
prop
_
e//er
1
ontrot/c
_
10 20 30 50 10 20 30
A p, Ib./sg. ft.
50
Figi’re 12.— The effect of A p on temperature difference with adjustable and control¬
lable propellers. Cowling 4-2-2; indicated horsepower, 430; specific fuel consump¬
tion, 0.57 pound per brake horsepower-hour; air speed, 80 to 110 miles per hour
approximately.
these tests for the baffled part of the cylinder. This
slope is somewhat lower than the value given in reference
1. This difference is probably due to the difference in
the location of the thermocouples in the two series of
Figure 14. — The effect of indicated horsepower on the percentage of heat carried
away by the cooling air for various cowling arrangements. Air speed, 100 miles per
hour; engine speed, 1,800 r. p m.
cooling results there. A suction fan behind the engine
would furnish just this type of cooling. A blower on
the front, connected to the propeller may, or may not,
develop the required turbulence for cooling. This
turbulence, which is so important in the cooling of the
unbaffled front of the cylinder and cylinder head, is of
no importance in the cooling of the baffled and rear
Figure 13— Horsepower required for cooling for various temperature differences at
several constant horsepowers. Xoses 2, 3, and 4; thermocouples 1 to 8.
parts of the cylinder. Here the only consideration is
the development of a value of Ap and, as a result, a
velocity flow over the surface of the fins, sufficient to
carry away the required amount of heat. The con¬
sistency of all the results for rear temperatures bear
out this statement. A slope of —0.22 in the plots of
AT
Ap against yj — is found consistently throughout
tests. In the former tests the thermocouples were
located at the rear of the barrel itself; in the present
series of tests the thermocouples were located on the
rear spark-plug boss. It is quite possible that there is
sufficient difference in the mechanism of cooling due to
\ Cow ling /- 2 - / j
Air speed 80 m.p.h.
Cowling i~2~ /
~ Air speed I ! O m.p.h.
~I Cowling U-3-7\
Am speed IOO m.p.h.
Cowling 4-1-1
Air speed IOO m.p.h.
340
Figure 15.
380 420 460 340 380 420 460 500
Observed indicated horsepower
-The effect of indicated horsepower on the percentage of heat carried away
by the oil for several cowling arrangements.
the finning near the spark-plug boss and the cylinder
barrel to account for the difference in slope. It is also
conceivable that the temperature of the spark-plug
boss is affected less by velocity than that of the fins
themselves. If this assumption is correct, the difference
is in the right direction.
458
REPORT NO. 596 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The effect of the propeller slipstream has also been
emphasized in the present report. The misconception
is often encountered that the propeller slipstream, re¬
gardless of the design of the propeller, increases the
Ap available for cooling. References 1 and 2 have
shown that, in general, this assumption is untenable.
On the contrary, the Ap at a particular slipstream con¬
traction is dependent on the blade-angle distribution,
especially near the hub. Moreover, it has been pointed
out that by designing for a large blowing action from
the blade sections near the hub, a considerable increase
in Ap can be realized. The large hub is not believed
to contribute directly to the lower Ap. Indirectly,
the difficulty encountered in designing a good airfoil
section near the axis of the propeller limits the available
blowing action.
No effect of engine speed on cooling could be found.
With a given indicated horsepower and Ap the engine
speed could be varied from 1,600 to 2,200 r. p. m.
without any measurable deviation in temperature. It
is obvious that, to the extent that Ap was changed,
there was a corresponding effect on the rear tempera¬
ture. It might be expected that the propeller would
superimpose some flow that would improve the cooling
on the front of the cylinder. No such effect could be
found.
The percentage of the indicated horsepower required
to cool varied from 1 to 1.5 and is based on the assump¬
tion that the Ap is developed at 100 percent efficiency.
Reference 1 shows that the efficiency varies with both
skirt shape and skirt opening. In the analysis of the
problem it has been shown that the useful power ex¬
pended in cooling is proportional to (A pY2. It follows,
then, that the values of 1 to 1.5 percent of the indi¬
cated horsepower apply to a particular Ap or to a
particular air speed alone. At higher air speeds, with
a given arrangement, a larger Ap will be developed
and a correspondingly higher power will be used.
The limiting indicated horsepower at various values
of Ap for three values of the temperature was found.
Both the percentage of indicated horsepower required
to cool and the limiting indicated horsepower, when
considered together, bring out clearly the expensiveness
of overcooling. The obvious recommendation is to
decrease the skirt exit and thus decrease the Ap at
high air speeds. It has been shown (reference l) that
by decreasing the skirt exit in the proper manner the
exit orifice or pump could be made to act more efficiently.
Thus the real cost of cooling will be lower than the
corresponding decrease in Ap would indicate. The
results presented here show that this engine, when
developing 500 horsepower, will cool so that the hottest
point (thermocouple 15) does not exceed 400° F. above
cooling-air temperature with a Ap of 25 pounds per
square foot. It has been shown (reference 1) that by
using closer baffling this value can be appreciably
reduced.
The amount of heat that must be dissipated to pro¬
vide adequate cooling was determined. The present
value, or any value, is useful only when all engine con¬
ditions, such as cylinder size, finning, baffling, tempera¬
ture distribution on the cylinder surface, compression
ratio, air-fuel ratio, and mechanical condition of the
engine are reproduced. The relative values of heat
dissipated at high and low values of the indicated horse¬
power are of the most importance. Comparatively,
the results should be usable.
CONCLUSIONS
Tests on an R-1340 SlHl-G Pratt & Whitney Wasp
engine with several cooling arrangements showed:
1. A pressure drop sufficient for cooling in climb under
full power can be developed.
2. The controllable propeller had no beneficial effect
on cooling and the adjustable propeller improved the
cooling only slightly.
3. Equally good cooling, for a particular pressure
drop, resulted from each of the cowlings tested. «
4. With a given baffling and finning on the cylinders,
the skirt is the controlling factor in cooling in climb.
Langley Memorial Aeronautical Laboratory7,
National Advisory Committee for Aeronautics,
Langley Field, Va., August 20, 1936.
REFERENCES
1. Theodorsen, Theodore, Brevoort, M. J., and Stickle, George
W.: Full-Scale Tests of N. A. C. A. Cowlings. T. R. No.
592, N. A. C. A., 1937.
2. Theodorsen, Theodore, Brevoort, M. .1., and Stickle, George
W.: Cooling of Airplane Engines at Low Air Speeds. T. R.
No. 593, N. A. C. A., 1937.
3. Weick, Fred E., and Wood, Donald LL: The Twenty-Foot
Propeller Research Tunnel of the National Advisory Com¬
mittee for Aeronautics. T. R. No. 300, N. A. C. A., 1928.
4. Gerrish, Harold C., and Voss, Fred: Mixture Distribution in
a Single-Row Radial Engine. T. N. No. 583, N. A. C. A.,
1936.
5. Schey, Oscar W., and Pinkel, Benjamin: Effect of Several
Factors on the Cooling of a Radial Engine in Flight. T. N.
No. 584, N. A. C. A., 1936.
6. Schey, Oscar W., and Ellerbrock, Herman H., Jr.: Perform¬
ance of Air-Cooled Engine Cylinders Using Blower Cool¬
ing. T. N. No. 572, N. A. C. A., 1936.
REPORT No. 597
AIR PROPELLERS IN YAW
By E. P. Lesley, George F. Worley, and Stanley Moy
SUMMARY
Tests oj a 8 -foot model propeller at jour pitch settings
and at 0°, 10°, 20°, and 30 0 yaw were made at Stanford
University. In addition to the usual propeller coeffi¬
cients, cross-wind and vertical forces and yawing, pitch¬
ing, and rolling moments were determined about axes
having their origin at the intersection oj the blade axis and
the axis of rotation.
The tests showed that the maximum efficiency was
reduced only slightly for angles of yaw up to 10° but that
at 30° yaw the loss in efficiency was about 10 percent.
In all cases the cross-wind force was found to be greater
than the cross-wind component of the axial thrust. With
a yawed propeller an appreciable thrust was found for
V/nD for zero thrust at zero yaw. Yawing a propeller
was found to induce a pitching moment that increased in
magnitude with yaw.
INTRODUCTION
Although airplanes are generally designed so that the
propeller axis lies approximately in the direction of
normal steady flight, the condition of yaw is found
during such maneuvers as curved flight and in flight at
high angle of attack. These maneuvers are usually of
short duration and, while the effect of yaw from these
causes may be, in specific cases, of interest, it is possibly
of no great consecpience. If, however, propellers are
to be yawed in the steady-flight condition, the effects
of yaw may be important. Such a condition would
arise in the case that a wing engine is placed, for struc¬
tural or other reasons, with its axis at an angle to the
longitudinal axis of the plane.
Air propellers in yaw have been the subject of both
theoretical and experimental investigation (references 1
to 5) but further information concerning the quanti¬
tative effect of small angles of yaw upon thrust, power,
cross-wind force, and efficiency seemed desirable and
therefore the present study was undertaken. While the
study was made with the propeller axis in the hori¬
zontal plane and the angle between the propeller axis
and the wind direction is thus called an angle of yaw,
the results may be applied as well to angles of pitch
since such body interference as was present would have
been the same in either case.
APPARATUS AND TESTS
Wind tunnel. — The experimental work was done in
the wind tunnel of the Daniel Guggenheim Aeronauti-
cal Laboratory of Stanford University. This tunnel
is of the open-throat type with a throat diameter of
7/2 feet. The maximum wind velocity is about 90 miles
per hour.
Dynamometer. — The propeller dynamometer con¬
sists essentially of a six-component balance. A driving
motor was rigidly suspended by a steel tube and pylon
of steel rods from a platform located above the wind
stream. The platform was completely restrained by
six electrically operated beam balances.
The general arrangement and appearance of the
dynamometer are shown in figures 1, 2, 3, and 4. In
459
460
REPORT NO. 597— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 2. — The propeller set-up shown in the yawed position.
carried the dead weight of the platform and suspended
motor. The lines labeled Cl, C2, and C6 (fig. 1) are
leads to counterweights used to give the necessary
initial loads on balances 1, 2, and 6.
The forward end-shield of the motor was elongated
so that tbe propeller was well ahead of any considerable
wind-stream obstruction. (See figs. 1, 2, and 3.) The
distance from the propeller to the center of the sup¬
porting tube was two-thirds the propeller diameter.
In figures 2 and 3 the motor is shown in the yawed
condition. The angle of yaw could be adjusted as
desired by a swivel joint provided in the supporting
tube.
The motor, and such parts of the suspension as were
in the wind stream, were shielded by a sheet-metal
cover. Thus only the forces acting on the propeller
were communicated to the platform and to the restrain-
Figure 3. — Upstream view of the propeller test set-up.
puted. For each pitch setting of the propeller, tests
were made at 0°, 10°, 20°, and 30° yaw.
As the model propeller driving motor was of the
constant-speed type (about 1,800 r. p. m.), variations
of the parameter VjnD were obtained by increasing
the wind velocity in suitable increments. The pro¬
peller tip speed therefore remained nearly constant at
about 280 feet per second. The Reynolds Number
figure 1, numbers 1 to 6 indicate the leads to the
restraining beam balances, the balances themselves
being similarly numbered in figure 4. As may be seen,
the A-frame or platform was restrained in the wind
direction by balances 1 and 2, in the vertical direction
by balances 3, 4, and 5, and in the cross-wind direction
by balance 6. In addition to these restraining or
measuring balances, there were three auxiliary beam
balances, designated by A in figures 1 and 4, that
ing balances. An electric bell gave warning of contact
between the motor or its supports and the metal cover.
Propeller. — The propeller used in this investigation
was a 3-foot metal right-hand adjustable propeller. It
is designated propeller xl in reference 6. It has a uni¬
form geometric pitch and a pitch-diameter ratio of 0.7
when the blade angle at 0.75 radius is 16.6°. Four
pitch settings were used: 16.6° (uniform pitch), 20.6°,
24.6°, and 28.6°; all pitch settings were measured at
the 0.7 oR station.
TESTS
Measurements were made of six components of the
air force acting on the propeller, three vertical, two in
the wind direction, and one in the cross-wind direction.
From these components and the arms of the restrain¬
ing balances, the rolling, pitching, yawing, and torque
moments about axes having their origin at the inter-
| section of the propeller axis and blade axis, were com-
AIR PROPELLERS IN YAW
461
Figure 4. — View of the electrical balancing units.
was about 0.1 full scale, assuming the full-scale pro¬
peller to be 10 feet in diameter operating at a tip speed
of 800 feet per second.
The observed thrust and power are reduced to the
usual coefficients
C
T
T
pn2D 4
Cp pnUP
_TXV_Ct v V
n~ ~P~ ~CpnD
n _ * I pV5 _ V"sl±
s"\ Pn2~nD\ CP
where
T, thrust of the propeller measured parallel to the
axis of the tunnel.
P, motor power.
p, mass density of the air.
n, revolutions per unit time.
D, propeller diameter.
V, velocity.
The vertical and cross-wind forces are reduced to
coefficients similar to the thrust coefficient,
F,
pn2DA
Cf —
cv.
pn'Ir
v\ nere
F., vertical force.
Fy, cross-wind force.
The moments about the three axes are reduced to
coefficients similar in form to the propeller torque
coefficient,
Q
pn2D 5
CQ=
rt _ _ L _
Ll pri2Db
C --
m
a =
M
pn2D 5
N
pn2D 5
where
Q. propeller torque.
L, rolling moment.
M, pitching moment
N, yawing moment.
REPORT NO. 597— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
RESULTS AND DISCUSSION
In table I are given the computed values of propeller,
force, and moment coefficients for different values of
V/nD.
In figure 5 the results of a test with the yaw dyna¬
mometer are compared with two earlier tests of the
same propeller made in the same wind-tunnel using the
Stanford University propeller dynamometer. The
tests by Lesley and Reid are reported in reference 6;
the tests by Babberger were made in connection with a
study of the scale effect on air propellers submitted as
a thesis at Stanford University in 1934. The agree¬
ment with Babberger ’s test at 2,000 r. p. m. is excellent,
but the thrust and power coefficients derived from the
yaw^dynamometer test are consistently lower than
those observed by Lesley and Reid. The angular
Figure o.-~ Comparison of data from different tests of the same propeller in the same
wind tunnel. Propeller set 16.6° at 0.75.R; 0° yaw
velocity in the latter test, however, was about 3,000
r. p. m. and Babberger found that, with this propeller,
the thrust and power coefficients increased slightly
with angular velocity. Substantial agreement with
Babberger’s test at 2,000 r. p. m. is regarded as evidence
of the accuracy of the yaw dynamometer.
Propeller, vertical-force, and cross-wind-force coeffi¬
cients are given graphically as functions of V/nD in
figures G to 21. In figures 22 to 25 efficiency r? and
V/nD are given as functions of the speed-power ceoffi-
cient Cs. The maximum efficiency and V/nD at zero
thrust are plotted in figure 26 against the secant of the
angle of yaw T. Figure 27 shows the ratio of cross-wind
force to thrust for different values of V/nD. In
figure 28 this ratio is plotted against the ratio of
V/nD to V/nD at zero thrust. Pitching-moment
coefficients are given as functions of V/nD in figure 29;
yawing-moment, rolling-moment, and torque coeffi¬
cients are plotted in figures 30, 31, and 32, respectively.
The power coefficient (figs. 6 to 21) is little affected
by yaw at low velocities of advance, i. e., at small
values of V/nD. At larger values of V/nD the power
coefficient increases with each increment of yaw.
The thrust coefficient is decreased by yawing the
propeller at low V/nD. This result is to be expected
since at ^ = 0 the axial thrust would be independent
of yaw, and the thrust in the wind direction would
be the axial thrust multiplied by the cosine of the
angle of yaw. At the larger values of V/nD the thrust
coefficient is increased by yaw and the value of V/nD
for zero thrust is also increased.
Over the normal working range of a propeller there
is thus a decrease in efficiency with yaw, although at
the larger values of V/nD, greater than those for maxi¬
mum efficiency, the efficiency is increased by yaw.
The manner in which efficiency varies with yaw in
the normal working range is seen to advantage in
figures 22 to 25 in which efficiency is plotted against
the speed-power coefficient Cs.
In figure 2G the maximum efficiency for each blade-
angle setting is plotted against sec \p. The resulting
parallel straight lines may be expressed by the equation
n max— 11 max 0 G-6 (sec x]/ 1)
where rjmax0 is the maximum efficiency at zero yaw.
In figure 2G the V/nD for zero thrust is also plotted
against sec \p. As with rjmax it is seen that V/nD for
zero thrust varies, over the range investigated, directly
with sec i p.
The vertical force coefficient of a propeller in yaw
is negligible (it does, however, show an increase with
yaw). Although in the graphical representation of
figures G to 21 this coefficient, as well as the cross-wind
force coefficient for zero yaw, appears to have consid¬
erable magnitude, it should be noted that the scale to
which it is plotted is ten times that used for the thrust
coefficient.
The vertical force coefficient, while generally positive,
appears in some instances to be negative at low V/nD
and to change in sign as higher values of V/nD are
reached. It is obvious that, assuming symmetrical
flow, the direction of the vertical force would depend
on the relation between the direction of propeller ro¬
tation and direction of yaw. In these tests the pro¬
peller rotation was clockwise when looking upwind and
the yaw' was positive. Had either been reversed it
seems evident that, with symmetrical flow, the sign of
the vertical force coefficient would have likewise been
changed.
As would be expected, the cross-wind force coefficient
shows a marked increase with vaw . The ratio of cross-
wind force to thrust is shown for the 28.6° propeller as
a function of V/nD in figure 27.
F V
The curves are drawn from points -Uf=tan^ at ^=0.
It is seen that at all values of V/nD greater than zero.
FVJT is greater than tan \p or that the resultant liori-
V
zontal force is, except for --^=0, inclined to the wind
direction at an angle greater than the angle of yaw.
AIR PROPELLERS IN YAW
463
The ratio of cross-wind force to thrust as a function
shown for all propellers in figure 28. It is seen that
FJT increases with propeller pitch setting as well as
with yaw.
It may be seen from these results that a propeller
with its axis in pitch would develop thrust if operating
at V/nD of zero thrust for axis parallel to direction of
motion. The thrust under this condition may he of
such magnitude that it should be considered in deriving
airplane polars from glide tests with propeller running.
For example, in glide tests of a VE-7 airplane (see
reference 7), the drag coefficient at 15.1° angle of attack
was found to be 0.143. From the present tests of pro¬
pellers in yaw it appears that the thrust exerted by the
propeller in the glide test may have been double the
amount credited to it and the drag coefficient thus have
been 0.148.
Further, in the derivation of the drag of the VE-7
airplane in the power flight tests of reference 7, a
quantity T sin B was credited to the propeller as a
liftwise force; B is the inclination of the propeller shaft
to the wind direction. The present tests show that
the credited amount should have been greater.
It may also be seen that the difference between power
and thrust coefficients of propellers in the flight and
wind-tunnel model tests of reference 7 is qualitatively
accounted for by the fact that in flight the propeller
axis was at an angle of pitch, while in the wind-tunnel
model it was parallel to the wind stream.
The lift developed by a propeller with its axis in
pitch is sufficient to account, in considerable degree,
for the high lift coefficients apparently developed by an
airplane at large angle of attack, power on. Millikan,
Russell, and McCoy show (reference 8) an increase in
lift coefficient of about 0.2 with power on at 20° angle of
attack. Interpolating from these tests in yaw and
allowing for the three-blade propeller used by Millikan,
Russell, and McCoy, it appears that the liftwise force
exerted by the propeller was sufficient to account for
more than half of the increase in lift coefficient found.
Pitching-moment coefficients for the propellers in
yaw arc shown in figure 29 as functions of V/nD.
Under the conditions of these tests, the sign of the
coefficient depends upon V/nD. It is generally posi¬
tive at large V/nD and negative at small V/nD. Like
the sign of the vertical force coefficient, it is obvious
that, assuming symmetrical flow, the sign of the pitch¬
ing-moment coefficient would also depend upon the
relation between the direction of rotation and direc¬
tion of yaw; a reversal of either would result in reversing
the sign of the pitching moment. Since the vertical
force is small compared with thrust, a positive pitching
moment shows a location of the line of action of thrust
below the Y axis and a negative pitching moment a
location above the Y axis.
Some verification of the observed change in sign of
pitching moment with V/nD may be derived through
analysis by simple blade-element theory. For ex¬
ample, it can be shown that for the 24.6° propeller in a
vertical position and at 30° yaw, the pitching moments
of the 0.75 radius elements are proportional 81 and
— 14 at V/nD 1.2 and 0.3, respectively. The ratio of
these calculated moments is —5.8. The test of this
propeller at 30° yaw shows a pitching-moment coeffici¬
ent of 0.0066 at V/nD =1.2 and —0.0018 at V/nD=0.S.
The ratio of pitching moments in the two cases is thus,
for the whole propeller, —3.7.
It is possible that a part of the indicated pitching
moment is due to a slight wind-stream asymmetry.
Wind-stream surveys, however, revealed not more
than 1}{ percent variation of velocity from the mean at
the propeller disk, which appears insufficient to account
for any considerable proportion of the pitching moment
found. It will be noticed that there are insufficient
observations to determine definitely the form of the
pitching-moment curve in the low V/nD range. As
this portion of the curve is of little practical impor¬
tance, rather arbitrary functions have been drawn that
become zero, as they should, at zero V/nD. It seems
unlikely that, in the operating range, the magnitude
of the pitching moment will be sufficient to affect
greatly the stability characteristics of an airplane.
The yawing-moment coefficients, shown for the 16.8°
and 28.6° propellers in figure 30, increase slightly
with yaw. Even for the 30° yaw tests, however, the
magnitude of the yawing moment about the axis
chosen is extremely small.
Figures 31 and 32, showing the torque and rolling-
moment coefficients for the 28.6° propeller, are of
interest because it may be seen that the rolling moment
increases more rapidly with yaw than the propeller
torque. Although this result is illustrated for only
one propeller, computations for the others show
| similar relations.
REPORT NO. 5 9 7 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
464
nD
Figure 8. — Characteristics of a propeller set 16.6° at 0.75 R; 20° yaw.
- - - - - - - j _
O .2 .4 .6 .8 1.0 I.Z
V
nD
Figure 9.— Characteristics of a propeller set 1G.6° at 0.75 R; 30° yaw.
AIR PROPELLERS IN YAW
465
nD
Figure 10.— Characteristics of a propeller set 20.6° at 0.75/?; 0° yaw.
nD
Figure 12. Characteristics of a propeller set 20.0° at 0.75/?; 20° yaw.
Figure 11.— Characteristics of a propeller set 20.6° at 0.75/?; 10° yaw.
0 .2 -4 .6 .8 1.0 1.2
V
nD
Figure 13.— Characteristics of a propeller set 20.6° at 0.75/?; 30° yaw.
466
REPORT NO. 597— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
7 iD
Figure 14. — Characteristics of a propeller set 24.6° at 0.752?; 0° yaw.
tiD
Figure 16.— Characteristics of a propeller set 24.6° at 0.75 R; 20° yaw.
nD
Figure 15.— Characteristics of a propeller set 24.6° at 0.75/?; 10° yaw.
IZ _ _ _ _ _ J _ L_ _ _ _ _ i _ ; _ L
O .2 A .6 .8 LO L2
V
nD
Figure 17.— Characteristics of a propeller set 24.6° at 0.75 R; 30° yaw.
AIR PROPELLERS IN YAW
467
Figure 18.— Characteristics of a propeller set 28.6° at 0.7 5R; 0° yaw
n!)
Figure 20— Characteristics of a propeller set 28.6° at 0.75 R; 20° yaw.
0 .2 .4 .6 .8 1.0 1.2
V
n D
Figure 19.— Characteristics of a propeller set 28.6° at 0.757?; 10° yaw.
0 .2 .4 .6 .8 LO 1.2
V
nD
Figure 21.— Characteristics of a propeller set 28.6° at 0.75 R; 30 °yaw.
468
REPORT NO. 597— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
C- _ _ I _ _ _ _ _ _ I _ I _ I _ _ I _
0 .4 .8 /2 16 2.0 2.4
Cs
Figure 22. — Variation of efficiency and VjnD with speed-power coefficient for a
propeller set 16.6° at 0.75 R and yawed different amounts.
Figure 24. Variation of efficiency and VjnD with speed-power coefficient for a
propeller set 24.6° at 0.757? and yawed different amounts.
Figure 23.— Variation of efficiency and VjnD with speed-power coefficient for
propeller set 20.6° at 0.75/? and yawed different amounts.
Figure 25. — Variation of efficiency and VjnD with speed-power coefficient for
a propeller set 28.6° at 0.75 Ii and yawed different amounts.
AIR PROPELLERS IN YAW
LOO 1.04 L08 1.12 U 6 1.20
Sec t
Figure 20.— Variation of V/nD at zero thrust and maximum efficiency with sec. \p
for propellers of four different pitch settings at 0.757?.
nl)
Figure 27. — Variation of the ratio of the cross-wind force to the thrust with V/nD
for a propeller set 28.6° at 0.757?.
O .2 .4 .6 9 LO 1.2
V/nD
(V/nD) o
Figure 28. — Variation of the ratio of the cross-wind force to thrust with the ratio of
V/nD to (V/nD)o for four pitch settings and three angles of yaw.
470
REPORT NO. 597— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 30. — Variation of yawing-moment coefficient with V/nD for two pitch set-
ings and four angles of yaw .
V
jiD
Figure 31. — Variation of rolling-moment coefficient with V/nD for a propeller set
28.6° at 0.75R for four angles of yaw.
V
nD
O .2 .4 .6 3 1.0 1.2
Figure 32. — Vaiiation of torque coefficient with V/nD for a propeller set 28.6° at 0.75R for four angles of yaw.
AIR PROPELLERS IN YAW
471
CONCLUSIONS
The results of these experiments showed that:
1. Over the normal working range of the propeller,
there was a decrease in thrust, an increase in power
absorbed, and a decrease in efficiency with yaw. Up
to 10° of yaw, the loss in maximum efficiency was not
more than 2 percent, but at 30° yaw it became about 10
percent.
2. The cross-wind force was greater than the cross-
wind component of the axial thrust. This result indi¬
cates that the corresponding lift due to a propeller with
its axis in pitch accounts for a larger proportion of the
increase of lift coefficients apparent in airplanes at high
angles of attack, power on, than would be estimated
from the vertical component of the axial thrust.
3. With the yawed propeller, there was an appreciable
thrust at V/nD for zero thrust at zero yaw. Conse¬
quently, airplane glide tests made with the propeller
idling at a V/nD for zero thrust at zero yaw should be
corrected for the thrust due to the yawed propeller.
4. Yawing the propeller induced a pitching moment
that increased in magnitude with yaw.
Daniel Guggenheim Aeronautical Laboratory,
Stanford University, California, October, 1936.
REFERENCES
1. Clark, T. W. K.: Effect of Side Wind on a Propeller. R. &
M. No. 80, British A. C. A., 1913.
2. Bramwell, F. H., Fage, A., Relf, E. F., and Bryant, L. W.:
Experiments on Model Propellers at the National Physical
Laboratory. R. & M. No. 123, British A. C. A., 1914.
3. Harris, R. G.: Forces on a Propeller Due to Sideslip. R. &
M. No. 427, British A. C. A., 1918.
4. Flachsbart, O., and Krober, G.: Experimental Investigation
of Aircraft Propellers Exposed to Oblique Air Currents.
T. M. No. 562, N. A. C. A., 1930.
5. Freeman, Hugh B.: The effect of Small Angles of Yaw and
Pitch on the Characteristics of Airplane Propellers. T. R.
No. 389, N. A. C. A., 1931.
6. Lesley, E. P., and Reid, Elliott G.: Tests of Five Metal
Model Propellers with Various Pitch Distributions in a
Free Wind Stream and in Combination with a Model
VE-7 Fuselage. T. R. No. 326, N. A. C. A., 1929.
7. Durand, W. F., and Lesley, E. P.: Comparison of Tests on
Air Propellers in Flight with Wind Tunnel Model Tests
on Similar Forms. T. R. No. 220, N. A. C. A., 1926.
8. Millikan, C. B., Russell, J. S., and McCoy, H. M.: Wind
Tunnel Tests on a High Wing Monoplane with Running
Propeller. Parts 1 and 2, Jour. Aero. Sciences, vol. 3, no. 3,
Jan. 1936, pp. 73-85.
TABLE I
COMPUTED VALUES OF COEFFICIENTS FOR DIF¬
FERENT PITCH SETTINGS AND VARIOUS ANGLES
OF YAW
Cp
Ct
V
C F y
Cfz
Cm
16.6° PITCH SETTING, 0° YAW
0. 124
0. 0402
0. 0873
0.269
-0. 00030
-0. 00030
0. 00047
-0. 00055
.254
. 0389
.0804
. 525
-. 00018
-. 00061
. 00067
-. 00061
.335
.0387
.0731
.633
-. 00012
-. 00049
. 00077
-. 00009
.419
. 0369
.0650
.738
— . 00006
-.00043
. 00004
-. 1X1049
. 484
. 0361
. 0573
. 768
-. 00006
-. 00079
-. 00005
-. 00045
.54(5
. 0331
.0489
.807
0
-. 00079
-. 00055
-. 00026
.592
.0310
. 0437
.834
0
-.00061
-. 00077
-. 00022
.648
. 0283
. 0349
.800
0
-. 00030
-. 00016
-. 00035
.703
. 0244
. 0274
. 790
0
-.00061
-. 00037
-. 00026
. 743
.0200
.0196
.728
. 00006
-. 00024
. 00004
-. 00035
.786
. 0153
.0110
.565
. 00006
-. 00030
. 00020
-. 00018
. 822
.0090
.0036
.329
. 00006
. 00006
. 00089
-. 00006
16. 6°
PITCH SETTING, 10°
YAW
0.081
0. 0382
0. 0884
0. 187
0. 0155
-0. 00024
-0. 00023
-0. 00030
. 203
. 0385
. 0828
.437
. 0150
-. 00024
-. 00004
-. 00020
.297
. 0387
. 0760
.583
. 0140
-. 00030
. 00026
-. 00008
.381
. 0376
. 0679
.688
.0130
-. 00018
.00012
. 00006
.441
.0371
. 0619
. 736
. 0121
-. 00006
. 00012
. 00008
.501
.0349
. 0549
.788
. 0112
-. 00018
. 00007
-. 00006
.551
. 0330
. 0487
.813
. 0103
-. 00024
. 00036
. 00010
.602
. 0319
. 0434
.819
. 0097
-. 00048
-. 00040
. 00008
.656
0276
. 0342
.813
.0084
-. 00036
. 00010
. 00032
.700
. C247
. 0276
. 782
. 0076
-. 001X19
. 00030
. 00040
. 736
.0217
. 0216
.733
. 0068
. 00006
. 00032
. 00050
.773
. 0169
. 0149
. 682
.0061
. 00042
.00111
. 00054
.840
.0098
.0014
. 120
. 0044
.00120
. 00148
. 00078
16. 6°
PITCH SETTING, 20°
YAW
0. 075
0. 0411
0. 0841
0. 154
0. 0308
0. 00012
-0. 00200
0. 00023
.224
.0398
.0784
.441
. 0300
-.00012
-. 00037
.00012
.283
. 0395
. 0758
.543
.0291
. 00012
. 00022
. 00026
.381
. 0393
.0682
.661
. 0273
. 00025
. 00067
. 00047
. 460
.0389
.0599
.708
.0248
-.00012
. 00021
. 00053
. 506
.0376
. 0549
.739
. 0234
-. 00006
. 00059
. 00057
.558
. 0357
.0491
.768
.0218
.00018
. 00071
. 00057
. 613
.0334
.0428
. 786
. 0200
. 00037
. 00098
. 00069
.674
. 0304
.0349
.774
.0179
. 00073
.00128
. 00083
.716
. 0279
. 0291
.747
.0164
. 00079
.00151
. 00106
.744
.0252
. 0247
. 730
. 0154
. 00067
. 00220
. 00108
.780
.0228
.0190
.650
.0139
. 00116
.00194
.00124
.820
.0178
. 0122
.562
.0122
. 00207
. 00290
.00136
.854
.0147
. 0067
. 390
. 0109
.00195
. 00307
.00140
.883
.0115
.0017
. 130
. 0096
. 00225
. 00332
. 00146
16. 6°
PITCH SETTING, 30°
YAW
0. 095
0. 0394
0. 0760
0. 183
0. 0448
-0. 00080
-0. 00190
-0. 00021
.255
. 0403
.0704
. 446
.0434
-. 00099
-.00113
. 00035
.350
.0396
.0651
.576
.0413
-. 00093
-.00029
. 00056
.419 !
.0393
. 0593
. 632
. 0388
-. 00037
-.00031
. 00070
.484 I
.0391
. 0545
.675
.0367
-.00012
-. 00012
. 00088
. .536
. 0376
.0496
.707
. 0345
. 00025
. 00037
. 00111
. 603
. 0367
. 0434
.713
. 0320
. 00043
. 00072
.00111
. 654
. 0345
. 0381
.722
.0298
. 00056
. 00109
.00117
.703
.0318
. 0325
.718
. 0276
. 00093
.00148
.00136
. 751
. 0291
. 0272
.702
. 0255
.00112
. 00206
.00159
. 792
. 0254
.0217
.677
. 0235
.00143
. 00256
. 00155
.834
. 0227
. 0160
.588
.0211
. 00173
. 00306
.00175
.882
.0201
.0100
. 439
. 0188
. 00242
. 00370
.00192
. 930
. 0150
.0034
. 211
.0162
. 00247
. 00415
.00185
20.6° PITCH SETTING, 0° YAW
V
ill)
Cp
Ct
V
CFy
Cfi
Cm
0. 124
0. 0639
0. 0884
0. 172
-0. 00018
-0. 00073
0. 00077
.270
. 0561
.0907
. 437
-.01X124
. 00440
. 00026
.359
.0535
.0890
.597
-.00024
-. 01X191
. 00018
. 441
. 0534
. 0833
.688
-.00018
-.1X1116
-. 00034
.509
. 0515
.0762
.753
-.00012
-. 00055
.00034
. 563
.0507
.0697
.774
-. 00012
-.00067
. 00022
. 634
. 0483
.0612
.804
-.00012
-. 00067
. 00033
.739
.0425
. 0483
.839
-. 00018
-. 00061
-. 00002
. 785
. 0398
.0427
.842
-. 00018
-. 00043
. 00014
.836
.0349
.0350
.838
-.00012
-. 00049
-. 00020
.874
. 0309
.0291
.823
-. 00006
-.00018
-. 00004
.920
.0258
.0210
. 749
0
-.00030
-. 00024
.963
. 0194
.0124
.616
.00012
-.00042
-. 00028
1.001
.0130
. 0049
.377
. 00024
-.00006
. 00007
1.015
.0105
.0013
. 126
. 00024
. 00030
. 00033
38548—38 - 31
472
REPORT NO. 597— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I — Continued
V'
nD
Cp 1
Ct
V
C Fy
cv.
Cm
20.6° PITCH SETTING, 10° YAW
0.081
0. 0632
0. 0883
0. 113
0. 0155
-0. 00095
-0.00174
.230
.0568
.0885
.358
.0164
-. 00066
-.00120
.294
. 0520
.0901
.504
.0170
-.00090
-. 00072
. 380
. 0528
. 0855
. 025
.0164
-. 00084
-. 00054
.440
.0528
.0818
.682
.0100
-.00126
-. 00092
..507
. 0507
.0747
. 747
.0150
-. 00102
-. 00072
. 553
. 0504
. 0094
.702
. 0144
-. 00078
-. 00050
. 590
. 0489
. 0646
.787
.0138
-.00055
.00002
. 002
. 0460
.0568
.817
.0128
-. 00048
-. 01X124
.708
. 0440
.0516
.819
.0122
-. 00036
-. 00030
.777
. 0392
. 0426
.844
.0112
-.00042
-.00002
.842
. 0344
. 0330
.808
.0101
-.00006
-. 00002
.900
.0270
. 0226
. 758
. 0091
. 00024
. 00043
. 938
. 0245
.0162
. 620
. 0085
-.00018
. 00050
. 990
.0150
. 0002
. 409
. 0078
. 00060
.00116
1.028
.0107
.0002
.019
.0068
. 00090
.00128
20.6° PITCH SETTING, 20° YAW
0. 088
0. 0017
0. 0854
0. 122
0. 0317
0. 00049
-0. 00206
.241
. 0529
.0857
.390
.0337
.00109
0
.342
. 0519
. 0849
. 560
.0339
. 00054
-. 00008
. 435
.0518
.0789
.662
.0325
. 00037
.00018
.507
. 0522
. 0735
.714
.0312
. 00092
. 00071
.623
. 0492
. 0010
.772
.0279
. 00080
. 00073
. 682
.0471
.0543
. 786
. 0262
. 00080
. 00092
.738
. 0444
. 0485
.806
.0248
. 00128
.00141
.786 .
.0416
. 0427
.806
.0235
.00147
. 00153
.841
. 0386
.0358
.780
. 0226
. 00159
. 00185
.880
.0337
.0299
.780
.0210
.00159
. 00235
. 925
. 0299
.0234
.724
.0197
.00184
. 00287
.967
. 0248
.0101
. 628
.0182
. 00197
. 00360
1.000
.0198
.0101
.510
. 0169
. 00249
. 00455
1.058
.0131
.0018
. 146
.0147
. 00276
. 00469
20.6° PITCH SETTING, 30c
YAW
0. 107
0. 0642
0. 0772
0. 129
0. 0460
-0. 00143
-0. 00376
.267
.0562
.0788
.374
. 0493
-. 00081
-. 00085
.358
.0539
.0772
.513
.0495
.00018
-. 00072
. 454
. 0533
.0718
.612
. 0478
-.00018
. 00003
. 540
.0525
. 0654
.673
.0454
.00031
. 00066
.018
.0516
. 0592
.709
.0432
. 00067
. 00085
.088
.0502
.0536
.735
.0417
. C0050
. 00144
.765
. 0409
.0400
.750
.0384
.00112
.00188
.831
. 0434
. 0385
.738
. 0359
.00174
. 00251
.892
. 0378
.0314
.741
.0335
.00169
. 00338
.944
. 0352
. 0253
.678
. 0316
. 00237
. 00379
. 998
.0297
.0183
.615
. 0293
. 00299
. 00505
1. 044
. 0270
.0127
.491
. 0275
.00314
. 00504
1.090
. 0231
. 0070
.332
.0257
. 00329
. 00594
1. 147
.0182
. 0006
.038
.0232
. 00365
. 00632
24.6° PITCH SETTING, 0°
YAW
0. 143
0. 0757
0. 0996
0. 188
-0. 00031
-0. 00063
0. 00032
. 210
.0780
. 0909
. 287
-. 00025
-. 00044
. 00050
. 444
. 0730
. 0945
. 575
-. 00024
-. 0009 i
. 00004
. 552
. 0704
.0901
. 700
-. 00018
-. 00098
-. 00020
. 660
.0685
.0784
.702
-. 00025
-. 00086
-. 00012
.743
. 0648
. 0693
.794
-. 00024
-. 00116
-. 00004
.811
.0618
.0615
• .807
-.00031
-. 00008
-.01X118
.867
. 0572
. 0548
.830
-. 00025
-. 00068
-. 00034
.918
. 0530
.0482
.835
-. 00012
-. 00049
-.00012
. 904
.0490
. 0422
.830
-.00006
— . 00055
-. 00038
1. 012
. 0424
. 0357
.852
. 00018
-. 00043
-. 00048
1. 050
. 0386
. 0292
. 795
. 00006
-. 00061
-. 00090
1. 092
. 0328
.0220
.752
. 00012
-. 00055
-. 00070
1. 131
. 0207
. 0153
.648
. 00018
-. 00074
-. 00070
1. 101
. 0200
.0084
.488
. 00024
-.00012
-. 00015
1. 202
.0118
. 0006
.001
. 00018
-. 00085
-.00034
24.6° PITCH SETTING, 10
3 YAW
0. 099
0. 0762
0. 0982
0. 128
0. 0175
-0. 00043
-0. 00067
.312
. 0750
. 0881
. 364
.0172
-. 00018
-. 00033
.449
. 0083
. 0940
. 622
.0189
-. 00000
. 00040
.551
. 0686
.0878
. 706
. 0181
-. 00030
.00045
. 664
. 0605
. 0764
. 763
. 0168
0
. 00082
.744
.0637
. 0683
. 798
. 0159
. 00037
. 00090
.815
. 0603
. 0597
.807
.0150
. 00068
. 00104
.807
. 0564
. 0534
.821
.0145
. 00074
. 00096
.918
. 0530
. 0174
.821
.0139
. 00074
. 00097
.970
.0470
.0104
.834
.0134
. 00105
.00145
1. 014
.0429
. 0339
.801
.0128
. 00123
. 00176
1.046
. 0.388
.0286
. 772
.0124
. 00129
. 0021 1
1.093
. 0336
.0214
. 690
.0119
. 00128
. 00208
1. 127
. 0288
. 0149
.583
.0114
. 00135
. 00256
1. 162
. 0200
. 0073
.412
. 0109
.00188
.00311
1. 202
1 .0152
.0006
.017
.0102
. 00207
. 00363
TABLE I— Continued
Cp
Ct
V
CFy
Cfi
24.6° PITCH SETTING, 20° YAW
0.094
0. 0740
0. 0950
0. 121
0. 0354
-0. 00068
-0. 00320
.286
.0741
.0885
.342
.0356
-. 00074
-. 00222
.381
.0734
.0875
.454
.0358
. 00043
-. 00057
.466
.0682
. 0891
. 609
.0377
-. 00006
-. 00002
.562
. 0682
. 0830
. 684
. 0365
-.00031
0001S
.047
.0670
. 0765
.738
.0352
. 00000
. 00053
.717
.0658
. 0699
.762
.0339
. 00031
. 00064
.771
.0632
.0644
.786
.0328
. 00068
.00112
.821
.0610
. 0592
.797
. 0316
. 00O93
. 00132
.874
.0585
. 0538
.804
. 0306
.00118
.00157
.922
. 0553
. 0482
.804
. 0295
. 00149
. 00226
.971
. 0509
.0418
. 798
. 0285
. 00143
. 00232
1.014
.0456
. 0359
. 798
. 0276
.00198
. 00328
1. 055
.0414
. 0295
. 752
. 0272
.00191
. 00387
1.098
. 0374
. 0238
.699
.0257
. 00254
. 00458
1. 141
.0319
.0181
. 648
. 0250
. 00254
. 00487
1. 175
. 0204
.0124
. 552
. 0239
. 00252
. 00534
1. 258
.0146
. 0004
.031
.0215
. 00258
. 00632
24.6° PITCH SETTING, 30° YAW
0. 117
0. 0742
0. 0868
0. 137
0. 0516
-0. 00019
-0. 00507
.343
.0724
.0808
.383
. 0527
. 00099
-. 00208
.458
.0713
. 0793
. 509
.0542
.00130
00087
. 567
. 0078
. 0770
. 649
. 0546
. 00025
. 00010
.674
.0672
.0703
. 705
. 0529
.00012
. 00097
.757
. 0669
. 0637
.721
.0510
. 00050
. 00130
.828
. 0638
. 0576
. 748
.0491
. 00093
. 00202
.883
.0614
.0522
. 751
.0478
. 00099
. 00249
. 937
. 0604
.0474
. 735
. 0466
. 00093
. 00243
.981
. 0561
.0427
. 747
. 0454
.00193
. 00386
1.028
. 0534
.0376
.724
.0441
.00212
. 00437
1.070
.0501
. 0326
. 696
. 0429
. 00255
. 00482
1. 115
. 0462
.0278
. 671
.0418
. 00256
. 00534
1.153
.0438
. 0235
.618
. 0407
.00301
. 00504
1. 189
.0408
. 0194
. 565
. 0397
. 00273
. 00650
1.229
. 0362
.0147
. 499
. 0384
. 00328
. 00722
1.269
. 0331
. 0105
.402
. 0372
. 00272
. 00750
1.315
.0289
.0056
.255
.0360
. 00340
. 00826
28.6° PITCH SETTING, 0° YAW
V
nD
Cp
Ct
V
Cl Fy
Cfz
Cm
C\
Ci and Cq
0. 229
0. 1002
0. 1006
0. 230
-0. 00032
-0. 00044
0. 00090
-0. 00046
-0. 0160
.369
. 0944
.0965
.377
-.00025
-. 00044
. 00055
-.00048
-. 0150
. 560
.0908
. 0952
.587
-. 00019
-. 00051
. 00068
—.00056
-.0145
.643
. 0894
. 0975
. 702
-. 00025
-. 00089
. 00055
-. 00054
-. 0142
.728
.0883
. 0909
. 750
-. 00025
-. 00064
. 00053
-. 00052
-.0141
.806
. 0857
.0834
.784
-. 00032
-. 00057
. 00034
-. 00043
-.0136
.864
. 0821
.0769
.809
-. 00032
-. 00089
-.00013
-. 00046
-.0131
.913
.0792
. 0716
.825
-. 00025
-. 00044
. 00030
-. 00039
-.0126
.976
. 0736
.0612
.812
-. 00006
-. 00025
. 00065
-. 00035
-. 0117
1. 024
. 0708
. 0582
.842
0
-. 00032
-. 00023
-. 00034
-.0113
1. 067
.0658
. 0519
.842
. 00006
-. 00019
. 00002
-. 00027
-. 0105
1. 124
. 0612
. 0455
.836
. 00006
-. 00038
-. 00019
-. 00028
-. 0097
1. 169
. 0552
. 0390
.826
. 00006
-. 00032
-.00011
-. 00014
-.0088
1. 263
. 0431
. 0254
.744
0
-. 00044
-. 00061
-. 00026
-. 0069
1.305
. 0343
.0179
.681
. 00012
-. 00032
-.00042
-.00012
-.0055
1.307
. 0343
.0184
.702
. 00006
-. 00057
-. 00080
-. 00029
— . 0055
1.345
. 0276
.0118
. 575
. 00032
-.00019
-. 00038
-. 00009
-.0028
28.6° PITCH SETTING, 10° YAW
V.
nD
Cp
Ct
V
CFy
Cf,
Cm
Cn
Ci
Cq
0. 218
0. 0988
0. 0986
0.218
0. 0187
-0. 00063
-0. 00159
-0. 00055
-0.0157
-0.0157
.317
. 0901
.0981
.345
. 0193
-. 00056
-.00111
-. 00071
-. 0144
-. 0143
.409
. 0901
.0926
.420
.0191
-. 00025
-. 00082
-. 00065
— . 0144
-.0143
.541
.0886
. 0925
. 565
.0198
-. 00063
0
-. 00078
-.0143
-.0141
.639
. 0892
.0960
.688
. 0207
-. 00095
-. 00072
-. 00018
-.0143
-.0141
.727
.0877
. 0901
.747
. 0204
-. 00057
. 00008
-. 00004
-. 0142
-.0140
.806
. 0854
. 0830
.784
. 0196
-. 00025
. 00017
.00011
-. 0139
-. 0136
.866
.0826
. 0768
.805
. 0191
. 00045
. 00145
. 00005
-. 0135
— . 0131
.924
. 0796
. 0706
.819
. 0187
. 00057
. 00093
. 00030
-. 0130
-.0127
.970
. 0758
.0636
.814
. 0182
. 00096
. 00047
. 00066
-.0124
-. 0121
1.027
.0716
.0581
.833
. 0179
. 00108
. 00131
. 00040
-. 0118
-.0114
1. 080
. 0670
.0518
.835
. 0173
. 00095
. 00135
. 00049
-.0110
-.0107
1. 122
. 0623
.0463
.834
. 0171
. 00102
. 00140
. 00049
-. 0103
-.0099
1. 174
. 0583
. 0395
. 796
. 0165
. 00089
. 00144
. 00069
-. 0097
-. 0093
1.220
. 0532
. 0330
. 757
. 0163
. 00095
. 00182
. 00068
-. 0089
-.0085
1. 263
. 0479
. 0262
.691
.0161
. 00158
. 00246
. 00079
— . 0082
-.0076
1. 306
. 0404
.0193
.624
. 0159
. 00202
. 00303
. 00085
-. 0070
-. 0064
AIR PROPELLERS IN YAW
473
TABLE I — Continued
TABLE I— Continued
V
nD
Cp
C T
V
Cp y
cFl
cm
cn
c,
Cq
V
Til)
Cp
Ct
V
C'Py
cFl
cm
Cn
C,
r„
28.6° PITCH SETTING, 20°
YAW
28.6° PITCH SETTING, 30°
YAW
o. no
0. 1049
0. 0957
0. 100
0. 0363
-0. 00082
-0. 00464
-0. 00053
-0. 0161
-0. 0167
0. 130
0. 1031
0. 0874
0. 110
0. 0536
0. 00038
-0. 00653
-0. 00043
-0.0151
-0.0164
.380
. 0957
. 0924
. 367
.0385
-. 00063
-. 00221
-.00067
-.0154
-.0152
. 365
. 0922
. 0839
. 332
. 0568
. 00212
-.00379
-. 00082
-. 0147
-.0147
.511
. 0894
. 0889
.508
. 0388
-. 00075
. 00046
-. 00088
-.0152
-.0142
. 520
.0875
. 081 S
.486
. 0584
. 00149
— . 00197
-. 00063
-. 0148
-. 0139
.632
. 0902
. 0881
.617
.0408
-. 00019
. 00034
-. 00066
-.0154
-.0144
. 645
.0884
. 0783
.571
. 0598
. 00256
-. 00060
-. 00091
—.0157
-. 0141
.721
. 0879
.0856
.702
.0413
. 00025
.00100
-. 00002
-. 0152
-. 0140
. 727
.0882
.0771
. 636
.0608
. 00307
. 00072
-. 00052
-. 0165
-.0140
.804
.0870
. 0803
.742
.0407
0
. 00134
. 00040
-. 0152
-.0138
. 805
.0854
. 0739
. 697
.0611
. 00275
. 00135
. 00011
-.0164
-. 0136
.865
. 0855
.0750
.759
. 0400
. 00076
. 00179
. 00072
-.0151
-. 0136
. 870
. 0853
.0701
. 715
. 0609
. 00245
. 00178
. 00053
-. 0167
-.0136
.923
.0828
. 0696
. 770
. 0393
. 00089
. 00226
. 00086
-. 0147
-.0132
.924
. 0844
. 0664
. 727
.0601
. 00233
. 00264
. 00086
-.0170
-.0134
.977
. 0805
. 0644
.782
. 0385
.00127
. 00264
. 00096
-. 0145
-.0128
. 978
.0812
. 0620
.747
. 0595
. 00257
.00318
. 00105
-.0168
-.0129
1. 029
. 0777
.0591
.783
. 0378
. 00102
. 00258
. 00104
-.0140
-.0124
1. 034
.0821
. 0573
.722
. 0590
. 00328
. 00406
. 00128
-.0169
-.0124
1. 076
. 0732
. 0535
.786
. 0371
. 00158
. 00342
. 00099
-. 0136
-.0117
1. 080
. 0766
. 0534
. 753
.0583
. 00284
. 00462
.00152
-. 0168
—.0122
1. 122
. 0689
. 0476
. 775
. 0363
. 00190
. 00398
. 00120
-. 0129
-. 0110
1. 131
. 0726
.0488
. 760
. 0579
. 00271
. 00515
. 00163
—.0164
-. 0116
1. 169
. 0627
.0418
.779
. 0355
. 00239
. 00469
. 00135
-.0125
-.0100
1. 178
.0718
. 0439
. 720
. 0570
. 00308
. 00552
.00180
-.0164
-.0114
1.215
. 0589
. 0362
. 747
. 0352
. 00258
. 00504
. 00138
-.0119
-. 0094
1. 229
. 0706
. 0392
. 682
. 0566
. 00285
. 00584
. 00190
—.0164
—.0112
1.264
. 0636
. 0295
. 696
. 0346
. 00264
. 00573
. 00152
-. 0112
-. 0085
1. 274
. 0653
. 0343
. 669
. 0560
. 00322
. 00696
.00197
-.0161
-. 0104
1.312
.0479
. 0234
.641
.0340
. 00326
. 00832
. 00144
-.0104
-. 0076
1.310
. 0567
. 0293
. 677
.0551
. 00356
. 00861
. 00193
-.0154
-. 0090
REPORT No. 598
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF
FLUCTUATIONS OF AIR SPEED IN TURBULENT FLOW
By W. C. Mock, Jr.
SUMMARY
Recent electrical and mechanical improvements have
been made in the equipment developed at the National
Bureau oj Standards for the measurement oj fluctuations
oj air speed in t urbulent flow. Data usejul in the design
oj similar equipment are presented. The design oj recti¬
fied alternating-current power supplies j or such apparatus
is treated briefly, and the effect oj the power supplies on
the perjormance oj the equipment is discussed.
INTRODUCTION
The demand for experimental data on fluctuations of
air speed in turbulent air flow still continues, and the
hot-wire anemometer remains the tool most frequently
used in the attempt to meet this demand. In three
earlier papers (references 1, 2, and 3) the development
of the equipment used at the National Bureau of Stand¬
ards has been described in some detail as has also its
application to various turbulent-flow investigations.
Since the publication of reference 3 further investiga¬
tions have been conducted (references 4, 5, 6, and 7).
The apparatus described in reference 3 has been exten¬
sively changed so that its use is simplified and its per¬
formance improved. It was therefore felt desirable to
publish a description of the revised equipment and to
provide certain design data that might be of use to
designers of similar apparatus. The paper first de¬
scribes the improved equipment now in use at the
National Bureau of Standards, gives a brief treatment
of the design of power supplies for such apparatus, and
discusses the effect of the power supply on the per¬
formance of the amplifier.
Recapitulation of the information contained in refer¬
ence 3 has been avoided as much as possible, so that the
entire paper may be considered a continuation of the
earlier one. The work was carried out at the National
Bureau ol Standards with the cooperation and financial
support of the National Advisory Committee for
Aeronautics.
The author wishes to acknowledge the valuable as¬
sistance and advice received from the other members
of the staff of the Aerodynamical Physics Section during
the design and construction of the apparatus and in the
preparation of this paper.
I. THE NEW NATIONAL BUREAU OF
STANDARDS EQUIPMENT
As stated in reference 3, the assembly of equipment
used for measurement of air-speed fluctuations consists
of five parts: (1) the wire itself; (2) a Wheatstone
bridge for measurement of the wire resistance at room
temperature; (3) an apparatus with suitable switching
arrangements for supplying the wire with heating cur¬
rent, measuring the voltage drop across the wire at
various air speeds for calibration purposes, and, finally,
transferring the fluctuating voltage drop across the
wire to the amplifier input; (4) a suitable amplifying
system, including the requisite compensation for the
amplitude reduction and phase lag of the hot wire; and
(5) a final measuring instrument.
Improvement of this equipment has been effected
through simplification of operation and maintenance
rather than by modification of the basic principle.
The major change has been the substitution of rectified
alternating-current power supplies for the battery
supplies previously used. This and other changes that
have been made will be considered separately for each
component of the assembly.
Figure 1 is a photograph of the present apparatus;
figure 2 is an outline drawing with the various compo¬
nents identified.
HOT WIRES
The hot-wire remains as nearly as possible pure
platinum 0.015 mm in diameter and 4 to 8 mm long.
Recent investigations (reference 7) indicate the advis¬
ability of using short wires; therefore the present hot
wires are usually 5 mm or less in length, whereas for¬
merly 8 mm was the usual length. Welding still proves
to be the most satisfactory method of attaching the hot
wire to its supporting prongs although, when the wire
is used in a slack condition, ordinary soft soldering
has been fairly satisfactory.
WHEATSTONE BRIDGE
The Wheatstone bridge used for measuring the resist¬
ance of the hot wire at room temperature remains
unchanged. It is a standard laboratory appliance.
475
476
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 1.— General view of the alternating-current apparatus.
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 477
CONTROL EQUIPMENT
The apparatus for supplying and measuring the heat¬
ing current, measuring the mean voltage drop across
the hot-wire, and transferring the fluctuating voltage
drop across the hot-wire to the amplifier remains essen¬
tially the same as described in references 1, 2, and 3 as
far as the electrical circuit is concerned, although its
mechanical arrangement has been modified in the
interests of ease of manipulation. The only electrical
change is the substitution of a two-circuit nonlocking
push button for the single-circuit galvanometer key
formerly used. This substitution allows the reference
battery circuit, as well as the galvanometer circuit, to
remain open except when a reading of the galvanometer
is to be taken and greatly reduces the drain on the
reference battery, making possible the use of standard
no. 6 dry cells instead of a storage battery.
lowest noise in the first stage and highest amplification
in the second and third stages were obtained with the
combination shown. It was not determined whether
this result was due to inherent differences between the
tube types or merely to individual differences between
the particular tubes available for trial. In another
amplifier a different combination might prove superior.
An incidental advantage of the new tubes is that in the
first two stages, where the voltage to be amplified is
quite low, a satisfactory grid bias may be obtained
from a 1.5-volt flashlight-type dry cell inserted in
series with the cathode. This arrangement allows the
grid resistors to be connected directly to ground, which
in turn makes it possible to place the amplification
control directly in the grid circuit where it acts also as
the grid resistor. The grid bias of the third stage was
made adjustable because of the larger input voltages
encountered by this tube.
Figure 2.— Outline drawing of the alternating-current apparatus.
AMPLIFIER
The fourth unit of the apparatus, the amplifier, has
been completely redesigned electrically, as may be
seen from the schematic circuit diagram of the entire
equipment (fig. 3).
TUBES AND GRID BIAS
For the previously used type 224 tetrode tubes, a
type 77 pentode lias been substituted in the first stage
and type 6C6 pentodes in the second and third stages.
These tubes have somewhat superior characteristics to
the ones that they replace. The improved characteris¬
tics result in considerably increased gain per stage and,
because of the pentode construction of the tubes, they
are much less critical in regard to screen grid voltage.
Although these pentodes supposedly have nearly
identical electrical characteristics, it was found that
AMPLIFICATION CONTROL
The use of an amplification control is necessary be¬
cause of the wide range of voltages to be measured.
The location of this control in the circuit is dictated by
considerations of protection of the tubes from overload
and the maintenance of a high ratio of amplified voltage
to noise. The noise is an important factor because its
magnitude determines the smallest voltage that may be
measured, while overloading sets the limit for the
largest.
The most important source of noise in an amplifier is
the first tube and the circuits associated with it. Noise
originating in the tube is caused by irregularities in
electron emission from the cathode, which pro¬
duce fluctuations in the plate current. Associated
circuit noise may be due to thermal agitation in the
478
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
input circuit or fluctuations in tlie power-supply volt¬
ages. Of these, input circuit noise will be negligible
because of the comparatively low input resistance (usu¬
ally less than 10 ohms), and power-supply voltage
fluctuations may be made negligible by proper design,
leaving only the tube noise as effective.
Since this noise originates in the plate circuit of the
first tube, it is important that full use be made of the
amplification of that tube in order that the voltage to be
measured may arrive at this point as large as possible
relative to the noise originating there. This require¬
ment means that the amplification control must not be
from one tap to the next the amplification is changed
by a factor of 2, the total range ol control being 64:1.
In the previous equipment this amplification control
acted also as the load resistance of the first tube and
therefore had in series with it the internal resistance of
the plate-voltage source. This source was a bank of
lead-acid storage cells, and their very low internal
resistance did not greatly affect the calibration of the
amplification control. In the case of the present ap¬
paratus, however, it was desired to use rectified alter¬
nating current for the plate-voltage supply and, be¬
cause of the much greater internal resistance of this
INPUT CIRCUITS OUTPUT CIRCUIT
Standard cell
placed ahead of the first tube. On the other hand, if the
amplification control is not placed in the circuit ahead
of the second tube, the large amplification of the first
stage may cause overloading of the second or following
stages when large values of turbulence are measured.
The amplification control is therefore located between
the first and second stages of the amplifier, as in the
previous equipment. The present amplifier, however, is
different in that this control is in the grid circuit of the
second stage rather than in the plate circuit of the first
stage. It consists of a resistor of 1,600,000 ohms. The
total resistance has taps so located that by switching
supply, the amplification control was moved to the
grid circuit of the second tube.
Another advantage of this arrangement is that the
possibility of a change in calibration due to unequal
heating of the resistors is reduced because no direct
plate current flows through the control. Furthermore,
as now arranged, the coupling condenser is now always
at the lowest possible voltage, which reduces the chance
of condenser leakage with its attendant change in grid
bias and amplification. As a result of this alteration,
the present control changes the gain by a factor of
exactly 2 per step.
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 479
COMPENSATION CIRCUIT
The only electrical change in the compensation cir¬
cuit is the return of one terminal to ground rather than
to the high-potential end of the plate resistor. This
change reduces the direct-current voltage drop across
the circuit, with consequent reduction in direct current
through the circuit, and the possibility of leakage
through the capacitor coupling the circuit to the follow¬
ing tube. It also allows one terminal of the resistor
controlling the compensation to be grounded, which
somewhat simplifies the mechanical construction.
In the foregoing discussion of the compensation cir¬
cuit, as well as in the discussion of the amplification
control circuit, the importance of reducing coupling
capacitor leakage has been stressed. With the large
capacitances required, space limitations dictate the use
of paper dielectric capacitors that have insulation prop¬
erties inferior to the more bulky mica dielectric capaci¬
tors. Undesirable effects, such as noise and variable
amplification that may result from the use of paper
coupling condensers, may be reduced by lowering the
voltage across them. Any circuit changes, therefore,
that will reduce the potential difference across the coup¬
ling capacitors will be an improvement.
OUTPUT STAGES
Reference to figure 3 will show that the output stage
of the present amplifier differs markedly from the ar¬
rangements used in previous equipment. Since it is
desired to measure only the alternating-current output
from the amplifier, it is necessary to provide some
means for keeping the direct plate current of the output
tubes from flowing through the measuring instrument.
Three general means to this end exist: first, the
use of a transformer to couple the meter to the output
tube or tubes; second, the use of a “bucking-out”
battery so connected that it supplies across the meter
a direct voltage drop equal and opposite to that caused
by the direct plate current of the output tube; third,
the use of some balanced system, such as that employed
in the present equipment, so arranged that the meter
is connected across points of equal direct voltage but
unequal alternating voltage.
A transformer has the advantages of simplicity and
complete elimination of direct current through the
meter, but unfortunately it is not possible, at present,
to obtain a transformer that will give uniform output
over the range of desired frequencies — namely, from
less than 5 to over 5,000 cycles per second.
The second system, the use of a bucking potential,
has been used in the previous equipment with success.
However, it generally requires a battery of some sort,
and one of the reasons for construction of the apparatus
described herein was to eliminate, as far as possible, all
batteries. In addition to the nuisance of battery
maintenance, a battery system has the disadvantage
of requiring careful adjustment of the operating voltages
and currents of the output tube to such values that
the direct-current voltage drop across the meter is
ecpial to some voltage that may be conveniently ob¬
tained from a dry-cell battery; that is, some multiple
of 1.5 volts. Otherwise some form of variable resistance
must be incorporated in the circuit so that the bucking
voltage may be made equal to the voltage drop across
the meter. The use of a resistance for this purpose un¬
avoidably inserts resistance in series with the measuring
instrument, with resultant loss in sensitivity and a
change in sensitivity with change in “bucking-battery”
voltage during the life of the battery.
The third system, the use of a balanced or “push-pull”
stage as in the present equipment, eliminates the buck¬
ing-battery troubles. It also offers the advantages of
greater alternating-current output and independence
of balance on tube operating voltages and currents as
long as both tubes operate under the same conditions
of input voltage and supply voltage. In practice
this system is balanced for no direct-current through
the meter as follows: The load resistors in the tube
plate circuits are first adjusted to the same resistance,
and the contact arm of the balance adjusting resistor
between them (fig. 3) is set on the midpoint. The
plate currents of the two tubes are then made equal to
each other, and to the desired value, by means of the
independent grid voltage controls. These operations
having been performed, the output-meter circuit is
attached, and the direct-current balance meter observed.
If this meter then shows no current, the balance is
correct. If some current is indicated, a slight readjust¬
ment of the grid biases should be made. Small un¬
balances may be corrected by means of the balance
adjusting resistor between the plate resistors. A final
check on the balance is made by applying an alternating
voltage of magnitude just less than that causing over¬
load of the amplifier. If the balance remains correct
under this condition, the output stage is in proper
adjustment. If the stage becomes unbalanced, dissimi¬
larity of the tubes is indicated, and other tubes must
be tried until a matched pair is found. Practically no
trouble of this nature has been experienced.
Experiments have shown that the most suitable
operating conditions for the output stage of the balanced
type differ somewhat from those of the single-tube
type. In the instance of the single-tube output ampli¬
fier used in the previous amplifier (reference 3), the
grid voltage was adjusted so that the tube operated
on the straight portion of its curve of grid voltage-plate
current characteristic, the “class A” mode of operation,
in which the average plate current is constant. With
the balanced or “push-pull” type, however, it has been
found that best operation is obtained when the adjust¬
ment is more nearly that of the “class B” mode, the
grid biases being adjusted so that the tubes operate
near plate current cut-off. (See fig. 4 (a).)
480
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
When so operated, the average plate current is not
constant but varies with the applied alternating voltage.
The distortion that would result if a single tube were
used under these conditions is avoided by the push-pull
connection. Attempts to operate the tubes with less
grid bias and higher plate current lead to a higher am¬
plification but to a reduced range of input voltages for
which a linear relation exists between input voltage
and output current. (See fig. 4 (b).) The best bias,
depending as it does on the type of tubes used, the
plate voltage available, and the load conditions exist¬
ing, should be determined by trial for each particular
installation. For preliminary design purposes the bias
may be approximated quite closely by extending the
straight portion of the curve of dynamic grid bias-plate
current characteristic until it intersects the axis of zero
plate current. The grid bias at which this intersection
takes place is then that bias which will give the bal¬
anced amplifier a linear characteristic over the greatest
range of input voltage. This is the adjustment illus¬
trated by figure 4 (a).
Tube / - >
Dynamic eg-ip
charac t eristic
of sing/e
tube — vy
Dynamic
character¬
istics of
push-pull
stage
Tube 2
-r Operating point
Opera¬
ting
point
Applied a. c.
grid voltage
(a)
Applied a.c.
grid voltage
(b)
Figure 4.— Mode of operation of output amplifier.
In the instance of the balanced output amplifier stage
now in use at the National Bureau of Standards, type
2A3 tubes are used because of their very high mutual
conductance. This characteristic gives a large change
in plate current for a given change in grid voltage.
Furthermore, their low plate impedance allows a rea¬
sonable match between meter-circuit impedance and
tube impedance without the necessity of insertion of
excessive resistance in series with the meter in order to
avoid distortion. With these tubes and a plate voltage
of 400 volts the best operation is obtained when the
grid bias is so adjusted that the plate current of each
tube is about 5 milliamperes without input voltage.
When input voltage is applied the plate current in¬
creases, becoming approximately 25 milliamperes per
tube at maximum allowable input.
PHASE INVERTER
The use of a balanced output stage introduces an
additional problem not encountered in the previous
equipment. Because of the manner in which they are
connected, the tubes of the balanced amplifier require
input voltages exactly equal in magnitude and wave
shape, but 180° apart in phase. In an ordinary am¬
plifier these voltages would be obtained by using a
coupling transformer having a center-tapped secondary,
the grids of the balanced amplifier being connected to
the opposite ends of this secondary winding. Since
transformers are not usable at the lower frequencies
under consideration, recourse must be had to some
other method.
One such method that has proved very satisfactory is
the use of a phase-inverting tube. This system takes
advantage of the fact that the amplified alternating
voltage appearing across a resistance load in the plate
circuit of a vacuum tube differs 180° in phase from the
applied alternating grid voltage that causes it. The
circuit is so arranged that the alternating voltage ap¬
plied to the grid of one of the balanced amplifier tubes
is passed through one more stage than that applied to
the grid of the other, this additional stage having an
amplification of 1:1. Thus the grids of the two bal¬
anced amplifier tubes receive voltages 180° apart in
phase but equal in magnitude.
A practical circuit of this type is that incorporated
in the present amplifier and illustrated by figure 3.
For economy of space a type 53 twin-triode tube is
used instead of two separate similar tubes. This type
53 tube consists, in effect, of two identical triodes, each
having a voltage amplification of about 20. The first
of these triodes is inserted directly between the higli-
gain amplifier and the grid of the upper of the two bal¬
anced amplifier tubes. The second receives its input
from a voltage-reducing tap on the plate resistor of the
first, amplifies this voltage, and applies it to the grid
of the lower balanced amplifier tube. The two bal¬
anced amplifier tubes thus receive grid voltages that
are 180° apart in phase and, when the voltage-reducing
tap feeding the second half of the type 53 tube is
properly adjusted, are equal in magnitude.
A similar result might be obtained by eliminating the
type 53 tube and feeding the grid of one of the balanced
amplifiers from a suitably located tap on the plate
resistor of the other. This arrangement would, of
course, sacrifice the voltage gain of approximately 20
that occurs in the type 53 tube as now used. The
choice of method employed thus depends somewhat on
the amplification necessary in a given installation.
OUTPUT METER
One of the greatest sources of annoyance in the oper¬
ation of the older equipment was the frequency with
which the highly delicate 0 to 5 milliampere thermo¬
element alternating-current milliammeter was burned
out by momentary overload. The output meter used in
the new' equipment was designed to overcome this
trouble and consists of a 0 to 500 microampere direct-
current microammeter operated by a separate heater-
type thermoelement. This combination gives a full-
scale reading with a current of 25 milliamperes through
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 481
the heater of the thermoelement and has a maximum
safe current-carrying capacity of 40 milliamperes. In
series with the heater, which has a resistance of 10 ohms,
is placed a fixed resistance of 300 ohms. The purpose
of this resistance is to prevent distortion by making the
total resistance of the meter circuit large enough to
act as a reasonable load for the output tubes of the
amplifier. The exact value of the resistance used is
not critical. No difference in performance of the am¬
plifier except a slight loss in over-all sensitivity could
be detected when the 300 ohms used was increased to
1,000 ohms. Resistances less than 300 ohms were not
tried, as no great increase in sensitivity, or any other
benefit, could be expected from their use.
Although the present meter is only one-fifth as sensi¬
tive as that employed in the previous equipment and
the sensitivity is still further reduced a slight amount
by the addition of the series resistance, the amplification
of the new amplifier is sufficiently greater than the
older one that the actual sensitivity of the equipment
from hot wire to meter reading is not decreased.
Furthermore, the ruggedness of the meter is so much
greater that no trouble whatever from meter burn-out
has been experienced in service.
POWER SUPPLY
The apparatus of reference 3 was entirely battery
powered, requiring a total of three 6-volt storage bat¬
teries, 1,200 small storage cells, three 45-volt dry bat¬
teries, and four 4.5-volt dry batteries. The great bulk of
this voltage-supply equipment, together with its weight,
its comparatively short life, and the almost constant
effort required to keep it in good working condition
made it highly desirable to use an alternating-current
power supply, rectifying and filtering wherever neces¬
sary. The new' equipment occupies approximately
one-tenth the volume of the old plate voltage supply
battery alone, weighs somewhat less, has almost un¬
limited life, and requires little or no attention.
HIGH VOLTAGE
Twro separate transformers, rectifiers, and filters are
used to supply the high direct-current voltage for
plates and screens. One of these sets takes care of the
requirements of the high-gain stages and the phase-
inverter stage; the other furnishes only plate voltage
for the output stage. Both supplies have the same
output voltage, namely, 400 volts direct current, but
differ in other respects.
The power supply for the high-gain and phase-
inverter stages is provided with taps giving 50 volts
direct current and 250 volts direct current for screens
and high-gain amplifier plates, respectively, as well
as the full output of 400 volts for the phase-inverter
plates. The filter for this supply consists of three
40-henry 60-milliampere chokes and a total of 180
microfarads of filter capacitance, arranged as shown
in figure 3. The rectifier tube used is a type 80 high-
vacuum full-wave rectifier.
The power supply for the output stage differs from
the above-described supply mainly in the amount of
filtering provided. Since the output stage has in itself '
very little amplification, and particularly because it
is not followed by any other amplifier, the filtering
necessary to keep the hum at the desired low level is
much less than in the case of the liigh-gain stages.
Two 20-henry chokes capable of carrying 200 milli¬
amperes are used in conjunction with 31 microfarads
of capacitance arranged as shown in figure 3.
It will be noted that series resonant circuits are
employed in this filter as well as the usual pi type
low-pass sections. These series circuits are resonant
at 120 cycles per second, the main ripple frequency
of the rectifier’s output wave; and their purpose is to
increase the filtering efficiency without the use of large
values of capacitance and inductance, particularly the
latter.
LOW VOLTAGE
The low voltages necessary for cathode heating in the
new equipment are supplied from the 110-volt alter¬
nating-current power lines by step-dow n transformers
or windings on the high-voltage transformers, instead
of bv storage batteries. This change results in a con-
siderable reduction in weight and bulk.
It was thought that excessive hum might be intro¬
duced by this change, but tests of the completed ampli¬
fier have shown that the total hum, both from this
source and from the high-voltage supplies, is too low
in magnitude to be measured by the output meter
even when maximum amplification is used.
Low voltage, of the order of 50 volts, for the screen
grids of the high-gain tubes is obtained from the high-
voltage power supply. The method of obtaining screen-
grid voltage for the first stage differs from that used in
the second and third. The reason for this difference is
discussed in the section of this paper dealing with the
effect of the power supply on the amplifier character¬
istics.
The last portion of the power supply proper is the
grid bias system. Here dry cells or dry-cell batteries
are used as in the previous equipment. The retention
of batteries for this purpose is justified because of their
long life in such service, their compactness, and their
low internal resistance compared with any practical sub¬
stitute. In almost all cases the drain on the bias bat¬
teries in the new equipment has been either completely
eliminated or substantially reduced so that greater
battery life may be expected than before.
VOLT A G E R EG ELATION
The use of rectified alternating-current power sup¬
plies with amplifiers capable of amplifying very low
frequencies leads to unexpected difficulties when the
power supply is operated from commercial power lines.
In addition to gradual changes of voltage, which are
annoying in that they cause corresponding changes in
482
REPORT NO. 598 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
amplifier sensitivity, sucli lines usually carry quite
rapid voltage fluctuations, caused by switching tran¬
sients and other load irregularities, which have fre¬
quencies high enough to be amplified by the amplifier.
Such fluctuations of the line voltage may produce an
excessively high and variable noise level, or dangerously
large transients in the amplifier. For this reason it has
been found necessary to provide voltage regulators
between the nominally 115-volt alternating-current line
and the power supplies of the amplifier.
Two types of regulation are used. First, a commer¬
cial automatic voltage regulator entirely removes the
slow changes in line voltage and reduces the transient
changes to a low magnitude. Second, a manual con¬
trol of voltage, in the form of an autotransformer having
a practically continuously variable voltage ratio, in¬
serted in the line between the automatic voltage regu¬
lator and the power supplies, takes care of voltage
changes due to line and power-supply heating and
makes possible intentional voltage changes. These
two types of voltage regulation almost completely elimi¬
nate all line-voltage troubles, making the amplifier inde¬
pendent of line conditions as long as the line voltage
remains between the limits of 90 to 130 volts.
MECHANICAL ARRANGEMENT
In the design of the apparatus considerable attention
was given to mechanical lay-out. It was desired to
have in the completed equipment a tool that might
be used with maximum convenience by one operator.
At the same time it was necessary to observe certain
precautions in the matter of electrical shielding and
power-supply location. Ease of repair and main¬
tenance also entered into the problem to a considerable
extent. The result of compromise between these some¬
times conflicting factors is the apparatus illustrated by
figures 1 and 2. Figure 1 is a photograph of the entire
equipment as used, including a small cathode-ray
oscillograph not properly a part of the assembly.
Figure 2 is an outline drawing showing the panel lay¬
out of the equipment.
Two separate units are used. That on the left in
both figures consists of the amplifier and all controls
directly associated with it, as well as calibrating and
testing equipment. That on the right contains the
power-supply equipment and controls.
Both units are assembled on standard steel relay
racks taking panels 19 inches in width and multiples
of 1% inches in height, with a horizontal clearance of
1714 inches between vertical rack members. All
apparatus is mounted from its panel, and each indi¬
vidual panel, with its associated apparatus, may be
removed as a unit for inspection or repair. The
apparatus behind each panel, in the case of the amplifier
rack, is fitted with a metal case or dust cover, which
also acts as a shield against stray electrical fields in the
room. The apparatus on the power-supply rack is
covered by one large dust cover supported from the
rack itself and removable as a unit. This general
method of construction is one that has been widely
used in the telephone and other communication fields.
It gives compactness with a maximum of accessibility
and requires a minimum of floor space.
The amplifier panel carries three direct-current
milliammeters, the amplification control switch, and
the fine adjustment for balance of the output stage.
By means of a plug-and-jack arrangement it is possible
to measure the plate current of the various tubes using
the three meters provided. Input and output con¬
nections to the amplifier are likewise made by means of
plugs and jacks.
The arrangement of the amplifier behind the panel
is such that all grid and plate leads are very short and
each stage is separated from the others by aluminum
shields. All grid and plate leads are kept as far as
possible from the metal shielding to reduce the loss of
amplification at high frequencies. All power-supply
leads are run in shielded cables with the shields grounded
to the amplifier framework at frequent intervals and
are kept well away from the grid and plate leads of
the tubes to reduce the possibility of hum pick-up.
The input lead to the amplifier is also shielded, and the
shielding is grounded, both to reduce pick-up of stray
fields in the room and to prevent coupling between input
and output circuits of the amplifier. The possibility
of such coupling is still further reduced by taking input
and output leads from opposite ends of the amplifier.
The compensation-circuit panel carries a four-dial
0-10,000-ohm decade resistance for compensation ad¬
justment, as well as a double-pole, double-throw, locking
push-button switch arranged to connect either the
compensation circuit or a 5,000-ohm resistor to the
amplifier, the resistor being used for amplifier calibra¬
tion. Behind this panel, supported by a bakelite shelf
in a large aluminum box, is the compensating coil. As
much space as possible was allowed around the coil in
order to prevent excessive reduction of its effective
inductance by the metal shield. Attempts to operate
with no shielding were unsuccessful because of the stray
field pick-up of the large compensation coil. This
trouble was experienced in the previous amplifiers also,
but to a much lesser extent because of the smaller
amplification of that equipment.
Below the compensating-coil panel is that of the
potentiometer and control apparatus. Here, conveni¬
ently grouped in one spot, are all the controls and meters
necessary for routine operation of the equipment with
the exception of the compensation adjustment, which
is within easy reach on the panel above. The use of an
arrangement such as this effects a worth-while saving
in time and effort.
The apparatus on the panel is as follows: From left
to right in the top row, the alternating-current micro¬
ammeter indicating the current input from the calibrat¬
ing oscillator; the tliree-dial decade 0-1,000-ohm
ALTERNATING-CURRENT EQUIPMENT FOR
THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED
483
resistance of the potentiometer for setting the heating
current and measuring the mean voltage drop across
the wire; and the direct-current microammeter used,
in conjunction with a thermoelement, as the output
meter. In the next row are the galvanometer for
indicating balance in the potentiometer circuit; the
coarse adjustment of heating current; a direct-current
milliammeter for rough indication of heating current;
the fine adjustment of heating current; and the direct-
current milliammeter used to indicate balance in the
output stage of the amplifier. The bottom row consists
of the combined galvanometer and reference-battery
key; a five- position, four-gang switch to be described
later; and the jack lor the output-meter key, which for
convenience is attached to a short, two-wire flexible cord.
The above-mentioned five-position, four-gang switch
replaces the cumbersome plug-ancl-jack system em¬
ployed in the earlier apparatus to control the potenti¬
ometer and amplifier input circuits. In the first of the
five switch positions the potentiometer and standard
cell are so connected that the voltage of the reference
battery may be measured. In the second position the
potentiometer is connected across a known fixed
resistance in the heating- battery circuit so that the
current through the hot-wire may either be measured
or set to some predetermined value. In the third
position of the switch the potentiometer is connected
across the hot-wire so that the mean voltage drop may
be measured. In the fourth position the hot-wire is
connected across the input of the amplifier so that the
fluctuating voltage drop may be amplified and measured.
Finally, in the fifth position, the amplifier input is
connected across a 20-ohm resistor in the oscillator
output circuit for calibration and testing purposes.
Thus the switch with five settings performs the same
functions as the six jacks and three plugs formerly used.
Behind the control panel are mounted the standard
cell, the reference battery, and the various fixed and
variable resistors associated with the potentiometer
circuit and oscillator output circuit, as well as the
thermoelement and resistor used in the amplifier out¬
put circuit. Shielding between input and output
circuits is provided, and all apparatus is contained in
can aluminum outer shield with a removable back.
The unit below the control panel is the General Radio
type 377B audio-frequency oscillator used for calibra¬
tion and testing. This oscillator is the one used with
the earlier equipment, adapted for rack mounting.
The last unit on the amplifier rack is a blank panel
covering space reserved for future expansion.
The power-supply rack carries all power supplies and
voltage controls, with the exception of the automatic
voltage regulator, which is mounted some distance
away so that the amplifier will be less affected by the
external field it produces. Starting at the top the first
two panels are blanks reserved for future use. The
third unit is the power supply for the high-gain and
phase-inverter stages of the amplifier. On this panel
.are mounted an on-off switch controlling the input to
the power supply, a red pilot lamp to indicate when the
power supply is in operation, and a set of small jacks
connected to the various high voltages available at the
power-supply output. The main panel of the power
supply is h-inc.h cold-rolled steel; this heavy material
is used because of the very considerable weight of the
power-supply equipment. The component parts, which
are of the “bottom connection” type, are mounted on
a vertical subpanel about 2 inches behind the main
panel and of the same material. The space between
main and subpanels is used for the wiring, which is
thus protected and hidden.
In order to reduce the external alternating-current
field of the power supply, all chokes and transformers
are enclosed in very heavy cast cases of high perme¬
ability iron alloy and as much of the wiring as possible
is confined to the space between main and subpanels or,
in the instance of output and input leads, to the in¬
terior of the channels forming the vertical members of
the rack.
The fourth unit is the power supply for the output
stage. This unit differs from the third unit only in
the electrical details that have been discussed previ¬
ously. The mechanical arrangement is identical to
that of the other power supply. The fifth unit is the
input-voltage control panel, and carries the main
alternating-current power switch, a pilot lamp, the
manual voltage control autotransformer, and an alter¬
nating-current voltmeter that indicates the input
voltage to the power supplies. The sixth unit is a
service panel carrying several outlets for alternating
and direct current and a battery-charging outlet. The
last panel carries a 2.5-volt transformer which supplies
heating current for the output stage filaments. On the
face of the panel are mounted a switch, a pilot lamp,
and an outlet that allows the 2.5 volts alternating
current to be used for any purpose.
As mentioned previously, a sheet-iron dust cover
encloses the rear of all apparatus on the power-supply
rack. This cover also provides some shielding in ad¬
dition to the iron cases of the individual components
of the power supplies. Further shielding is obtained
by enclosing all leads connecting the two racks in
grounded lead-foil coverings.
PERFORMANCE
The important features of the performance of the
complete equipment are summarized by the two curves
of figure 5.
In comparison with the performance of the previous
equipment (figs. 9 and 11 of reference 3), it is seen that
some improvement has been effected in the frequency
characteristic of the uncompensated amplifier. The
new apparatus maintains its amplification constant to
3,000 cycles per second, whereas the older amplifier
started to lose amplification at about 1,600 cycles per
second.
484
REPORT NO. 598- NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 5.— Frequency characteristic ot apparatus.
Tlie comparison between the compensated frequency
characteristics of the two sets of apparatus is not
quite so favorable. Because of the unavoidable de¬
crease in the effective inductance of the compensa¬
tion coil, caused by proximity to its shielding box, the
resonant frequency has been lowered from 4,000 to
3,500 cycles per second. This fact, together with other
effects probably due to the use of a power supply
having high internal impedance compared with the
storage cells formerly used, causes the frequency charac¬
teristic to depart from the ideal at a somewhat lower
frequency than before. The height of the resonant
peak, however, has been reduced and it is felt that the
slight sacrifice in frequency-characteristic performance
is offset by the increased reliability and usability of the
apparatus.
Other features of the performance, not evident from
the curves shown, are a sixfold increase in sensitivity,
which allows the use of a more rugged meter without
loss in effective sensitivity, and an improvement in the
constancy of amplification control setting ratios.
II. POWER-SUPPLY DESIGN
In the selection of a power-supply system for an
amplifier there is no doubt, from the standpoint of
electrical design, that batteries, particularly storage
batteries, offer the best results. The cost, the bulk,
and the problem of maintaining a battery power supply
make it desirable, however, to design an alternating-
current operated power supply that will give satisfac¬
tory electrical performance.
For cathode heating, alternating current of the proper
voltage may be directly applied to the heaters of the
indirectly heated cathode type tubes and successful
performance obtained even in high amplification am¬
plifiers. In the output stage of the amplifier, directly
heated cathode tubes are generally satisfactory. The
only precautions necessary are: grounding of the zero
potential point of the heater supply circuit, shielding
of the supply wires to the tube sockets, the use of some
discretion in the placement of these supply wires relative
to grid and plate wiring in the amplifier, and the use of
magnetically well-shielded transformers located some
distance from the amplifier and of ample capacity for
the load to which they are connected.
The design of the high-voltage supply is a more com¬
plicated matter. It divides itself more or less naturally
into two phases. First, the treatment of the problems
peculiar to the power supply itself, namely, the provision
of sufficient filtering and power capacity. Second, the
consideration of the effect that the power supply will
have on the characteristics of the amplifier, entirely
apart from the possible introduction of hum and noise.
These phases will be discussed separately.
FILTER DESIGN
A rectified alternating-current power supply consists,
in general, of a transformer to raise the commercial line
voltage to the required high voltage, rectifiers to change
this high voltage from alternating current to pulsating
direct current, and a filter system to remove, as nearly
as possible, all these pulsations, leaving only a pure
direct current of the desired high voltage.
INDUCTANCE INPUT FILTER
Many types of transformers, rectifiers, and filters may
be used in various combinations, but certain combina¬
tions are more common than others. Of these the most
KTrans former^Rec ti f/er j-
Filter -
3
(a) Schematic circuit diagram.
(b)
(b) Voltage relations.
Figure 6.— The inductance input filter.
common is the single-phase full-wave transformer and
rectifier working in conjunction with an inductance
input filter. This type is shown in figure G (a). Tlie
output from the system consists of a series of voltage
pulses having twice the frequency of the alternating
current supplied to the transformer. Neglecting the
minor effects of voltage drop in the rectifiers and
transformer leakage reactance, these voltage pulses
approximate the shape of arches of sine waves, as shown
in figure 6 (b).
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 485
If the input inductance of the filter is made
sufficiently large to satisfy the inequality
wL\ > € ac
Rl ~ &dc
(1)
where uLx is the reactance of to lowest frequency in
rectifier output;
RL, load resistance into which the filter works;
eac, amplitude of the lowest frequency component
in the rectifier output voltage;
and edc, direct-current voltage in rectifier output;
a fairly constant input current to the filter will be
maintained. Under this condition the voltage across
Ci will fluctuate only slightly about a value equal to the
average voltage of the rectifier output pulses (fig. 6 (b)).
The action of L2 and C2 is to reduce still further the
magnitude of the fluctuation. It is possible to reduce
the fluctuation components to as small a portion of the
total output voltage as may be desired by making
L i, L2, Ci, and C2 sufficiently large, or by adding similar
sections.
Assuming that the input inductance is large enough
to satisfy relation (1), the residual fluctuation compo¬
nents in the filter output may be computed with suffi¬
cient accuracy by considering that the output voltage
wave, eu from the rectifier has the form given by the
Fourier series 1
2c/ 2 2
Ct — — ( 1 — w COS 2c — COS 4 bit
7T \ 3 15
2 2
— cos 6o^ . - ~ cos no ot), (2)
Li to Ln, series inductances;
Ci to C„, shunt capacitances;
and / is the frequency of the component under con¬
sideration.
For the two-section filter of figure 6 (a) equation (3)
becomes
— = - - - (4)
c; rfLiLoCiC* ' •
In the application of the preceding approximate
equations the magnitude and frequency of each com¬
ponent of the rectifier output may be substituted in
turn, and the resultant magnitude of this component
in the output from the filter obtained. In order to
simplify this procedure, equation (2), giving the magni¬
tude of the components of the rectifier output, may be
written in tabular form as follows, by giving the direct-
current output voltage the value 1.00.
TABLE I
Voltage Relations in Single-Phase Full-Wave
Rectifiers
Root mean square a. c. voltage applied to each rectifier _ 1.11
The d. c. output voltage at rectifier terminals _ 1.00
Peak value of lowest frequency a. c. component _ 0. 607
Peak value of second harmonic of lowest frequency a. c.
component _ 0. 133
Peak value of third harmonic of lowest frequency a. c.
component _ 0. 057
Frequency of lowest frequency a. c. component _ 2/
Frequency of supply voltage _ /
In table I it will be noted that the lowest frequency
component has a frequency twice that of the supply
where e is the peak value of alternating-current voltage
applied to rectifier,
W = 27t/,
and j is the supply-voltage frequency.
The output wave of the form shown in equation (2)
may be applied to the filter under consideration, and the
network solved for the value of the components in the
filter output by the usual methods for complex networks.
This procedure is somewhat laborious, however, and
sufficient accuracy may be obtained by means of a
simplified computation.
Assuming that the reactance of each series inductance
is large compared with the reactance of the preceding
and following shunt capacitances and that the reactance
of the output capacitance is small compared with the
load resistance, the following expression is approxi¬
mately true,
(x>'n{JLiL2
1 c0
Ln){CxC2 • • • • Cn) e’
(3)
where is the magnitude of a given alternating-current
component applied to filter;
e0, magnitude of the same component at the out¬
put of the filter;
n, number of sections in the filter;
A
Q
U
c
C,
rl::
<
f
Figure 7. — Schematic circuit diagram of capacitance input filter.
voltage. Since in most cases the supply will be from
the usual 60 cycles per second lines, this lowest fre¬
quency component will have a frequency of 120 cycles
per second and the next two higher frequency com¬
ponents will have frequencies of 240 and 360 cycles per
second. In view of the fact that the amplitude of the
higher frequency components decreases rapidly with
increase in order, while the smoothing action of the
filter increases as the 2 n power of the frequency, it is
generally sufficient to consider only the lowest frequency
component of the rectifier output in computing the
filter performance.
CAPACITANCE input filter
Another type of rectifier and filter combination often
used is the single-phase full-wave rectifier and capaci¬
tance input filter, for which a typical schematic circuit
diagram is given in figure 7. The advantages of this
1 This is the Fourier expansion of the half-sine wave shown in fig. 6 (b).
486
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
arrangement, in comparison with the inductance input
system, are an approximately 25-percent increase in
filtering action from a given amount of inductance and
capacitance and a considerably higher direct-current
output voltage for equal alternating-current inputs to
the rectifiers. The disadvantages are the poor voltage
regulation of the system under a varying load and the
increased load on the rectifier tubes. Neither of these
disadvantages is serious when the rectifier and filter
are to be used to supply high voltage to a light and
constant load, such as that offered by the high-gain
stages of a turbulence-measuring amplifier.
The action of a capacitance input filter is somewhat
different from that of the inductance input type in
respect to the wave form of the voltage applied to the
first inductance. In the inductance input filter this
voltage depends only on the rectifier, whereas in the
capacitance input filter it also depends on the capaci¬
tance of the input condenser.
Each time the alternating-current voltage applied to
a rectifier anode reaches its peak value, the input con¬
denser Ci charges to this same value. Then, as the
alternating-current voltage at the rectifier falls, the
condenser discharges into Lx until the other rectifier
anode reaches its peak potential and the condenser is
charged again. Since during most of the cycle the
condenser is more positive than either rectifier anode,
the rectifier current flows for only a short time. Dur¬
ing the discharge period of the condenser its voltage
drops at a nearly uniform rate because the inductance
Lx tends to draw a constant current. The result of
this action is that an approximately saw-tooth voltage
wave form is applied to the inductance Lx.
In order to compute the action of the filter under the
above-outlined conditions, it is necessary to assume
that the impressed wave form has a true saw-tooth
shape with a peak amplitude equal to the peak ampli¬
tude of the alternating-current voltage applied to the
rectifier. This voltage, eu can then be considered to be
represented by the Fourier series
e f 2.1 1
Cj= - < 1+ (sin ut— - sin 2ojt -j- — sin 3co/—
1 , tt l cot illL 2 3
where e is the peak value of alternating-current voltage
applied to rectifier;
Ci, input capacitance;
RL, load resistance;
and /, supply voltage frequency.
The accuracy of the assumptions on which equation
(5) is based increases as the voltage variation across Ci
decreases, for instance, as Ct and/or Lx are increased,
but in the worst cases likely to be encountered in
practice the equation will still give results of sufficient
accuracy for most purposes.
It is possible to compute the magnitude of the residual
fluctuations in the output voltage from the filter by
solving equation (5) for the magnitude of the fluctua¬
tion components in the voltage applied to Lx and then
using ecpiation (3) exactly as in the case of the induct¬
ance input filter. The fact that the direct-current
output from the rectifier and the ratio of the fluctuation
components to this direct-current voltage both depend
on the magnitudes of Cx and RL complicates the pro¬
cedure somewhat by making it impossible to reduce
equation (5) to a simple table, as equation (2) was
reduced to table I. Equation (5) must be solved using
the values of C{ and RL that apply to the particular
problem.
RESONANCE FILTER
A third type of filter to be considered is that in which
resonant elements are used. Filters of this type find
their greatest application where economy of weight is
important, or where considerations of voltage regulation
make it desirable to use low-resistance series induc¬
tances in the filter circuit. Very low resistance in the
series inductance is generally accompanied by low
inductance, unless unusually large reactors wound with
large wire are used. If the series elements are made
parallel resonant at the lowest frequency present in the
rectifier output, it is possible to obtain high attenuation
to this frequency from comparatively small values of
inductance. Alternatively the shunt elements of the
filter may be made series resonant to the main fluctu¬
ation frequency and a similar effect obtained.
The principal disadvantage of such resonant filter
arrangements is that the large attenuation is obtained
only at the resonant frequency. The higher frequency
fluctuation components are attenuated comparatively
little and may reach the output of the filter with large
amplitude. A further disadvantage is the fact that the
inductance of an iron-core coil, such as a filter reactor,
depends on the direct current through the coil. Since
this direct current is likely to be variable the inductance
may also vary, making it impossible to keep the resonant
element resonant at the proper frequency.
For these reasons it is generally best to employ
resonant filter elements in conjunction with ordinary
series and shunt filter elements so that they do not bear
all the burden of filter action. It is also advisable to
use series resonant circuits shunted across the filter
network, because such circuits carry no direct current
and are thus free from the detuning effects of load cur¬
rent changes. The filter used in power supply 2 for
the output stage of the amplifier of figure 3 is an ex¬
ample of the combination of series resonant and ordinary
filter elements.
If resonant filter elements are combined with ordinary
filter elements so that an inductance or capacitance
input filter is formed, the resultant network may be
solved for the magnitude of the fluctuation com¬
ponents in its output voltage by assuming the input
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 487
voltage to have the form given by either equation (2)
or equation (5).
If a resonant element forms the filter input the com¬
putation becomes more difficult. In general, it will be
necessary to determine the shape of the input wave
form from an oscillograph record.
CAPACITANCE RESISTANCE FILTER
A fourth type of filter that is occasionally used is one
composed of resistance and capacitance elements, in¬
stead of inductances and capacitances. The chief appli¬
cation of this type is to power supplies to give fairly high
voltage and small current. Its advantages are economy,
compactness, and small external field, all of which are
due to the fact that no filter inductances are used. Its
disadvantages are the need for higher transformer volt¬
ages for a given direct-current output voltage and its
poor voltage regulation under variable load. Since
such filters are not ordinarily used with a variable load,
the voltage regulation is not of great importance and it
is usually best to use a capacitance input to the filter,
thus increasing the direct-current voltage obtainable at
Figure 8.— Schematic circuit diagram of capacitance input resistance— capacitance
filter.
the filter input from a given transformer alternating-
current voltage. Figure 8 shows such an arrangement.
The computation of the smoothing action of this
arrangement may be carried out by assuming the input
voltage to have the form given by equation (5) and
solving the network, consisting of Rl R2 . . . Rn and
t\C2 . . . Cn, for the fluctuation components of the
output voltage by the usual methods.
Assuming the resistances of Ri R2, etc., to be large
compared with the reactance of C\ C2) etc., it is pos¬
sible to derive a simplified formula, similar to equation
(3), the general form of which will be
!_0= _ 1 _
et «* (ffiffa . . . /o (C1C2...Cny W
In the instance of the two-section filter of figure 8 this
equation becomes
1 /7N
et a mjRzWi {n
FILTER PERFORMANCE
Regardless of the type of filter involved, its suitability
for a given purpose depends on the magnitude of fluctua¬
tion voltage allowable, which in turn is controlled by the
magnitude of the lowest useful amplifier input voltage.
In the case of turbulence-measuring equipment, 0.001
volt might be set as the lower limit of the range of
voltages to be measured, and it would be desirable to
keep the effect of power-supply hum, at the amplifier
output, less than %0 the reading produced by this
minimum input voltage Emin.
The most important point of introduction of hum in
the amplifier is in the plate circuit of the first tube, and
the voltage introduced here is equal to the hum com¬
ponent of the plate current multiplied by the coupling
resistance of the first tube. That is,
E
JP _ IT} EPS
tLh — ±nc-rr-i
■t^dc
(8)
where Eh is the hum voltage across Rc due to plate
power supply;
I, plate current of first tube;
Rc, coupling resistor of first tube;
Eac, magnitude of principal fluctuation com¬
ponent in plate voltage;
and Edc , the direct-current plate voltage.
Making allowance for possible hum from other sources
by the use of the factor 100 instead of 50, and for the
fact that the input voltage is amplified by the first tube
before it reaches the point where the hum is introduced,
the relation between minimum input and maximum
allowable hum may be written as
' <
tlmax —
AEmir.
100 7
(9)
where Ehmax is the maximum allowable hum voltage
across Rc>
Emin, minimum input voltage,
and Au amplification of first stage.
By the use of equations (2) or (5) with (3), (8), and
(9) it is possible to determine whether or not an existing
rectifier and filter, or a proposed design, will give
satisfactory results. As an example of such a deter¬
mination, consider the power supply for the high am¬
plification stages of the amplifier described in this
report.
This power supply has a three-section inductance
input filter with an output of 400 volts direct current
at 0.016 ampere, working from a full-wave single-phase
rectifier. First, the values
Lx= 40 henries,
AT=25,000 (0.016 ampere at 400 volts),
CO =2t r (120),
and — = 0.667 (from table I),
Cdc
are found to satisfy relation (1). This result indicates
that equation (2) and table I may be safely used to
represent the input wave to the filter. From these
it is determined that the principal fluctuation frequency
of 120 cycles per second (for 60 cycles per second power
supply) will have an input peak magnitude of 267 volts.
488
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The ratio of the magnitude of this fluctuation in the
filter output to its magnitude in the input will be given
from equation (3) by substituting the values Lu L2,
and 73=40 henries, C\ and C2—0. 00002 farad, C2=
0.00004 farad, and u = 2tr (120), and is —=5.35 X 10"9.
@ i
From this the value 1 .43 X 10~G volts peak is obtained as
the magnitude of the principal hum component in the
output from the filter. The ratio of this component
to the direct-current output is then
— =3.75X 10~9.
&dc
Since a resistance voltage divider is used to reduce
the 400-volt direct-current output from the filter to
the 250-volt plate voltage for the first tube, the hum
component will be reduced by the same ratio as the
direct current and the foregoing ratio will remain the
e E
same. That is, — =rr' Substituting this ratio in
Gc -U/ dc
equation (8), with 7=0.001 and 7^=200,000, gives
^ = 7.15X10-7 volts peak, or 5.06X10"7 volts r. m. s.,
which is the hum voltage at the output of the first
tube.
Substituting this value in equation (9) using vl1 = 100
as the amplification of the first stage, and 0.001 volt as
the minimum voltage to be measured, the relation is
satisfied and no measurable hum should be expected in
the amplifier output. Tests of the completed amplifier
verify this conclusion.
In the design of a transformer, rectifier, and filter
combination, various factors influence the choice of
the components used. In this discussion of the prob¬
lem, only the full-wave single-phase rectifier will be
considered, because this is the most common type.
In connection with the filter, little need be said except
that the condensers should be of ample voltage rating
for the voltage to be used and that the filter reactors
should be capable of maintaining the desired inductance
when carrying the direct current required from the
filter. Generally, if the direct-current voltage does not
exceed 400 volts, electrolytic condensers will be satis¬
factory and have the advantage of compactness.
If the peak voltage encountered by the condenser
exceeds 400 volts, as might be the case of an input
condenser in a capacitance input filter, it is best to use
paper dielectric condensers with continuous service
direct-current voltage ratings at least 1.5 times the
peak voltage.
The filter reactors chosen should preferably be
magnetically shielded by heavy cases of cast-iron alloy.
In the selection of the reactors due regard should be
given to their resistance, as well as inductance, espe¬
cially if the filter works into a variable load. Further¬
more, it is well to minimize the effect of load variation
as much as possible by the use of a fairly low-resistance
voltage divider on the filter output, and it is necessary
to consider the current drawn by this resistor, as well
as the load current to the amplifier, when determining
the required current carrying capacity of the reactor.
There is little choice available in the matter of
rectifiers. Two general types may be had in the sizes
suitable for use in power supplies of the type under
discussion, namely, hot cathode mercury vapor recti¬
fiers and high vacuum thermionic rectifiers. Of these
types, the first should be avoided, unless its large current
capacity and low voltage drop are necessary, because
of its tendency to produce high-frequency disturbances.
Tubes such as the type 80, 83V, or 5Z3 will prove satis¬
factory and the choice between them depends only on
the voltage and current required from the rectifier
filter system.
These high vacuum rectifiers have a large and
variable voltage drop, the magnitude of which must be
determined from the characteristics published by the
manufacturer. It is of importance in the determina¬
tion of the transformer voltage necessary to produce
the required output voltage from the system.
The choice of a transformer for use in a given power
supply is based on the direct-current output voltage
desired, the power required, and the type of filter to be
used. Assuming that an inductance input filter is to
be used, the transformer voltage and power capacity
can be determined as follows. From table I it is found
that the required alternating-current voltage from
each end of the secondary winding to the center tap is
1.11 times the direct-current voltage desired, neglecting
the voltage drop in the transformer, filter, and rectifier.
Therefore, to compute the actual alternating-current
voltage required to give the desired direct-current
output voltage, it is necessary to determine these
neglected voltage drops, add them to the desired
direct-current voltage, and multiply by 1.11. In this
computation it is usual to neglect the voltage drop in
the transformer secondary and the effect of transformer
leakage reactance. Both of these factors are small
in any good transformer.
If a capacitance input filter is to be used, the required
alternating-current voltage may be determined in the
same manner as for the inductance input filter case
except that the ratio of alternating-current secondary
voltage to direct-current output voltage must be deter¬
mined from equation (5). Once this ratio is known for
a given filter and load, the rectifier and filter voltage
drop may be added to the desired direct-current output
voltage and the required alternating-current voltage on
each side of the secondary center tap, computed.
The mechanical lay-out of the power supply is not
important. The components, with the exception of the
rectifier tube, may be arranged in any manner that is
convenient. Provision must be made for ventilation
in placing the rectifier tube, and the tube should pref¬
erably be mounted vertically. If the tube must be
mounted horizontally, it should be so oriented that the
filaments do not tend to sag toward the plates.
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 489
III. THE EFFECT OF THE POWER SUPPLY ON
THE AMPLIFIER
In any multistage amplifying system there is a great
difference between the energy levels of the first and
last stages and, if even a very small portion of the
output energy is allowed to return to the input circuits,
the amplification characteristics of the system will be
greatly affected. The most frequent medium for such
back coupling is the internal resistance of a common
power supply, such as illustrated by figure 9. Here it
will be noted that the internal impedance Zc of the
power supply is common to all plate circuits, hence any
voltage drop ec across Zc, caused by the plate current
of one tube, will transfer energy to all the other stages
in the amplifier. Since the plate current of each stage
contributes to the voltage drop ec, and because energy
is transferred to each stage by ec, the exact mechanism
of the action of Zc on the amplifier is a very complex one.
However, Terman has shown (reference 8) that quite
accurate results may be obtained by neglecting the
interaction between all stages but the first and the last.
This procedure is justifiable because the difference in
energy level between any other two stages is much
smaller than that between the first and last. An analysis
of the action of Zc may be made quite easily on this
simplified basis.
Figure 9.— Schematic circuit diagram of multistage amplifier with common plate
voltage supply.
If the schematic circuit of figure 9 is redrawn in the
form of the approximate equivalent circuit of figure 10,
it is seen that the voltage drop across the power-supply
impedance, caused by the amplified alternating currents
in the last tube is
where tx2
Cl,
e2,
rv2,
^1)
and
ec — — fx2e2
Ze
Z0+R2+r
— cox4c = G A i Ac
1>2
(10)
is the amplification factor of last tube;
a. c. input voltage to second stage;
a. c. input voltage to last tube;
load resistance of last tube;
internal impedance of last tube;
amplification between output of first tube
and input to last tube;
Z,
Ac — ecje2 — A<aZe+£2_|_r '
Since the impedance Zc is generally very small com¬
pared with rv and R, the voltage ec may be represented
as a source of negligible internal impedance in series
with the plate circuit of the first tube.
Hence
— l*R , Tp
R-\-r„ R-\~rp
qrr (n)
where e is the alternating-current input voltage to the
amplifier ;
ix, amplification factor of the first tube;
R, load resistance of the first tube;
rp, internal impedance of the first tube;
and A, amplification of first stage, neglecting the
effect of Zf.
f- -~st stage Intermediate stages Last stage
Figure 10.— Approximate equivalent circuit of multistage amplifier with common
plate voltage supply.
Rearranging equation (11) in the form
r„
eA=e i( 1— AiA,
R+r
or
A
1 sUA-
an expression for -=Ae, the effective amplification of
the first stage, is obtained. For convenience of analysis
this expression may be further rearranged by multi¬
plying the right-hand term of the denominator by A,
and bv which is 1 A. That is,
ixn
A =^!=-
A
1—AAiA.
r,> R + >\
R d~ >‘p f-R
or
A£ = -
A
1 ~AA'Arrfi
(12)
The final result is an expression for Ae, the effective
amplification of the first stage, in terms of known or
readily measured characteristics of the amplifier.
These characteristics, with the exception of n, R, and
rp are vectors and must be treated accordingly.
490
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
In this connection it should be noted that A i and A
will either be very nearly in phase or very nearly 180°
out of phase over most of the frequency range of the
amplifier. If an odd number of stages is used in the
amplifier, the plate currents of the first and last stages
will be approximately in phase, and the general effect
of Zc will be an increase in amplification. If the total
number of stages is even, a decrease in amplification
will occur. In either case the modification of amplifi¬
cation is not likely to be uniform over the frequency
range of the amplifier because Zc will generally be
reactive in character and hence will change in magni¬
tude and phase angle as the frequency changes, thus
changing Ac and, through Ac, the effective amplifica¬
tion Ae of the first stage.
T1 iree general methods may be employed to eliminate
or reduce the effect of Zc on the amplification. First,
Zc may be entirely eliminated by the use of separate
power supplies. Second, its effect may be reduced by
making Zc unimportantly small over the frequency
range of the amplifier. Third, filters may be inserted
in each plate circuit to reduce the common coupling
effect of Zc.
The first method is, of course, the most satisfactory
as far as ease of obtaining the desired result is concerned
but has the disadvantage of requiring several power
supplies. However, the stages most likely to give
trouble are those of the high-gain amplifier, and these
stages generally have very modest power requirements.
If advantage is taken of this fact and individual power
supplies with small low-current high-voltage trans¬
formers and resistance capacitance filters are used, it
may be possible to provide the required number of
power supplies in the available space and without ex¬
cessive cost. Sometimes it will be found that the
desired result may be obtained by providing a separate
power supply for only the first stage.
The second method depends for its practicability on
the fact that Ze in most rectified alternating-current
power supplies has a predominantly capacitive react¬
ance. It is possible to make the alternating-current
voltage drop across Zc negligible throughout the high-
and medium-frequency ranges and well into the low-
frequency range of the amplifier by shunting the output
terminals of the power supply with suitably large values
of capacitance. However, as the frequency is lowered,
the effect of Zc will eventually become very evident,
usually as a violent low-frequency oscillation of the
amplifier if an odd number of stages is used or, as a
marked lack of low-frequency amplification, if the
number of stages is even. Because of this difference in
the effect with odd and even numbers of stages, slightly
different remedies are usually employed in its elimina¬
tion.
If the number of stages is odd, the usual method of
attack is to add enough capacitance across Zc to cause
the frequency at which its effect becomes troublesome
to be lower than the lowest frequency that it is desired
to amplify. The amplifier is then so arranged, for
instance, by reduction of coupling capacitance, that its
amplification decreases rapidly for frequencies less than
the desired lower limit; that is, in the frequency range
where Zc begins to have an important effect. By a
suitable balance of the increase in amplification due to
the effect of Zc against the decrease in amplification
introduced into the amplifier to counteract the effect
of Zc, it is often possible to extend the lower limit of
useful amplification to a considerably lower frequency
than the constants of the amplifier circuit alone would
indicate.
If the number of stages is even, the only solution is
to add sufficient capacitance to the power-supply output
terminals to make Zc so small that its amplification
reducing effect does not become important at the lowest
frequency it is desired to amplify. In the case of
turbulence-measuring equipment, or any amplifier to be
used at very 1owt frequencies, this method requires very
large values of capacitance. However, since the output
voltage of the power supply is usually not over 400
Figurl 11. — Schematic circuit diagram of multistage amplifier with common plate
voltage supply and decoupling filters.
volts, it is generally possible to use electrolytic capaci¬
tors and thus obtain large values of capacitance without
undue bulk or expense.
Generally, it will be found necessary to provide a
separate power supply for the final stage of the system
because of the comparatively large drop across Zc pro¬
duced by the large alternating-current component in
the plate current of this stage. Power supplies for the
remaining stages may be provided as convenience or
necessity dictate. Usually if an excess of amplification
exists in the system, as was the case in the amplifier of
figure 3, the desired performance may be obtained most
easily by connecting even numbers of stages to the same
power supply. If no amplification may be sacrificed, it
may be necessary to arrange the circuit so that each
power supply serves an odd number of stages.
The third method for eliminating the effect of Zc, the
use of “decoupling filters” is illustrated by figure 11
and by the approximately equivalent circuit of figure
12. This method depends for its operation on the
insertion of a resistance RF in series with each plate
circuit, and the use of capacitances CF connected be¬
tween the junction of the load resistors R, Rh R2, etc.,
with RF, and the zero potential side of the circuit.
ALTERNATING-CURRENT EQUIPMENT FOR THE MEASUREMENT OF FLUCTUATIONS OF AIR SPEED 491
The function of the capacitors CF is to provide a low-
impedance path to ground for the alternating-current
components of the plate current of each tube. The
function of the resistors RF is to insert a high impedance
between the bypass circuits and Zc, the common cou¬
pling element of the circuit, thus helping to confine the
alternating-current components to the bypasses and to
keep them out of Zc.
The performance of the amplifier power supply com¬
bination, when such filters are used, may be estimated
by use of equation (12). It is necessary, however, to
solve the circuit of figure 12 for an appropriate ex¬
pression for Ac. If this solution is accomplished,
using the same resistance for both resistors RF and the
same capacitance for both capacitors CF, it is found
that
(13)
A ~-c —
- -
M2
XAZr.
e (rP2+R2) (. RF+Xcy2+Zc[2 (rP2+R2) (flr+Xe)+Xc(2Rr+Xe) +RFXC{R+Xe)]
where RF is the resistance of decoupling filter
resistors,
and Xc is the reactance of CF=~ L-v •
1-kJL f
The other symbols have the same significance as in
equation (12). If dissimilar resistances are used for
the resistors RF or dissimilar capacitances for capacitors
CF, an equivalent, but more complicated, expression
may be derived.
lie
-AAAAA/V — r - VWWV-
R, ru R
a
*
R>
I p
Cf
-Rtez A
=-fj, e:.4:U
J
Figure 12.— Approximate equivalent circuit of multistage amplifier with common
plate voltage supply and ‘'decoupling” filters.
Because the decoupling filter action depends on the
maintenance of a high ratio of RF to Xe, this system
also becomes ineffective at very low frequencies, unless
large values of capacitance are used at CF. The system
is one that is widely used, however, and, if the output
voltage of the power supply is great enough so that
high voltage drops in RF can be tolerated, the filters
can be made effective at any reasonable desired low
frequency. The usual procedure is first to make the
output voltage from the power supply as high as is
is economically possible, then to drop this high voltage
to that needed for proper operation of the amplifier by
making RF large, and finally to add capacitance at
CF until the desired low-frequency performance is
obtained.
If an even number of stages is used in the amplifier,
the decoupling filters tend to give somewhat better
results than might be indicated by equations (12) and
(13), because as the frequency is decreased, Xc increases,
and its bypassing action decreases. This result allows
RF to become increasingly a part of the load resistance
of the stage concerned, which in turn increases the
amplification of that stage, thus tending to offset the
decrease in amplification which would normally occur
due to the action of Zc. If an odd number of stages
are used, this effect becomes a detriment rather than
an advantage because the effect of Zc is then to increase,
rather than to decrease, the amplification.
Of the three described methods for eliminating the
common coupling effect of the power supply on a
multistage amplifier, the first is undoubtedly the surest
and most satisfactory, especially if extremely low
frequencies must be amplified. The second method
is the simplest, where practicable, and should always
be attempted before resort to more complicated systems.
The third method is a very useful one, especially where
amplification at only moderately low frequencies is
necessary.
In the description and analysis of the action of the
power supply on the amplifier, as outlined here, it
has been assumed that the tubes used were triodes.
The results may be extended to multigrid tubes
because, in general, the extra elements are at zero
potential to the alternating-current components of the
voltages being amplified, and the tubes became equiva¬
lent triodes.
When the extra element, for example, the screen grid
of a pentode or tetrode, must be maintained at some
positive direct voltage, it may be connected either to
a tap on the plate voltage power supply or to a separate
power supply. In either case some impedance will exist
between the point of connection and the zero potential
side of the circuit and, if several tubes are connected to
the same supply, a state very similar to that discussed in
connection with the plate power supply will exist. Each
tube will then act as a triode composed of the regular con¬
trol grid, the cathode, and the screen grid acting as an
anode and will have a load impedance consisting of the
impedance of the screen voltage power supply, which
also acts as a common coupling link between tubes.
Fortunately, the conditions will usually be such that
the amplification of these accidental triodes will be
quite low, and their effect on the main amplifying action
of the amplifier will be still lower. The effect may
become troublesome, however, and provision for its
elimination should always be incorporated in either the
amplifier or the power supply. Since the screen voltage
required is usually of the order of only 50 volts, condi¬
tions are ideal for the application of the decoupling
filter method. Excellent decoupling action may be
492
REPORT NO. 598— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
obtained by dropping the full power supply output
voltage down to the required screen voltage through a
very high resistance and by using a large bypass capac¬
itance between the screen and the zero potential part
of the amplifier circuit. Quite often it will be necessary
to use this method only in the first stage of the ampli¬
fier, as is the case in the amplifier of figure 3. The
remaining stages may usually be supplied with screen
voltage from a tap at the proper point on the power
supply voltage divider. This tap should be bypassed
to the negative terminal of the power supply by a very
large capacitance. Because of the low voltage involved,
electrolytic condensers are especially suitable for tliis
service.
PRACTICAL DESIGN PROCEDURE
Iii the design of an amplifier and power-supply com¬
bination, due consideration should be given to the
factors discussed and every effort be made to arrive at
a suitable design before construction. It should not,
however, be expected that the completed system will
prove to be free from trouble. So many unknown and
undeterminable factors are involved in such a highly
complex problem as a three or more stage amplifier with
two or more power supplies, that the approximations
necessary usually fall short of complete validity. In
general, the best that may be hoped for is an amplifier
that may be made satisfactory by minor changes of
circuit constants, rather than by complete recon¬
struction.
Such an amplifier having been obtained, the proced¬
ure to be used in the adjustment of its characteristics is
one of the cut-and-try type. Each amplifier is a unique
problem and must be treated as such. As an example,
the procedure in the case of the amplifier and power,
supply system of figure 3 will be considered.
This apparatus was originally intended to consist of
three high-amplification stages operating from one
power supply and a phase inverter-output stage com¬
bination on a separate power supply. Upon comple¬
tion it was found that the three-stage amplifier had
excessive low-frequency amplification and that the
phase inverter-output stage combination was unstable.
By trial it was found that the instability could be cured
by using separate power supplies. With this end in
view, the phase inverter was attached to the same
power supply as the first three stages and, in addition
to curing the trouble in the phase inverter-output
stage combination, this change greatly reduced the low-
frequency distortion of the first three stages.
Further reduction of the frequency distortion in the
first four stages was obtained by changing the screen
voltage supply circuit so that the first tube received
its screen voltage through a 1-megohm dropping
resistor from the 250-volt plate voltage supply, instead
of from the 50-volt tap on the power supply voltage
divider. It was found necessary to use a paper dielec¬
tric condenser for the bypass at the screen grid of the
first tube because of the large voltage fluctuations that
resulted when an electrolytic condenser, with its more
variable leakage resistance, was used. For the 100-
microfarad bypass condenser across the 50-volt tap
for the screen voltage of the other tubes, electrolytic
condensers proved satisfactory.
Tests now indicated that the frequency character¬
istic of the complete amplifier system was satisfactory,
except for a slight loss of amplification at the lower
frequencies, but that the over-all amplification was
excessive. By a reduction of the amplification at the
grid of the fourth stage, thus at the same time producing
a reduction of the current through Zc, it was possible
to bring the over-all amplification to the desired level
and to improve the frequency characteristic. The final
result is illustrated by figure 5.
CONCLUDING REMARKS
It is hoped that the material presented will prove
useful to others faced with the problem of designing
similar apparatus. No attempt has been made at an
exhaustive treatment. The aim, rather, has been to
present, under one cover, sufficient data so that a person
not particularly familiar with the design of such
apparatus may proceed on a sound basis. For addi¬
tional information the reader should refer to any of the
standard works on communication engineering, for
instance, reference 8.
National Bureau of Standards,
Washington, D. C., March 1937.
REFERENCES
1. Dryden, H. L., and Kuethe, A. M.: The Measurement of
Fluctuations of Air Speed by the Hot-Wire Anemometer.
T. R. No. 320, N. A. C. A., 1929.
2. Dryden, H. L., and Kuethe, A. M.: Effect of Turbulence in
Wind Tunnel Measurements. T. R. No. 342, N. A. C. A.,
1930.
3. Mock, W. C., Jr., and Dryden, H. L.: Improved Apparatus
for the Measurement of Fluctuations of Air Speed in
Turbulent Flow. T. R. No. 448, N. A. C. A., 1932.
4. Schubauer, G. B.: A Turbulence Indicator Utilizing the
Diffusion of Heat. T. R. No. 524, N. A. C. A., 1935.
5. Schubauer, G. B., and Dryden, H. L.: The Effect of Turbu¬
lence on the Drag of Flat Plates. T. R. No. 546,
N. A. C. A., 1935.
6. Dryden, Hugh L.: Air Flow in the Boundary Layer of a
' Plate. T. R. No. 562, N. A. C. A., 1936.
7. Dryden, Hugh L., Schubauer, G. B., Mock, W. C., Jr., and
Skramstad, H. K.: Measurements of Intensity and Scale
of Wind-Tunnel Turbulence and Their Relation to the
Critical Reynolds Number of Spheres. T. R. No. 581,
N. A. C. A., 1937.
8. Terman, F. E.: Radio Engineering. McGraw-Hill Book
Co., Inc., 1932.
REPORT No. 599
FLIGHT TESTS OF THE DRAG AND TORQUE OF THE PROPELLER
IN TERMINAL- VELOCITY DIVES
By Richard V. Rhode and Henry A. Pearson
SUMMARY
The drag and torque oj a controllable propeller at various
blade-angle settings, and under various diving conditions,
were measured by indirect methods on an T6C-j airplane
in flight. The object oj these tests was ( 1 ) to provide data
on which calculations of the terminal velocity with a
throttled engine and the accompanying engine speed
could be based and (2) to determine the possibility oj
utilizing the propeller as an air brake to reduce the terminal
velocity.
The data obtained were used in the establishment oj pro¬
peller charts, on the basis oj which the terminal velocity
and engine speed could be calculated jor airplanes whose
characteristics jail within the range of these tests. It was
found that the propeller reduced the terminal velocity
about 11 percent with the normal blade-angle setting oj
19.0° and about 85 percent with a 5.5° setting. Indica¬
tions were that the terminal velocity could be still further
reduced by using even lower blade-angle settings. A
method is given jor the calculation of the terminal velocity
with throttled engine and the engine speed.
INTRODUCTION
In cooperation with the Bureau of Aeronautics, Navy
Department, and the Army Air Corps, the National
Advisory Committee for Aeronautics has been making
a study of rational methods for establishing the struc¬
tural design conditions for airplanes. In the course of
this study, a method was established in 1930 for cal¬
culating the terminal velocity of a diving airplane,
taking propeller drag into account. The method was
based on the results of small-scale propeller tests by
Durand and Lesley (references 1 and 2), supplemented
by the then unpublished results of a few tests of a 4-foot,
metal propeller in the N. A. C. A. propeller-research
tunnel. Because of insufficient data on torque or power
coefficients from these tests, no provision could be
included for calculating the engine speed and the
method was therefore based on the assumption of such
an engine speed, which, for structural-design purposes,
was limited to an arbitrary permissible value.
The interest aroused in this work because of the
increasing use of the terminal-velocity dive in military
tactics led to an extension of the study to determine the
feasibility of using the propeller as an air brake to reduce
the terminal velocity. As a result, the wind-tunnel tests
of the 4-foot propellers were extended to include tests
at the lower blade-angle settings and with different
propeller-body combinations. At the same time, a
program of dive tests to be made of a conventional
airplane with a controllable propeller was formulated,
the purpose of which was to evaluate the influence of the
propeller under full-scale conditions at the high tip
speeds associated with a terminal-velocity dive. The
present report presents the results of the flight tests
in a usable form for the quantitative determination of
the influence of the propeller on the terminal velocity
and the engine speed.
The flight tests were made in September 1932 by the
N. A. C. A. at Langley Field, Va.
APPARATUS AND METHOD
A Navy F6C-4 airplane equipped with a Pratt &
Whitney R-1340-CD engine was used in these tests.
The pertinent data concerning this airplane arc given in
table I and a general view is given in figure 1 . The
propeller used was the Hamilton controllable model
described in reference 3. This propeller was not com¬
pletely adjustable in flight, as it could be set at only
two positions, the locations of which depended upon
the setting of stop nuts. As delivered, the range of
blade-angle settings available was between 13° and 22°,
which range was extended down to 5° for these tests
by the use of special links. The pitch-changing mecha¬
nism consisted of a hydraulic piston and centrifugal
weights, which actuated the blades through a system of
push-pull rods. The action of the centrifugal weights
tended to increase the blade angle; the engine-oil pres¬
sure, when acting on the piston, forced the blades to the
lower setting.
The airplane was equipped with four synchronized
standard N. A. C. A. photographically recording instru¬
ments — air-speed meter, tachometer, altimeter, and
air-temperature thermometer — and a dive-angle indi¬
cator developed especially for these tests.
The diagram of figure 2 shows the simplicity of the
dive-angle indicator. Its principal merit lies in the
fact that it is not affected bv accelerations, as its
operation depends upon the reflection of a ray of sun¬
light onto a frosted-glass scale.
493
494
REPORT NO. 599— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The air-speed head was mounted at the outer strut
location on a boom one chord length forward of the
leading edge of the wing, in order to reduce the inter¬
ference on the air-speed measurements to a minimum.
The air-speed installation was calibrated over a speed
course, and a constant error of 2 percent for speeds
between 130 and 150 miles per hour was found. It was
assumed that the correction for the diving conditions
was also 2 percent.
From data obtained in high-speed level flight the
minimum drag coefficient of the airplane was calculated.
where W, weight of the airplane.
7, flight-path angle.
C Dmxn, minimum drag coefficient of the airplane.
q, dynamic pressure corresponding to the desired
zero-thrust or basic terminal velocity.
Sw, wing area.
In order to obtain these dive angles in the flight tests,
a curve of the elevation of the sun against time was
plotted, and a pointer on the dive-angle indicator was
set to indicate the proper dive angle corresponding to
the elevation of the sun existing at the instant the dive
Figure 1.— The F6C-4 airplane.
The method employed consisted of deducting the
calculated induced drag from the total drag, which had
been evaluated from the known engine power and the
estimated propeller efficiency. On the basis of a study
of full-scale propeller-body tests, the propulsive efficiency
was estimated in this case to be 75.5 percent.
The main tests consisted of terminal-velocity dives,
with the engine fully throttled and with the ignition
on, starting at 12,000 feet and continuing to approxi¬
mately 5,000 feet altitude. The dives were made at
various predetermined dive angles to simulate con¬
ditions for airplanes of various zero-thrust or “basic”
terminal velocities. For each basic terminal velocity,
tests were made with propeller blade-angle settings of
5.5°, 9.5°, 14.5°, 19°, and 22.5° at 0.75 radius.
The dive angles at which the tests were made were
determined from the relation
^DminqSio
was to be started. Continuous records of indicated air
speed, engine speed, air temperature, and barometric
pressure were taken throughout all the dives.
PRECISION
The corrected dynamic pressure measurements at ter¬
minal velocity are probably accurate to within 2 per¬
cent. During the entry into and accelerated portions
of the dive, the precision may be slightly less because
of lag in the air-speed system. The tachometer read¬
ings are correct to within 30 r. p. m. Barometric pres¬
sures were measured to a precision of about 2 percent,
and the temperature to about 2° C. The maximum
error in the dive angle was about 2° and was caused
primarily by the inability of the pilot to maintain the
airplane in a steady condition at all times.
RESULTS
The recorded measurements were first plotted as time
histories of the cpiantities measured, to insure proper
THE DRAG AND TORQUE OF THE PROPELLER IN TERMINAL-VELOCITY DIVES
495
evaluation of these quantities at the terminal velocity.
A representative time history is shown in figure 3. From
curves such as these, the indicated terminal velocities
Figure 2.— Dive-angle indicator. Prism has blackened surface with horizontal
scratch. In operation, pilot heads into the sun so that light through the slit in the
hood makes a vertical image on the frosted glass. He then pushes into a dive until
the horizontal image reaches a predetermined mark on the scale.
and the accompanying engine speeds were obtained.
These quantities were then plotted against the appro¬
priate blade-angle settings for each of the basic terminal
velocities, as shown in figure 4. No flight-test points
Figure 3. — Time history of a vertical dive. Blade-angle setting, 14.5° at 0.75 R.
are shown in this figure, as these curves are the results
of cross-fairing an intermediate set of curves of the
measured values. This cross-fairing was necessitated
by the fact that the pilot found it impossible in some
cases to dive at exactly the specified time, with the con¬
sequence that the angle of dive did not correspond to
an integral value of basic terminal velocity. The
engine speeds given in figure 4 are those for a standard
sea-level density. The engine speed at any other alti¬
tude can be obtained by multiplying these values by
the square root of the ratio of the sea-level density to
the density at altitude. It is assumed that the indi¬
cated terminal velocity does not change materially with
altitude.
Figure 4.— Variation of engine speed and terminal velocity with propeller blade-
angle setting for different zero-thrust velocities. The engine speeds are corrected
to standard sea-level density. The parameter is zero-thrust terminal velocity.
The variation of air speed with engine speed during a
number of dives is shown in figure 5. Two runs, repre¬
senting the extreme values of the dive angles at which
the tests were made, are shown for each blade-angle
setting.
DISCUSSION
From figure 4 it can be seen that the terminal velocity
decreases with blade-angle setting for the range investi¬
gated. Indications are that a further decrease in pitch
would lower the limiting velocity still more. However,
there is a critical value where a decrease in terminal
velocity no longer accompanies a decrease in blade-
angle setting, unless power is used to increase the
engine speed. This fact is not apparent from the curves
of figure 4, as the range of blade-angle settings could
not be extended sufficiently low with the propeller
used in these tests. The engine speed at terminal
velocitv increases as the blade angle decreases, down
496
REPORT NO. 599— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
to about 8°; thereafter, the engine speed decreases
with decreasing blade angle.
There is some doubt whether the 22.5° points are
correct, since there is a reversal in curvature between the
19.0° and 22.5° settings. Further, on the ground with
the stop nuts set for 22.5° the engine speed was not
sufficient for the centrifugal force to bring the blades
quite against the stops. As the airplane was available
for only a limited time, there was no opportunity to
Figure 5.— Relation between engine speed and air speed for several dives made with
the F6C-4 airplane.
construct t he apparatus necessary to determine whether
the blades were actually against the stops during the
dives.
The significance of the curves in figure 5 is that the
value of n/V at which the propeller operates during the
major portion of any throttled dive is approximately
constant, if the influence of tip speed is neglected, it
may be said that the thrust coefficient is also nearly a
constant, since the propeller, for a given blade-angle
setting, operates at roughly the same value of nD/V.
The over-all drag coefficient, which is the sum of the
airplane and propeller drag coefficients, is thus approxi¬
mately constant throughout any dive. This relation
suggests that methods for the determination of time-
altitude and velocity-altitude relations may be con¬
sidered sufficiently precise for practical purposes if
based on the assumption of a constant drag coefficient,
which, of course, should include a proper allowance
for the propeller.
DERIVATION OF PROPELLER CHARTS
The coefficients that were found to be most adaptable
for reducing propeller data in the negative range are
defined as follows:
and
Q = — 9 -
Vc pV2D3
where T is the propeller thrust, lb.
Q, propeller torque, lb. -ft.
D, propeller diameter, ft.
V, air speed, ft. per sec.
p, mass density of air, slugs per cu. ft.
These coefficients were computed from the corre¬
sponding values of thrust and torque evaluated from
the following relations:
T= W sin y-0D„Jr£s.
.. 550 f.hp.
2irn
in which f.hp. is the friction horsepower of the engine
and the other symbols have their usual significance.1
The experimental thrust and torque coefficients so
computed for the 14.5° blade-angle setting are shown
plotted against nD/V in figure 6. It will be noted that
the points for the various dives made with this setting
fall at nearly the same value of nD/V; further, it will
be seen that the vertical displacement of the points
tends to vary with tip speed. Results for the other
blade-angle settings are similar in character to those for
the 14.5° setting, but occur at different values of nD/V
as indicated by the dashed lines of figure 7, which give
the median lines through the test points for different
blade-angle settings.
Because of the close grouping of the test points at
each blade-angle setting, the establishment of a pro¬
peller chart (fig. 7) was necessarily based in part on in¬
formation from other sources. The method and mate¬
rial used in establishing this chart are explained in the
folio win g pa ragraplis .
The form of the propeller-characteristic curves was
determined from the tests by Durand and Lesley and
from the unpublished results of the tests made in the
‘The friction horsepower used in these computations was obtained from a 50-hour
endurance test of the Pratt & Whitney “Wasp” aircraft engine. The results are
shown in fig. 9. The friction-power characteristics existing under the flight-test
conditions may, for a number of reasons, have been at variance with the characteris¬
tics determined under the conditions of the engine test. Any such disagreement, of
course, results in erroneously derived torque coefficients but, as will be shown later,
these errors have a negligible influence on the terminal velocity calculated from the
charts and only a small influence on the engine speed.
THE DRAG AND TORQUE OF THE PROPELLER IN TERMINAL-VELOCITY DIVES
497
propeller-research tunnel. The quantitative establish¬
ment of the curves involved: (1) determination of the
end points on the basis of data from outside sources;
rxD
V
0 .2 .4 .6 .3 1.0 1.2 1.4
Figure 6— Measured thrust and torque coefficients. Blade-angle setting, 14.5° at
0.75 R. All points labeled for tip speed.
(2) fairing of curves through the F6C-4 dive-test points;
(3) establishment of tip-speed corrections, which were
based largely on the dive-tests results but partly on
tests in the propeller-research tunnel (reference 4).
The end points of the Tc curves at zero nD/V were
established on the basis of a consideration of Diehl’s
formula (reference 5), Lock’s formula (reference 6), and
the data given in reference 7. The quantitative values
chosen represent a weighted mean of the data obtained
from the three sources. The end points of the Qc
curves at zero nD/V were based entirely on the data of
reference 7, which were the only data available.
Values of nDJV at zero Tc and Qc were partly estab¬
lished by calculations based on the assumption that the
aerodynamic characteristics of the blade element at
0.75 radius, considered as an airfoil, represent the action
of the propeller as a whole in a condition near zero
thrust. For these calculations the angle of zero lift
was determined by Munk’s method, given in reference
8. Since these points are affected appreciably by
interference from the fuselage, consideration was also
given to the slopes of the curves of reference 7, with an
estimated allowance for fuselage interference, in com¬
bination with the requirement that the curves pass
through the experimental points from the dive tests.
The propeller-characteristic curves were passed
through these end points and through the experimental
points (tip speed less than 1 ,050 feet per second) ob¬
tained in the dive tests. As thus drawn, the curves
are applicable to cases involving propellers having the
proportions of the one used in the dive tests.
In order to make the curves more convenient to
apply, they have been corrected to a mean blade-width
ratio of 0.1, as presented in figure 7. (Mean blade-
width ratio is defined as the ratio of the mean blade
498
REPORT NO. 599— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
width between 0.2 R and R to R, where R is the radius.)
The mean blade-width ratio is a measure of the blade
area when the diameter is known. This area must be
taken into account in applying a single general set of
propeller characteristics to any particular case, in the
same manner that the wing area must be taken into
account in dealing with wing forces. The coefficients
therefore vary directly with the blade area or with the
mean blade-width ratio. Since the curves of figure 7
apply to propellers having a mean blade-width ratio
of 0.1, the coefficients must be multiplied by the ratio
of the actual mean blade- width ratio to 0.1 when using
the curves for any other case.
The curves of figure 7 are labeled for blade-angle
setting in degrees at 0.751? for metal propellers based
on either the Clark Y or KAF-6 sections. In order to
make the charts more general, values of V/nD for zero
thrust are given in two forms, either one of which may
be used in lieu of blade-angle setting for selecting the
curves in cases involving sections other than the
Clark Y or KAF-6. Measured values of V/nD for
zero thrust should be used only if the measurements
have been made with the proper body interference.
Computed values are determined on the basis of a
setting determined at the 0.75 R section and with the
zero-lift angle of that section found by Monk’s method
as given in reference 8.
TIP-SPEED CORRECTION FACTORS
As given in figure 7, the propeller characteristics
apply only to cases in which the tip speeds are below
the critical value, and they agree well with the flight-
test data only for such cases. When the tip speed is
above the critical value (approximately 1,050 feet per
second), which is the usual case in a dive, the char¬
acteristics are different from those given in figure 7.
This effect is apparent from figure 6, where the points
shift with increasing tip speed. In general, it may be
said that there is, for a given propeller and propeller
load, a separate set of characteristics for each tip
speed above the critical value. The characteristics
will, in general, also vary with load at a given tip
speed because of variations in the blade deflection
with changing load. The characteristics at the higher
tip speeds may be determined approximately by intro¬
ducing conversion factors, which can be used to trans¬
form the basic characteristics into those applicable at
various tip speeds above the critical value. A method
used in determining such conversion factors on the
basis of the F6C-4 data follows.
It can be shown qualitatively that as the tip speed
increases above the critical value, the value of nDjV
for a given value of Tc also increases. Further, it
can be shown that at a given value of nDjV the value of
Qc decreases numerically with increasing tip speed
above the critical value. These considerations imply
that as the tip speed increases above the critical value,
the curves of Tc are shifted to the right and the curves
of Qe are shifted upward. The conversion factors
evolved are based on these considerations with their
numerical values determined by comparing results
calculated from the characteristics of figure 7 with the
experimental results.
Specifically, the terminal velocities and the engine
speeds were calculated for the various dive angles,
using as given data the measured weight and the drag
coefficient of the airplane, the friction-horsepower
curve of the engine, and the propeller characteristics
of figure 7. The factors necessary to convert the
calculated engine speeds to the experimental values
were plotted against tip speed. The mean curve
drawn through these points is the conversion curve for
nDJV. In a similar manner, conversion factors for
J-2
o
1 8
o
Cb
b -6
£
4
_ _
nD/V
'
—
*■** . _
Qc
'
1000
UOO 1200
1300
Tip speed, f.p.s.
Figure 8. — Correction factors for tip speed.
Qc at the corrected values of nD/V were plotted to
give a conversion curve for Qc. These conversion
factors include both -the influence of blade deformations
with changing load and the influence of tip speed.
They are shown in figure 8.
APPLICATION OF CHARTS TO THE CALCULATION OF
TERMINAL VELOCITY
PRINCIPLES INVOLVED
The fundamental principles involved in any calcula¬
tion of terminal velocity where propeller drag is to be
taken into account are: (1) At terminal velocity the
component of weight along the flight path must equal
the total drag; (2) the shaft power of the propeller
must equal that absorbed in friction by the engine.
Obviously, the point of intersection of the curves of
shaft power of the propeller and of power absorbed in
friction by the engine, plotted against velocity, meets
the conditions required.
Specifically, the following procedure is employed, in
the calculation of terminal velocity and engine speed:
1. Assume a series of terminal velocities in the in¬
terval given by the following formula whose solutions
roughly approximate the F6C-4 data:
Vt{nd=K(0.0178 0+0.89 ±0.05)
where V , is the indicated terminal velocity, in miles
‘ind - 7
per hour.
K, the indicated terminal velocity with zero
thrust, in miles per hour.
THE DRAG AND TORQUE OF THE PROPELLER IN TERMINAL-VELOCITY DIVES
499
9, the difference, in degrees, between the nor¬
mal high-speed blade-angle setting and
that on which the calculations are based.
The angle 9 is positive when the blade-
angle setting under consideration is
larger than the normal setting.
2. Compute Tc for the series of assumed velocities
from the formula
U sin ~SU
PV2D2
3. At the appropriate blade-angle setting obtain from
figure 7 the values of nD/V and Qc corresponding to the
computed thrust coefficients.
4. Compute the values of n from the known values
of nD/V, 1), and 17
5. Compute the propeller torques from the formula
Q = QcPV>&
6. Using the computed values of Q and n, compute
the shaft horsepower of the propeller from the formula
p _ 2 irQn
1 ~ ~55(U
7. Plot the results from step 6 against those from
step 1.
8. Plot the friction horsepower of the engine against
the velocities of step 1.
The curve of power absorbed in friction by the engine
against velocity is obtained from a curve of friction
horsepower against engine speed using the values of
n from step 4. The intersection of the two curves gives
the point satisfying the conditions and is the calculated
terminal velocity. The speed of the engine can be
found by plotting the computed values of n against the
assumed velocities and finding n existing at the calcu¬
lated terminal velocity. The foregoing procedure
involves no corrections for tip speed or mean blade-
width ratio. The manner in which these corrections
are applied is best shown by an illustrative example.
A complete series of calculations will not be given but
a sample computation using the final calculated termi¬
nal velocity for an F6C 4 airplane will be used.
ILLUSTRATIVE EXAMPLE
Given:
Airplane _ F6C-4.
Weight (IF) _ 2,830 lb.
Wing area ( Sw ) _ 252 sq. ft.
Minimum drag coefficient
(CD . ) _ 0.0513.
v umin'
Engine _ Pratt & Whitney
R-1340-CD.
Friction-horsepower
(fig. 9)
c u r v e
Engine speed, r.p.m.
Figure 9. — Friction horsepower for P. & W. R-1340-CD engine.
Propeller:
Diameter ( D ) _ 9 ft.
Mean blade-width ratio _ 0. 123.
Blade-angle setting at
0.75 R _ 19.0°.
It is required to find:
1. The indicated terminal velocity in a vertical
dive (y = 90°) at 3,000 ft.
2. The propeller revolution speed at terminal
velocity at this altitude.
Assume Vt.nd = 258.2 m. p. h.
= 378.9 f. p. s.
q = 170. G Ib./sq. ft.
Negative propeller thrust, T— W sin y—CDminqSw
T=2830X 1—0.0513X170.6X252 = 623 lb.
T JL. JL 623 n99r9
c PV2D 2 2 qD2 2X170.6X81 °w
Tc corrected to mean blade-width ratio of 0.1 to allow
0 1X0 02252
entry into charts= - ^ ^9 - =0.01831
~ at Tc=0.01831 for 19.0°=0.940 (fig. 7).
0.940 X378.9XVWP ,,
n— - q — ~ — 1 — ^ — =41 .35 r. p. s.
■yj po/ p at 3,000-foot altitude= 1.045 (reference 9).
Tip speed = V {^Dri) 2 + p0/p Vt Ul(l2 =1,235 f. p. s.
Correction factor for ^^=1.038 (fig. 8).
Correction factor for Cc=0.80 (fig. 8).
Corrected 1.038 X0. 940=0.975.
Corrected n—n'= 1.038X41.35=42.9 r. p. s.
(r. p. m.y =60X42.9=2, 575.
Qc at —y- =0.00094 (fig. 7).
Q,c corrected for tip speed = 0.80X0.00094 =0.000752.
500
REPORT NO. 599— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Qc corrected to mean blade-width ratio, 0.123
0.123
0.1
X
0.000752 — 0.000925.
Q=QC 2 q D*= 230 lb. -ft.
Shaft horsepower of the propeller, P
2-irQn'
”550
113.0.
At a value of n equal to 42.9 r. p. s. and an engine
speed of 2,575 r. p. m., the horsepower absorbed in
friction by the engine, using the engine friction-horse¬
power curve, is 113.5. Since the conditions of equi¬
librium are satisfied, i. e., the total drag equals the
weight and the shaft horsepower of the propeller equals
that absorbed by the engine, the indicated terminal
velocity is 258.2 miles per hour and the engine speed is
2,575 r. p. m.
If, in the preceding example, the problem had been
solved for a minimum altitude of 6,000 feet, the values
for the indicated terminal velocity would have been
258.0 miles per hour, and the accompanying engine
speed, 2,676 r. p. m. The influence of air density on
the indicated terminal velocity is seen to be slight, but
its influence is appreciable on the engine speed, which
varies approximately inversely with the square root of
the density.
It has been previously stated that errors in the
friction-horsepower curve have but a small influence
on the final result. A critical analysis, based on figure
7, of the interrelations of the several variables involved
indicates that this statement is true for all reasonable
cases. It is perhaps sufficient here, however, to point
out that in figure 7 the steepness of the Qc curves in
the neighborhood of the dotted line indicates that
fairly large variations of Qc may occur without greatly
affecting the engine speed at given values of D and V.
At the same time, small variations in nD/V do not
result in as large a change in thrust. Hence, it would
bo expected that quite large variations in friction horse¬
power can be taken up by the propeller without greatly
affecting either the engine or the airplane speed. As
an extreme example, if the friction horsepower of the
engine used in the illustrative example is doubled, the
terminal velocity is found to be 256 miles per hour and
the engine speed about 2,400 r. p. m. These values
compare with the original values of 258.2 miles per
hour and 2,575 r. p. m., differing by 0.85 percent and
6.8 percent, respectively.
It has been found, in most cases, that the propeller
operation in a throttled dive will be defined by char¬
acteristics falling close to the dotted lines of figure 7.
To operate at greatly lower values of nD/V for any
blade-angle setting would require an abnormally small
propeller, while to operate at much higher values would
require the application of engine power.
table II. This comparison merely indicates the degree
to which factors other than those included in the method
of calculation affect the result. Part of the discrep¬
ancies are, however, attributable to experimental
error. It will be seen that the percentage error in the
terminal velocity is small, the maximum being 4.3
percent, while the average is less than half that value.
The average errors in the engine speed are slightly
higher, with the maximum error 6.8 percent. As these
comparisons cover a wide range of blade-angle settings
and dive angles, the agreement is considered to be
reasonably good.
Table III includes a comparison between calculated
and experimental results for three airplanes on which
data were available. The agreement for airplanes A
and B is good in regard both to terminal velocity and
engine speed. These airplanes were somewhat similar
to the F6C-4 airplane in their general features; in
particular, the power plants were of the same type and
the performances were similar. Hence, a good agree¬
ment between the calculated and experimental results
on these airplanes was perhaps to be expected.
In the case of airplane C the agreement in terminal
velocity is poor although the agreement in engine speed
is fair. The experimental results indicate a very slight
reduction in terminal velocity due to the propeller,
whereas the calculated results indicate a reduction of
the same order as those noted for the other airplanes
listed. As far as can be determined, there is no unusual
feature in airplane C to account for this discrepancy.
The airplane minimum drag coefficients as determined
from three independent sources agreed within 2 percent.
Although the drag coefficient used in the calculations
holds for a Reynolds Number corresponding to high¬
speed level flight and there is evidence that a reduction
in drag coefficient with increasing Reynolds Number is
to be expected, the influence of such a scale effect
should not be felt in this case alone. In other words,
the influence of scale effect is implicitly allowed for
roughly in the method of calculation because of the
empirical nature of the method. There is a possibility
that the degree of turbulence in the slipstream with the
propeller operating at negative thrust may have a
critical effect on the drag of some parts of the structure
within the slipstream. At the present state of know¬
ledge it would be practically impossible to take such a
phenomenon into account.
It is somewhat difficult, because of the lack of experi¬
mental cases, to say whether the method of calculation
as presented will generally hold good. It is felt that
within the following limitations the method will yield
satisfactory results except in cases where unusual or
unpredictable influences occur.
COMPARISON OF EXPERIMENTAL AND CALCULATED RESULTS
LIMITATIONS
1. The propeller-body combination should be approxi¬
mately similar to that of the F6C-4.
A comparison between the experimental and calcu¬
lated results using the tip-speed corrections is made in
to
THE DRAG AND TORQUE OF THE PROPELLER IN TERMINAL-VELOCITY DIVES
501
Blade-angle settings should not be extrapolated, par¬
ticularly in the low range.
3 Mean blade-width ratios should not be less than
0.09 nor more than 0.17.
4. The propeller blade sections should be based on
either the Clark Y or KAF-6 sections and should
be of normal thicknesses.
5 Tip-speed correction factors should not be extrapo¬
lated.
RULES OF THUMB
In calculated results for a number of airplanes of
widely different characteristics, such as those listed in
table Ill, consistent trends which indicate the feasibility
of quick rules have been noted. Thus, the percentage
reduction in terminal velocity caused by the propeller
in a vertical dive with engine fully throttled and with
normal blade-angle setting is given by the equation
REFERENCES
1. Durand, William F.: Experimental Research on Air Pro¬
pellers. T. R. No. 14, N. A. C. A., 1917.
2. Durand, William F., and Lesley, E. P.: Experimental Re¬
search on Air Propellers, II. T. R. No. 30, N. A. C. A.,
1920.
3. Anon.: Hamilton Standard Has Variable Pitch Propeller.
The Aviation News (McGraw-Hill Co.), Oct. 18, 1930, p. 6.
4. Wood, Donald H .: Full-Scale Tests of Metal Propellers at
High Tip Speeds. T. R. No. 375, N. A. C. A., 1931.
5. Diehl, Walter S.: Engineering Aerodynamics. The Ronald
Press Co., 1928, p. 135.
6. Lock, C. N. H., and Bateman, H.: Airscrews at Negative
Torque. R. & M. No. 1397, British A. R. C., 1931.
7. Hartman, Edwin P.: Negative Thrust and Torque Charac¬
teristics of an Adjustable-Pitch Metal Propeller. T. R.
No. 404, N. A. C. A. 1933.
8. Munk, Max M.: The Determination of the Angles of Attack
of Zero Lift and of Zero Moment, Based on Munk’s In¬
tegrals. T. N. No. 122, N. A. C. A. 1923.
9. Diehl, Walter S.: Standard Atmosphere — Tables and Data.
T. R. No. 218, N. A. C. A., 1925.
R (percent) =0.011 Wi,+9.7
in which Vh is the terminal velocity (m. p. h.) in a
vertical dive with no thrust in standard sea-level
conditions of atmosphere.
Engine speed (r. p. m.) is given by the equation
in which Vt is the terminal velocity with the foregoing
correction for the propeller effect.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Ya., August 22, 1933.
TABLE I
CHARACTERISTICS OF
F6C-4 AIRPLANE
Type -
Tractor biplane, land-
plane.
Engine — — - - -
Pratt & Whitney,
R-1340-CD.
Horsepower _
450 at 2,100 r. p. m.
Weight (as flown). _ -
Principal dimensions:
2,815 and 2,830 lb.
Span (upper wing).
__ 31 ft. 6 in.
Span (lower wing) - -
26 ft.
Length _
__ 22 ft, 6 m.
Height - - - . —
. 9 ft. 6 in.
Total wing area
252 sq. ft.
Gap _
.. 4 ft. 5 /1 6 in.
Stagger _
. 3 ft. 2% in.
CD . (from flight tests).-
‘-'min v ~
__ 0.0513
REPORT NO. 599— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE II
COMPARISON BETWEEN CALCULATED AND CROSS-FAIRED EXPERIMENTAL VALUES
Dive angle
(deg.)
Basic
terminal
velocity
(m. p. h.)
Blade-
angle
setting at
0.75 n
(deg.)
Indicated terminal velocity
Engine speed
Calculated
(in. p. h.)
Experi¬
mental
(m. p. h.)
Difference
(m. p. h.)
Difference
(percent)
Calculated
(r. p. m.)
Experi¬
mental
(r. p. m.)
Difference
(r. p. m.)
Difference
(percent)
90
290
22.5
271.2
263.0
8.2
3.1
2, 272
2, 320
-48
-2. 1
90
290
19. 0
258. 7
257.0
1.7
.7
2, 483
2, 385
98
4. 1
90
290
14. 5
241.4
241.0
.4
.2
2, 670
2, 540
130
5. 1
90
290
9. 5
215.4
214. 5
.9
.4
2, 745
2,730
15
.5
90
290
5.5
195.0
190. 0
5.0
2.6
2,713
2,680
33
1.2
59
270
22.5
252. 3
242.0
10.3
4.3
2,114
2, 160
-46
-2. 1
59
270
19.0
240. 8
239. 5
1.3
♦ 5
2,310
2, 225
85
3.8
59
270
14.5
224. 2
224.5
-.3
-. i
2, 483
2, 400
83
3.5
59
270
9. 5
200. 1
199. 5
.6
.3
2, 562
2, 605
-43
-1.7
59
270
5.5
180. 8
175.0
5.8
3.3
2, 530
2,520
10
.4
47
250
22.5
233.6
225.0
8.6
3.8
1,953
1,980
-27
-1.4
47
250
19.0
223. 1
224. 0
-. 9
-.4
2, 140
2, 055
85
4. 1
47
250
14. 5
207. 9
209. 0
-1. 1
-. 5
2, 309
2, 225
84
3.8
47
250
9. 5
185. 3
185. 0
.3
. 2
2,377
2, 460
-83
-3.4
47
250
5.5
167. 1
164.0
3. 1
1.9
2, 340
2, 360
-20
—.8
38
230
22.5
214. 1
208.0
6, 1
2.9
1,786
1,780
6
.3
38
230
19.0
204. 9
205. 5
— . 6
-.3
1,954
1,875
79
4.2
38
230
14.5
191.4
193.0
-1.6
-.8
2, 117
2, 085
32
1.5
38
230
9.5
170. 5
172.0
1. 5
-.9
2, 177
2, 295
-118
5. 1
38
230
5. 5
153.4
153. 0
.4
.3
2, 124
2,215
-91
-4. 1
31.75
210
22. 5
196. 7
194.0
2.7
1.4
1,640
1,585
55
3.5
31.75
210
19.0
187.8
190. 0
-2.2
-1.2
1,785
1,700
85
5.0
31.75
210
14.5
1 75. 6
181.0
-5.4
-3.0
1,930
1,925
5
.3
31. 75
210
9.5
156. 6
160. 0
-3.4
-2. 1
1 , 995
2, 140
-145
-6.8
31.75
210
5.5
141.0
142. 0
-1.0
. 7
1,951
2, 060
-109
-5.3
TABLE III
COMPARISON OF CALCULATED AND EXPERIMENTAL RESULTS
A ir-
plane
Engine type and power
Sea-
level
high
speed
(m.p.h.)
Pro¬
peller
diam¬
eter
(ft.)
Mean
blade-
width
ratio
Blade-
angle
setting
at
0.75 R
(deg.)
Dive
angle
(deg.)
^ h'nd
(sea
level)
zero
thrust
(m.p.h.)
^ On d
(sea
level)
closed
throttle
(in. p. h.)
K. p. m.
(sea
level)
closed
throttle
Per¬
cent¬
age
reduc¬
tion
due
.to
pro¬
peller
Exper¬
imental
V<ind
(sea
level)
closed
throttle
(m.p.h.)
Exper¬
imental
r. p. m.
(sea
level)
closed
throttle
Per¬
cent¬
age
error
in
calcu¬
lated
Per¬
cent¬
age
error
in
calcu¬
lated
r. p. m.
A _
P & Ww 450-2,100 _
140
9
0. 1285
17.0
90
288.0
253. 3
2, 600
12.0
258.0
2, 600
-1.8
0
B _
PA W w 450- 2, 100 _
160
9
. 125
18.0
90
290. 5
254.7
2,528
12.3
255. 0
i 2, 500
-. 1
1. 1
B ...
P & Ww 450-2,100 _
160
9
. 138
18.0
90
290. 5
252. 0
2, 520
13.2
255. 0
i 2, 500
-1.2
.8
C 2...
P & Wh 575-2, 100 _
131
10
. 134
16.0
41
246. 3
219.4
2, 260
10.9
238.0
2,200
-7.8
2.7
Wright B-1510. _
194
8.5
. 166
26.0
90
416.0
361. 5
2, 720
13. 1
E...
Wright R-1820F1 _
201
9.5
. 129
23.3
90
430.0
371. 5
2, 775
13. 6
1 Indicated r. p. in
Calculations made for 4,000 feet.
REPORT No. 600
an analysis of the factors that determine the periodic twist of an
AUTOGIRO ROTOR BLADE, WITH A COMPARISON OF
PREDICTED AND MEASURED RESULTS
By John B. Wheatley
SUMMARY
An analysis is presented of the factors that determine
the periodic twist of a rotor blade under the action of the
airforces on it. The results of the analysis show that the
Fourier coefficients of the twist are linear expressions
involving only the tip-speed ratio, the pitch setting, the
inflow coefficient, the pitching-moment coefficient of the
blade airfoil section, and the physical characteristics of
the rotor blade and machine. The validity of the analysis
was examined by using it to predict the twist of a rotor
whose twist characteristics had previously been measured
in flight. The agreement between the calculated and
experimental results was satisfactory. An examination
of the assumption used in the analysis — that the twist is a
linear function of the radius — disclosed that the approx¬
imation introduced no appreciable error. From this ex¬
amination, a formula for the torsional rigidity of the
rotor blade was derived.
INTRODUCTION
The development of the wingless direct-control auto¬
giro has been hampered by a number of secondary
difficulties. Probably the most troublesome are the
avoidance of excessive or unstable center-of-pressure
travel in the rotor and the elimination of rotor and
control-stick vibrations. The production of a few
designs that are satisfactory in these respects has
demonstrated that the difficulties are the designer’s
problem and are not inherent in the direct-control type
of rotor; however, the large number of unsuccessful
machines is evidence that the basic factors controlling
the behavior of the rotor are as yet not clearly under¬
stood.
A general survey of the problem indicated that both
center-of-pressure travel and rotor vibrations are
markedly affected by the periodic twist of the rotor
blade arising from the interaction of air forces, elastic
forces, and inertia forces during the flapping oscillation.
It was accordingly decided that the factors controlling
this twist must be understood before any real attack on
the initial problems would be fruitful. This paper pre¬
sents an analysis of periodic blade twist in which the
factors controlling the twist are studied. The analysis
is supported by a comparison of predicted and measured
twist on a direct-control type of autogiro.
ANALYSIS
The motion of an autogiro rotor blade consists chiefly
of rotation about the rotor axis, oscillation about the
flapping hinge, and oscillation in twist about the blade-
span axis. Additional components of the motion are
oscillation as a pendulum in the plane of the rotor disk
about a second hinge and oscillation in bending in a
plane containing the blade span and the rotor axis.
Experimental evidence has shown that these additional
components have only a second-order influence on the
air forces acting on the rotor blade, and they will
consequently be neglected in the subsequent discussion.
The coefficients of the air-twisting forces on an ele¬
ment of the autogiro rotor blade are diagrammed in
figure 1. In general, the air forces on an airfoil will not
pass through the aerodynamic center but will assume
such a position that the moment of the air forces ex¬
pressed in coefficient form is constant about the aero¬
dynamic center. The component of the centrifugal
force normal to the blade and the inertia forces of the
blade pass through the center of gravity of the blade.
Then the moment of the air forces about the center of
gravity is the twisting moment on the blade. Let CM
be the moment coefficient of the air forces about the
center of gravity; then from figure 1
0)
m n ( h I t
Cm= — CA - COS aT-\ — Sin ar
11 \c c c
+ Cd(Ctc sin a
.+ - COS a^\
c /
18548—38
38
503
504
REPORT NO. 600— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
where the symbols are defined by figure 1 ; cT is positive when the center of gravity is farther from the leading
edge than the aerodynamic center, and l is positive when the center of gravity is below the aerodynamic center.
From the definition of moment about the aerodynamic center, if h is positive from the aerodynamic center
toward the trailing edge,
— Cmc
cr »)
where Cm is the coefficient of the moment about the aerodynamic center. Then
c l
CM=CmJr-^{CL cos ar + CD sin ar)—-(CL sin aT—CD cos aT) (3)
It will be assumed that aT is sufficiently small that the cosine differs negligibly from unity and the sine can be
equated to the angle; also, CL will be assumed a linear function of the angle of attack. These assumptions do
not accurately represent the conditions in the rotor when the resultant velocity is small and the angle of attack
high, but the error introduced by them has been found to be small (reference 1). Then
Cm— Cm-\-aT-^(a-\-CD) — -(( lOLr 2 — Cd) (4)
0 c
where a is the lift-curve slope (in radian measure).
The lift-curve slope a at infinite aspect ratio lies between 5.8 and 5.9 for most airfoil sections. Inasmuch as
CD will have actual values varying from 0.009 to 0.03 below the stall, with a weighted average of about 0.015, it
is thought unnecessary to use the CD term in the expression for CM. In addition, l/c will normally be less than
0.02 and ( aaT 2 — CD) will be of the same order of magnitude; the l/c term will consequently be dropped.
From reference 1, if xR be substituted for r, the nondimensional velocity components at the blade element
of an autogiro rotor traveling at a speed V equal to uttR/cos a are:
'U'f
UT
fl R
x-\~n sin \[/
(5)
Up
UF
+ cos xa,i+^nb^ sin \p-\-(^na1+2xb^ cos 2\ p
+ —2xa2J sin 2\p-\-~na2 cos S\p-\-^nb2 sin 3 \p
(6)
where uT is the component of the resultant velocity perpendicular to the blade-span axis and to the rotor axis, uP
is the component of the resultant velocity perpendicular to the blade-span axis and to ur, and \p is the azimuth
angle of the blade from its down-wind position. Also
ut2=x2jt^2-\-2ijlx sin i A~ t>m2 cos 2\p
(7)
u
rUp=x\+^n% + ( — — ^fJLxa2^ cos \p+(^n\— ax|j£2 — sin xp
nxa1Jr2x2bC) cos 2^+^— ^n2a0-\-nxbi — 2x2a^ sin 2^+( — ^n2bi-\-^nxa2 ) cos
Jr{\c^iJr^iixb2 sin 3^— ^Cb2 cos 4^+^m2«2 sin 4 \p
(8)
The acute angle /3 between the blade and the plane perpendicular to the rotor axis is described by the expression
/3=a0—a! cos i/' — 61 sin ^—a2 cos 2^— 62 sin 2^—. . . (9)
The notation of reference 1 will be used throughout this analysis; a list of symbols employed and of their
definitions is given at the end of this section.
The calculation of the air-twisting moment MQ at the hub end of the blade will be made on the assumption
that the air forces lie in a plane perpendicular to the blade span and depend only upon the resultant velocity in
that plane. The angle <p between the resultant velocity and the plane perpendicular to the rotor axis will be
assumed equal to its sine and tangent, and to have a cosine of unity. On this basis, the angle of attack of a blade
element is
Up
ANALYSIS OF FACTORS THAT DETERMINE THE TWIST OF AN AUTOGIRO ROTOR BLADE 505
where 0 is the pitch angle of the blade, measured as the acute angle between the plane perpendicular to the rotor
axis and the zero-lift line of the blade airfoil section.
The pitch of the rotor blade will be the sum of the pitch setting and the instantaneous value of the angle of
twist to which the blade is deflected by the twisting moment. If the pitch setting is given as d0-\-xdi and it is
assumed that the twist is a linear function of the radius, the pitch angle 0 may be expressed in the form
d—d0-]rXdi-\-X€0-\-xei cos i/'+XTh sin \pJrX€2 cos 2^+2% sin 2 \p-\-. . . (11)
The use of a Fourier series in \p for the angle of twist is justified, as it was for the flapping angle /3, by the
fact that the twist angle must be a repeated function of i p. Some question concerning the assumption that the
twist is linear along the radius naturally arises; the problem will subequently be examined in more detail.
The air-twisting moment at the blade hub can now be expressed in integral form as
Mq= rLimVCWdx (12)
JO 2
The integration is performed from B to 0 (where B is arbitrarily assigned the value 1 — c/2R) to allow for tip losses.
Substituting for CM from (4)
MQ= r\PWWc2uT2(cm + aa^jdx (13)
Expression (10) for aT can now be used
Mq= r|pSiW«I.2(cra+a^[g+«])(fo (14)
Substitute for 0, uT 2 and uT uP ; then integrate and collect; and
Md=^i&2R?cacT J(J X/i-'—ft, |”|b3 + |/i2bJ + <u £ jB* + j/^B2 J + 3»1’hB3— gMV?2
+ (^[|b2 + |m2b] ) ■ + ( ■ - ImOoB2 + 6, [jB3 + |m2b] - \imJP + «, [ jB‘ + + f ^B3 - §/A3B2) cos i
,3B2+M^B2)sm * +(-|M!^-|M2«,B2+^a,B2+|62B3
(15)
-rM2«»B2-|OT1B3+«[jB‘+h!B2]+5M-)3B2-i^B) cos
+ (-^a0B+^btB3-~a2B3 + ^e1B3 + sin 2*
+ (-i^61B+j/xa2B2-gf.!eIB2-^M>l2B3+e3[|B,+|f.2B2J) cos 3^
+ ^a1B+^b2B1-^2mB2 + ^e1B3 + ri^-iBt+^2B2'J) sin 3*}
In order to examine the variation of blade twist with radius, it is necessary first to establish an expression
for the total air-twisting moment ^/Lqx outboard of any station x. This moment can be expiessed simply as
=r k^BW(0n+a^r+i
dx
(16)
506
REPORT NO. 600 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Substituting as in (14) and integrating
MQ=±pMPcacT\(f\±e 0+ 1 + [I M- jm2«i + |m^][S2-x2] + [1«„+
[S3 — a^] + [A 0! + A«„l [S* — + F Am26 , [-B — *]+ r — i Mao — i M02 4- i m2*! — g M2*a] [B2 — a:2]
+[i&i+|^2][JB3— ar>J + cos^ + ([ftX+|M2<i1][B-*]+K[eo-|62 + ^~+|M%-gM2»3]
[B2-:c2] + [-|al+|/<ft+|^0-iMJ[B3-ri]+|-„[£‘-x‘j)sin^+(M2[-i9l)-|^l[S-4
+ [ — J: M2e , — F M2eo + 1 Mai + i M2e2^[ [B2 — x2] + [| 6,, — | , + 1 a.^,] [ B3 — x3] + i e, — a:*] cos 2^
+ (- iM2a„[B-x] + [1^! + ;j;M2>)2][B2-x2] + [- 1 <h+ 1 Me,- ^llB’-x^+i^ [B4-x4]) sin 2*
+(-jM2<',[fi-x]+[jMCI2-gM2el + ]M2esl[fi2-x2]-|M^[B3-r,]+le3(B<-x,])cos3f
+(lM2a,[B-x]+[jMi'2-lM2i,+jM2>!3][B2-x2l+iMe2[S3-xi]+j%[B4-x<])sin3^}
The torsional deflection of tlie rotor blade can now be determined. Let G designate a twisting moment
that is distributed along the radius in the same manner as MQx and is of such magnitude that the blade tip is
deflected through 1 radian; then denoting the instantaneous torsional deflection at the tip of the blade by v
q~ + Gi,=MQ (18)
where q is the equivalent moment of inertia of the blade about the elastic axis and
r=e0+ei cos <A+?7i sin rp-j-e2 cos 2^+173 sin 2^ + . . , (19)
The value of q may be arrived at by considering the problem to be that of the torisonal deflection of a bar
connecting two masses having moments of inertia of infinity and zero. The system then has but one degree
of freedom and only principal modes of vibration will be assumed existent. Rayleigh’s approximation to the
exact solution of the problem (reference 2, p. 59), which is sufficiently accurate for use here, is
(20)
where i is the moment of inertia of the bar per unit length, and l is the length of the bar.
For a particular case, f=0.0050, Z=20, 67=1,700, and 0=21; then ^=0.0333 and 02g=14.7. It is seen
that 4 02g and even 9 O2^ are quite small in comparison with 6 ; consequently inertia effects on the torsional
vibration will be neglected. Then
G{ e0 -j-ej cos \p-\-i ?! sin \p-\-e2 cos 2 i/'-j- 172 sin 2^-J-e3 cos 3^ + 773 sin 3^}
= 3caCl.J(i M?2 + 00[-3-S2 + |m!b] + e,[ JJS4 + |m2.B2] + jM2i2B + 6o[ jB4 + ;m2B2] + - |m2^K2
^”'-[5'e3 + h25]) + (-|MaoB2+61[|B3+|M2j5]-lM«2S2+e,[ls4+gM2S2]+|M^-B3-gM%-B2]ccs *
(ICn
+(mXB+m0„B2+|m0,B3-Oi|jB3-Im2B -iM62B2+|Me„B3+n,riB4+gM2B!
+ M~B2)sin ^+(-I(12SoB-ip29,B2+ho1B2+|62B3-iMW-IM„B3 +
i *+\/B
•]
+ lM^B3-h2“B)cos2((- + (-h2«oB+iM61B2-|a2B3+iMe,B3 + P2RB4 + iM2B2]-iMe3Bi
1
acT
3
sin 2\p
1
1
+ -7M26,B+2Ma2B2-iM2eiB2-^,2B3+ei ^-B'+-yB 2
0J
1
1
+ ( — + T#4 + 7M2R2
ft
cos 3^
sin 3^!
(21)
ANALYSIS OF FACTORS THAT DETERMINE THE TWIST OF AN AUTOGIRO ROTOR BLADE 507
The expressions for the thrust and the flapping-motion coefficients have been established in reference 3 for
the rotor with varying twist; they are:
5 ?)+*(&+ l SB- 9V)+‘’'(iB*+ i - 53"4)+^3"'
+ i ShB + eo(i B' + i SB1- - ~ s) + - g S^B2\
io=lT{xG£3+0-080'‘a)+e°(iB,+l'‘252"'^M4)+s,GBS+
+e„(|B5+ 1
Ur
B^-nW
bi=-
4m
f-K|s3+0.035M)+I^-S(|^+T^_l,2Bi
a2-
M2 7
72Z?8 + 144} 1 6
1 ci
2 Vi
7y2Bs
108
24
+ ^(t + mr) + 9,B’( 1 2 + tm-) + 1 2 + 1
7y2B‘
80
yB»+^B' + i^2yB
V‘2
30 m
5 m
5 M2
5 m2
(22)
(23)
(24)
(25)
(26)
^=Wis| ^5+ i^“+ iW n ^7+ Jr++ Wi^ I ?SB- <27>
It will be expedient to substitute average values for B and 7 in a2 and b2\ in actuality, B will be but little
different from 0.970 for solidities near 0.05, and 7 will be between 10 and 18 for present rotor blades. The
assumption that B is 0.970 and that 7 is 15.0 will accordingly introduce little error. The substitution will be
made in such a way that the resultant expressions will be linear, and the coefficients of A, 6, e, and 77 will have the
same form and exponents as the similar factors already present in the expressions for the twisting moment and
the flapping motion. Examination of these equations discloses that the consequent forms for a2 and b2 are:
a2=M2{O.O8547\5+O.O74670oB2+O.O5887(0i + eo)£3}
+ M { - 0 . 0 1 84ei + 0 . 00 1 2 77?^ } + 0 . 0 1 507e255 -h 0 .2200772J5
&2= —M2{ 0.306 Ai?-3 + O.3820oZ?~2-f- 0.294 (dxJre0)B~1}
_ (02200 5_4 o.o184 }_o.2200e25+^^7725-3
17 J '7
(28)
(29)
Inspection of (26), (27), (28), and (29) shows that substitution for y2Bs has been made in the denominator
of (26) and (27), and in the numerator of (26) whenever 7 has been raised higher than the first power. The
quantity in braces of (27) has been divided by Bs and the resultant 7 2BS outside the braces has been evaluated.
The solution of equation (21) for e and 77 now will follow, after substituting for the a and b coefficients, by
equating the coefficients of identical trigonometric terms in (21). Before this operation is performed, the work
may be simplified to some extent by considering the order of accuracy required in the substitution.
It has already been shown (reference 1) that the expressions for the thrust and torque are evaluated to a
sufficiently high order of m (the fourth) if a0, a2, and b2 are expressed to the order m2 and a x and bx to the order
m3. Reference 3 shows that the same order of accuracy for the thrust and torque will be obtained if e0 is evalu¬
ated to m4j *i and r]X to m3> and e2 and rj2 to m2- The coefficients e3 and 773 do not, to the order of m4, influence the
thrust and torque. Reference to equation (21) establishes that en and r)n are of the order p.n, a fact that has already
been implied by the form of the expressions for a2 and b2.
It is seen now that ax and bx may be expanded in a linear form which is developed only to the m" order and
that all terms in aQ above the order m2 may be dropped. Then, substituting for a2 and b2,
Xff + ye„(~B< + +B2) + 7 (<V + 60) (■ j+s- 4- +!B3) +
(30)
508
REPORT NO. 600— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
0.704ju
B2 1
0.853 pe2
^ )++;
1.768
' M»?2
8
3 B
1.588+\, , J'
—g 3 ) + MWl + €o)( 2
1.196p2\ , 0.147 2 , / 4
~ r++v5r,‘£l+,,\5
/;
1.412/d
B
)
(31)
&i=M7x(gS2-O.O542M2)+l*70oCB3+O.133O,12£)+M7(0i+^)(^+O.O836M2B2)— e/|B-0.055£)
+0.1G76M27i)i5I+0.0100M7e2ft4-0.853fii)2
(32)
Tlie term Mw //iO2 in a0 has been neglected, since it amounts to 2 percent or less of a0.
Substitute for a0, d\, bx, a2, and b2 in (21); there results a set of linear equations in e and rj that can be solved
in succession by starting with the highest order. Thus, from the coefficient of cos 3 +
(3,£3=ipl22hJ3cacr{0.0085/x37Xi?3 + 0.0143iuV(>54+0.0108M37(^ + fo)S5+0.062lM2e152 + 0.0009iu2777i56
+0.0112 iiye2B7 —0.1 683 n^B3 }
(33)
From sin 3\p
^3=;^2^3cacr|o.271^X+ 0.381 A+ 0.280m3 (01+eo)5-^||^/x2e1 + 0.06 12M2^2+0.1683/xe253+^^Mi72} (34)
From cos 2 \p, retaining only tenns in p2 or lower,
6fe2=^pl22i?3cacr{o.796/i2\+O.578+0oB+O.554ju2(0i+eo)52— ^^)U€i+ 0. 055jU7/153+ 0.1 033e2B4+— 7—172
7
1 2^m fj)
— oP - /)|
2 acr J
(35)
From sin 2^,
6ri72=^pf22i?3cacr{ — 0.0291m2tX54— O.O29O+70O#5— O.O225/i27(01 + eo).B0— 0.0544/ievB3— 0.0008|U7i/jZ?7
- 0 . 0 1 007e2£8 + 0 . 1 03 3y]2BA )
From cos + retaining all terms up to p4,
Ge,=+ma<'rj-,<7x(TAft5-0.01GlM!B3)-M7»»(+S8-0.0049PJB*)-M7(«, + «o)(+)B;-0.0048(*2ft:
e,(TB,-0.0.73PB2)-0.0069P7HiB6-0.0005M7€2B7-0.0°57MiiJB3
(36)
(37)
From sin \p,
(?„=|ptl2fi3CMr{Mx(|s+0.341^)+^0(lB2+0.233/it2)+0.175P(«,+e„)B+5^iM2f1+>G+S,-0.008M2B!
+0.006 - °++. + M+«2j
From the constant term
Gt0 = \ pS22«3Cacr{~ X/++ «„(+ + |pft) + 0/+ + jm2B2)+ +.>« + <o(+ + +B2) + +,B3 - g mV?2
+1pS!W<7,,,(++|m2b)
(38)
(39)
ANALYSIS OF FACTORS THAT DETERMINE THE TWIST OF AN AUTOGIRO ROTOR BLADE
509
Comparison with (22) shows that the first part of (39) differs only by insignificant terms from the thrust
multiplied by cctIo-kR, or, since <r is bc/irR,
&0 = IT + + |m2#)
(40)
Let pcatt2R3cT/2G be put equal to A; then after substituting from (35), (36), (37), and (38) for e2, r?2, «i, and 771
and neglecting insignificant terms, the final expressions for the twist coefficients are obtained:
Co
Tct
TO
+a(^(\b‘+Lib)
acT\6 2 /
(41)
e1=-M7^jx(T^gBs-0.016lM2B3)+9„(TLB5-0.0049M2B4)+(e1 + <„)(1|5^-0.0048M!i?s)}
+ m37^2|o.OO21XB7+O.OOO79oB»-O.OOO2(01 + 6o)S9+O.OO71 — SSJ
l (LCt J
„ = M/l|x(|B+0.341^)+#0(iB2+0.233M2)+0.175M!(91 + eo)B+^B3j
+ ,x3/l2|o.007XB3+0.006«oi?4+0.005(«1 + e0)Bs-0.003— 'j?).
I UCjT J
e2 = M2^jo.796A+O.5780()B+O.554(01 + eo)52-i^CJBj
- p2A2\ 0.032 \B4+ OM4d0B5-\- 0.039 (dl + e0)B 6- 0.055— #5)
l (LCt J
V2=-p2yA{0.0291\B4+ O.O29O0o55 + O.O225(01 + eo)56}
-M27^2|O.OO78X#8 + O.OO570a£9+O.OO52(01 + eo)£lo-O.OO5O— £9}
[ (LCt J
e3 = m37^|0 .0085 \B 3 + 0.0 1430(>B4 + 0.0 108 (0, ■ + e0)55J
+ M37^2!o.0135X57 + 0.0111^8+0.0097(^ + eo)j59-0.0047^C5s)
(LCt J
r73=M3^{^^X+O.3810o+O.28O(0I+€o)J5}
+ M3^2(o.098X53+0.048^4+0.049(^1+eo)JB5-0.023^C54}
i OU7’ J
■ (42)
(43)
I
(44)
,
■ (45)
4 (46)
> (47)
The expressions for the twist coefficients disclose that
only e0, rju and e2 involve the factor A^^j which reduces
(LCt
to ,jg pc2tt2R3Cm and is independent of cT . The rest
of the coefficients — eu rjo, e3, and rj3, and parts of e0,
rji, and €2 — are proportional to A and consequently to
CT ■ Thus if cT is zero, only t0, 77!, and e2 differ from zero,
and then only if Cm is not zero. Exclusive of the
moment arising from Cm, the factor A represents in
non dimensional form the ratio of the moment of the
air forces to the torsional rigidity of the rotor blade.
The probable magnitude and range of values of A
can be estimated. The rigidity G will be proportional
to the polar moment of inertia of the blade spar and
inversely proportional to the length of the blade. The
moment of inertia of the spar will be proportional to the
fourth power of the blade thickness. Then
rifi
<?cc C-f (48)
where t is the blade thickness divided by the chord.
The numerator of A can be examined by the following
considerations. In the design of a rotor the pitch
setting chosen is almost invariably the one that results
in the highest efficiency. The rotor speed is then
adapted to varying maximum speeds by adjusting the
solidity. The rotor disk loading is fixed between fairly
510
REPORT NO. 600 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
narrow boundaries by the requirement of good low-
speed performance. For a given pitch setting, CTI a
(ratio of thrust coefficient to solidity) is constant and
CTpQrR2 is equal to the disk loading. Thus, apU2R2 will
be almost constant. Now, from (48) and this discus¬
sion,
Aloe
R3ct
bcA t*
(49)
S -1 n O 7rR
Or, from
Aloe
b2cT
RAt*
(50)
It has been found that a value of A of 0.600 is
associated with a rotor that has a radius of 20 feet, a
chord of 1.00 foot, a blade thickness ratio of 0.175, and
cT equal to 0.038 foot. It seems unlikely that RJd will
increase by more than 25 percent above the value given
here of 114; assuming this increase, and an increase in
CtIc from 0.038 to an upper limit of 0.06, Al would
become approximately 1.90. The lower limit is ob¬
viously zero, since cr/c may become zero. It will be
found that normal designs will result in a value of A
of less than unity and that the given value of 0.600 is
larger than the average.
a , rotor angle of attack, radians.
Cm, pitching-moment coefficient of rotor-blade
airfoil section.
Mt, thrust moment about horizontal hinge.
Mw, weight moment of blade about horizontal
hinge.
urQR, velocity component at blade element per¬
pendicular to blade span and parallel to
rotor disk.
UpQR, velocity component at blade element per¬
pendicular to blade span and to urttR.
T, rotor thrust.
CT=T/p£l2TrRi
a, slope of curve of lift coefficient against angle
of attack of blade airfoil section, in radian
measure.
7 =
, -i up
</> — tan 1 —
uT
aT, blade-element angle of attack, radians.
cpaR 4
TT’
mass constant of rotor blade.
c
B=1 — o/F ^acf°r allowing for tip losses.
G, torsional rigidity of rotor blade, ft.-lb. per
radian.
LIST OF SYMBOLS
R, blade radius.
b, number of blades.
c, blade chord.
cT, distance between aerodynamic center and
center of gravity of rotor-blade element.
r, radius of blade element.
x, r/R.
60, blade pitch angle at hub, radians.
6h difference between hub and tip pitch angles,
radians.
en, coefficient of cos n\p in expression for 8 ,
radians.
tin, coefficient of sin n\p in expression for 8,
radians.
8, instantaneous pitch angle, radians.
> A, blade azimuth angle measured from down
wind in direction of rotation, radians.
12, rotor angular velocity, d\p/dt, radians per
second.
X12 R, speed of axial flow through rotor.
pV.R, component of forward speed in plane of disk,
equal to V cos a , where I7 is forward speed,
feet per second.
/3, blade flapping angle, radians.
a„, coefficient of cos n\p in expression for /3,
radians.
bn, coefficient of sin rup in expression for /3,
radians.
I\, mass moment of inertia of rotor blade about
rotor hinge.
FLIGHT TESTS AND CALCULATIONS
Data for investigating the validity of the analysis
were obtained in flight tests of a Kellett KD-1 direct-
control wingless autogiro. The physical characteristics
of the machine and its rotor are given in table I. Meas¬
urements were made in a steady glide of the air speed,
the rotor speed, and the blade motion. The air speed
was obtained with a trailing pitot-static head and an
N. A. C. A. air-speed recorder; the rotor speed was ob
served with a calibrated rotoscope; and the blade motion
was photographed with a motion-picture camera mounted
on and turning with the rotor hub. The photographs
obtained with the motion-picture camera established
the blade flapping motion and, in addition, the instan¬
taneous twist at the rotor radius of the markers on the
blade.
TABLE I.— PHYSICAL CHARACTERISTICS OF KD-1
AUTOGIRO
Gross weight, W. _ 2,100 pounds.
Rotor radius, R _ 20.0 feet.
Blade weight, wb _ 61.5 pounds.
Blade-weight moment, Mw _ 482 pound-feet.
Blade moment of inertia, I\ _ 175 slug-feet2.
Blade chord, c _ 1.00 foot.
Chordwise location of blade center of gravity
from leading edge _ 0.280 foot.
Chordwise location of aerodynamic center
from leading edge _ 0.242 foot.
Number of blades, b _ 3.
Rotor solidity, <j _ 0.0478.
Blade airfoil section _ Gottingen 606.
Blade pitch setting (constant), 60 _ 0.0960 radian.
Airfoil section moment coefficient, Cm (about
aerodynamic center) _ —0.056.
Blade torsional rigidity constant, G _ 1,700 pound-feet.
ANALYSIS OF FACTORS THAT DETERMINE THE TWIST OF AN AUTOGIRO ROTOR BLADE
511
In order to investigate the validity of the analysis,
the flight-test data were used in two ways. The analy¬
sis was checked directly by predicting the blade twist at
0.75 R from the physical constants of the rotor and the
value of the inflow coefficient X. The factor X was
calculated from the experimental thrust coefficient by
the substitution of known values in the expression for
the thrust coefficient given in the analysis. A further
examination of the analysis was made by substituting
the experimental values of the inflow factor, the blade-
motion coefficients, and the twist coefficients at one tip-
speed ratio in the equation expressing the twisting
moment as a function of the radius. The resultant
twist deflection for a blade of constant rigidity followed
directly and could be qualitatively compared with the
basic assumption of a linear variation of twist with
radius.
RESULTS ANI) DISCUSSION
Measured values of rotor speed and thrust coefficient
are shown in figure 2, and derived values of the inflow
factor X are given in table II. The experimental blade-
motion coefficients are presented in figure 3.
Figure 2.— Rotor speed and thrust coefficient of KD-1 autogiro rotor as measured in
flight; p= 0.00231 slug/cu. ft.
TABLE II.— DERIVED VALUES OF INFLOW FACTOR X
X
X
X
0. 125
.150
. 175
0.0214
.0213
.0212
0.200
.225
.250
0. 0209
. 0204
.0197
0. 275
.300
.325
0.0191
.0185
.0179
The twist coefficients shown in figure 4 represent a
comparison of the experimental points with the cal¬
culated values for the radius at which the measurements
were made. The agreement of theory with experiment
is satisfactory, and strikingly so for rjh the largest
coefficient. The calculated e0 is consistently smaller
than the measured value, but a reasonable explanation
of the disagreement will be given later. Unfortunately,
the experimental results for ex and e2 are badly dispersed;
the mean of the points is not appreciably different,
however, from the predicted values.
The variation of twisting moment and twist angle
with radius is illustrated in figures 5 and 6. The
Figure 3. — Flapping motion coefficients of KD-1 autogiro rotor as measured in
flight.
twisting moment at the hub for each component of the
twist has been considered unity; the blade rigidity
from £= 0 to £=0.05 has been considered infinite as
an approximation to the high rigidity inboard of the
vertical pin; and the rigidity outboard of £=0.05 was
chosen to make e0 unity at £=1.00. Examination of
the figures discloses that e0 attains a larger value at
£=0.75 for the same twisting moment at the hub
than any of the remaining components of twist. This
result can be considered a partial explanation of the
underestimation of e0 in figure 4. The curves in figures
5 and 6 further indicate that the assumption of linear
twist is a reasonably accurate approximation to the
actual variation.
The curves in figures 5 and 6 suggest that it would
be erroneous to calculate the torsional rigidity from
38548—38 - 34
REPORT NO. 600— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
0
<u - /
•o '
rQ
o -2
<o
* 0
O
<D
>-/
-<?
1 r
□
o
±
-o - o"
— □ - J
+
+
+
L (+)
— ■
o
o
o
o
o \
\
eo(.0)
o
c
'o/cu
la tea
_
A A
A A
A a
A
\
X
V
X
'>
:x
\
RiM
X
0 ./ .2 .3 A .5
Tip-speed ratio, p
Figure 4.— Measured and calculated twist coefficients of KD-1 autogiro rotor.
Figure 5.— Radial distribution of twisting moment and twist angle of KD-1 autogiro
rotor; cos n<P components; v =0.325.
the twist produced by a constant moment along the
blade. Instead, it is recommended that a moment be
assumed which has a value G at the blade root and
varies with the radius according to the expression
(B2—x2). The definition of G suggested is that it be
the moment at the hub, distributed as indicated, which
will produce a twist of 0.80 radian at 0.75 R. Thus, if
Ip is the polar moment of inertia of the blade cross
Assumed --
Calculated
0 .2 A .6 .8 1.0
Radius, x
Figure 6.— Radial distribution of twisting moment and twist angle of KD-1 autogiro
rotor; sin nty components; n= 0.325.
section, R the radius (blade length), and Es the modulus
of elasticity in shear,
r_ 64 EJV
Cr~585 R
where G is in pound-feet.
Es is in pounds per square inch.
Iv is in inches4.
R is in inches.
The value of 0.80 rather than 0.75 radian for the deter¬
mination of G appears to result in a curve that is
better approximated by a straight-line distribution to
1 radian at the tip, as evidenced in figures 5 and 6.
The merit of the analysis made in this paper depends
upon the accuracy and facility with which it may be
used to predict the twist of a rotor blade before the
rotor itself has passed the drawing-board stage of
design. The use of the analysis in this manner is not
obvious since at first it appears that the rotor speed is
required in order to calculate the twist; whereas the
calculation of the rotor speeds can be made only after
the twist, and consequently the thrust coefficient, is
known. In one sense this objection is valid but in
another the difficulty mentioned is not insurmountable.
Assume a rotor design in which the known factors are
ANALYSIS OF FACTORS THAT DETERMINE THE TWIST OF AN AUTOGIRO ROTOR BLADE
513
the blade moment coefficient, the distance between the
aerodynamic center and the center of gravity, the radius,
the chord, the torsional rigidity, and the design maxi¬
mum speed. Because of the variation of rotor effi¬
ciency with tip-speed ratio, it is mandatory that at
maximum speed the tip-speed ratio shall be between
0.40 and 0.45. When the tip-speed ratio for design
maximum speed is chosen, the tip speed is fixed. The
twist coefficients e0, yi, and e2, which depend principally
upon Cm, can now be found with satisfactory accuracy
bv using the values of pitch setting and inflow coeffi¬
cient X that would be assigned to the rotor if the twist
were zero. For a given airfoil section there is a mean
lift coefficient which results in maximum efficiency and
which fixes the ratio Crj<j; the values of X and the pitch
setting corresponding to this mean lift coefficient should
be used. The coefficients e0, vi, and e2 now are known
and fixed, and their effect upon CT/a can be evaluated.
The desired value of CT/cr is now attained by adjusting
the pitch setting to offset the effect of twist, and all
design requirements have been met. A final check of
the twist coefficients using the final values of X and the
pitch setting can be made but, since Cm dominates the
only coefficients that influence CT/a, it is found that only
in exceptional and peculiar designs will the twist
coefficients be affected.
CONCLUSIONS
1. The assumption that the twist of a rotor blade
varies linearly with the radius is a satisfactory approxi¬
mation to actual conditions.
2. The analysis of blade twist predicted without
important error the twist of a rotor used as an example.
3. The torsional rigidity of the rotor blade should
be calculated on the basis that the twisting moment
varies with radius as (B2—x2).
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., April 14, 1937.
REFERENCES
1. Wheatley, John B.: An Aerodynamic Analysis of the Autogiro
Rotor with a Comparison between Calculated and Experi¬
mental Results. T. R. No. 487, N. A. C. A., 1934.
2. Timoshenko, S.: Vibration Problems in Engineering. D. Van
Nostrand Co., Inc., 1928, p. 59.
3. Wheatley, John B.: An Analytical and Experimental Study of
the Effect of Periodic Blade Twist on the Thrust, Torque,
and Flapping Motion of an Autogiro Rotor. T. R. No.
591, N. A. C. A., 1937.
REPORT No. 601
TORSION TESTS OF TUBES
By Ambrose IT. Stang, Walter Ramberg, and Goldie Back
SUMMARY
Torsion tests of 63 chromium-molybdenum steel tubes
and 102 17 ST aluminum-alloy tubes of various sizes and
lengths were made to study the dependence of the torsional
strength on both the dimensions of the tube and the physical
properties of the tube material. Three types of failure
were found to be important for sizes of tubes frequently
used in aircraft construction: (1) failure by plastic shear,
in which the tube material reached its yield strength
before the critical torque was reached; (2) failure by elastic
two-lobe buckling, which depended only on the elastic
properties of the tube material and the dimensions of the
tube; and (3) failure by a combination of ( 1 ) and (2), that
is, by buckling taking place after some yielding of the
tube material.
An adequate theory exists for explaining failure by ( 1 )
or (2). Most of the tubes failed by the combined failure
(3), for which a theoretical solution seems unattainable at
this time. An analysis of the data showed that the tor¬
sional strength of these tubes could be expressed by an
empirical formula involving only the tensile properties of
the tube material in addition to the dimensions of the tube.
Design charts were computed from this empirical formula
and a number of examples were worked out to facilitate the
application of the charts.
INTRODUCTION
Thin-wall tubes are commonly used in airplanes to
transmit torques to the ailerons and other control sur¬
faces. It is well known that the maximum fiber stress
in torsion that a thin-wall tube will support depends
on the ratio (t/D) of its wall thickness to its diameter.
Tests have been made (references 1, 2, 3, and 4) to
determine the relationship between torsional strength
and t/D ratio for tubes of various materials, but the
available data resulting from these tests were insufficient
to lead to general conclusions or even to determine a
fairly accurate design formula for a given material.
It seemed desirable, therefore, to carry out a
series of tests with a sufficiently large number of tubes
of various lengths and t/D ratios and, if possible, of
several materials to supply such data. The present
report describes the results of torsion tests of 63
chromium-molybdenum steel tubes and 102 tubes of
17ST aluminum alloy. These tests were made at the
National Bureau of Standards with the cooperation of
the Bureau of Aeronautics, Navy Department, and the
National Advisory Committee for Aeronautics.
APPARATUS AND TESTS
TUBES
The lengths L of the steel tubes ranged from 19 to 60
inches, outside diameters D from % to 2% inches, thick¬
nesses t from 0.03 to 0.125 inch, t/D ratios from 0.0134
to 0.0840, and L/D ratios from 7.6 to 80.0. The alumi¬
num-alloy tubes wrere cut in lengths of 20 and 60 inches;
their outside diameters ranged from 1 to 2 inches, their
wall thicknesses from 0.019 to 0.221 inch, their t/D
ratios from 0.0101 to 0.1192, and L/D ratios from 10.0 to
60.2.
The first five lengths (A0, B0, C0, D0, E0) of chro¬
mium-molybdenum steel tubes used in the tests were
purchased under Army Specification 57-1 80-2 A; the
other tubes (F0 to V0) wrere bought under Navy Depart¬
ment Specification 44T18. Table I shows that the
tensile properties required by these specifications are
the same. Somevdiat higher properties are required by
the more recent Navy Department Specification
44Tl8a, which is included in table I for the sake of
completeness.
TABLE I.— MECHANICAL SPECIFICATION FOR
CHROMIUM-MOLYBDENUM STEEL TUBES
Specification
Tensile strength
(minimum)
(lb./sq. in.)
Y ield strength
(minimum)
(offset 0.2
percent)
(lb./sq. in.)
Elongation
in 2 inches
(minimum)
(percent)
Army 57-180-2A _
95, 000
60,000
10
Navy 44T18 - -
95,000
60,000
10
Navy 44T18a - - -
95,000
75,000
10
The aluminum-alloy tubes w'ere contributed by the
Aluminum Company of America. They were manu¬
factured to satisfy Navy Department Specification
44T21. The mechanical properties listed in this speci¬
fication are given in table II.
515
516
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE II.— MECHANICAL SPECIFICATION FOR
HEAT-TREATED ALUMINUM-ALLOY TUBES
Specification
Nominal outside
diameter (in.)
Tensile
strength
(minimum)
(lb./sq. in.)
Yield
strength
(minimum)
(offset 0.2
percent)
(lb./sq. in.)
Elongation
in 2 inches
(minimum)
(percent)
\U to 1 _ _
55, 000
40, 000
16
Navv 44T21 . .
■,'Over 1 to 1K> . .
55,000
40, 000
14
(Over ix/i to 4 _ _
55,000
40,000
12
The chemical composition of a few of the steel tubes
was determined and the Vickers hardness numbers and
tensile properties of each length of tube were obtained
before carrying out the torsion tests.
Table III gives the results of analyses made by the
Chemistry Division of the National Bureau of Stand¬
ards on five of the steel tubes selected at random.
TABLE III.— PERCENTAGE OF CHEMICAL ELEMENTS
PRESENT IN CHROMIUM-MOLYBDENUM STEEL
TUBES
Speci¬
men
Carbon
Manga¬
nese
Phos¬
phorus
Sulphur
Chro¬
mium
Molyb¬
denum
D
0.34
0.54
0. 022
0.011
1.09
0. 19
K
.30
.49
.022
.009
.86
. 18
N
.31
.59
. 029
.013
1. 11
.24
O
.39
.49
.021
.013
.86
.23
s
.32
.53
.023
.015
.97
.23
No such analyses were made of the aluminum-alloy
tubes, but the nominal composition furnished by the
manufacturer is given in table IV.
TABLE IV.— NOMINAL CHEMICAL COxMPOSITION OF
17ST TUBES AS GIVEN BY MANUFACTURER, PER¬
CENTAGE
Copper - - 4.0
Manganese _ . 5
Magnesium _ _ .5
Aluminum _ 95.0
Vickers hardness tests were made at both ends of
each tube. The results for the chromium-molybdenum
steel tubes are given in table V and those for the alumi¬
num-alloy tubes in table VI. For the steel tubes the
Vickers numbers varied from 204 to 311. The average
variation for a single tube was less than 5 percent and
in only one case (tube 00, 13.2 percent) did it exceed
10 percent. The Vickers numbers for the aluminum-
alloy tubes varied from 125 to 142, the maximum varia¬
tion for a single tube being loss than 2 }{ percent.
The dimensions of the chromium-molybdenum steel
specimens used in the torsion tests are included in table
VII and those of the 17ST aluminum-alloy specimens,
in table VIII, together with data obtained from the
torsion tests.
TENSILE TESTS
Tensile tests were made on specimens 19 to 20 inches
long cut from each length of tubing. The specimens
were fitted with plugs similar to those described in
Navy Department specification 44T18 and were held
in V-type jaws attached to the two heads of the testing
machine. A hydraulic machine of 100,000-pound
capacity was used to test all except one of the chro¬
mium-molybdenum steel tubes; this one specimen was
tested in a machine of the lever type because its diam¬
eter of 2 ){ inches was too large for the jaws provided
with the hydraulic machine. All the aluminum-alloy
tensile specimens were tested in lever-type machines of
2,000-, 50,000-, and 100,000-pound capacity. All of
the steel specimens except A0, D0, and E0 were pre¬
stressed in tension to about 30,000 pounds per square
inch. The prestressing served to seat the strain gages
and to cold-work the material sufficiently in the low-
stress range to obtain from it an approximately straight
stress-strain curve, from which the Young’s modulus of
the material could be derived. The aluminum-alloy
tubes had already been prestressed at the factory and
only enough load was put on the specimen before test
to seat the strain gages securely.
Tensile strains on the steel tubes were measured with
a Ewing extensometer using a 2-inch gage length
(smallest scale division 0.0001 in. /in.) for specimens
1){ inches in diameter or less, and with a Huggenberger
extensometer using a 1-incli gage length (smallest scale
division 0.00015 in. /in.) for tubes of larger diameter.
Tuckerman optical strain gages with a 2-inch gage
length were used for all aluminum-alloy tubes. The
smallest scale division on the vernier of this gage corre¬
sponds to a strain increment of 0.000002 in. /in.
The strain gages on each of the tensile specimens
were placed 8 to 9 inches, or 4 to 9 diameters, away from
the jaws gripping both ends of the specimen. A study
of the stress distribution in a 2.5X0.032X36 inch tube
of chromium-molybdenum steel held between V-type
jaws making contact at opposite pairs of points 60°
apart had shown that the average of the strains at two
ends of any diameter in a cross section removed 3
diameters or more from the ends gave the same value
within the error of observation. At a cross section
diameters from any pair of jaws the average strains
varied ±6 percent about an average stress of 15,000
pounds per square inch and through ±2.6 percent
about an average stress of 27,000 pounds per square
inch. From these observations it was concluded that
the average strains as measured in the present series of
specimens from 4 to 9 diameters from the jaws were
correct within the error of observation. The contact
points of the jaws in these specimens wrere more than
60° apart except for some of the 1-incli tubes for which
they wrere a little closer; in the latter case, liovmver,
the gages wTere about 8 diameters away from the jawTs.
From each stress-strain curve the yield strength was
determined as the stress at wdiich the strain was 0.002
in. /in. in excess of the elastic strain with an assumed
Young’s modulus of 30X106 pounds per square inch for
the chromium-molybdenum steel tubes and a modulus
of 10X106 pounds per square inch for the aluminum-
alloy tubes. The values are given in table Y for the
steel tubes and in table VI for the aluminum-alloy
tubes. It is seen that the yield strength of the steel
TORSION TESTS OF TUBES
517
tubes varied from 67,700 to 110,000 and that of the
aluminum-alloy tubes, from 44,300 to 50,000 pounds
per square inch.
Young’s modulus E was obtained by plotting against
stress a the difference Ae between the observed strain
and that computed from an assumed modulus E0 of
30X106 pounds per square inch in the case of the steel
tubes and a modulus of 10X106 pounds per square inch
in the case of the aluminum-alloy tubes and by measur¬
ing the slope A e/a of the straight line giving the best
fit to the plotted points. The true modulus E is then
computed from this slope using the simple relation
Tables V and VI show that the Young’s modulus for
Examination of the stress-strain curves for the steel
specimens showed that the material could be divided
into two groups with markedly different stress-strain
curves. For the greater number of steel tubes the
curves were nearly straight until near the yield stress,
where they bent fairly sharply. In these specimens the
ratio of tensile strength to yield strength varied from
1.03 to about 1.18. Three of these curves (for speci¬
mens H0, R0, K0) are shown in figure 1(a). For other
specimens, however, the slope of the curves decreased
gradually with no sharp bend. For these specimens
the ratio of tensile strength to yield strength was much
higher, ranging from 1.37 to 1.63. Figure 1 (a) also gives
three of these curves (for specimens I0, V0, N0). In
each of these groups there existed a rough association
between different tensile properties. Low tensile
Figure 1. — Stress-strain curves of chromium-molybdenum steel tubes. Tensile specimens Ho, Ro, Ko, with sharp knee near the yield strength were cut from the same three
lengths of tubing as shear specimens Hi, Ri, K2, respect ively; similarly tensile specimens, Io, V 0, No, with relatively rounded knee near the yield strength, were cut from the
same three lengths as shear specimens Ii, V2, Ni, respectively. The ratio of tensile strength to yield strength in tension is shown as a number on each tensile stress-strain
curve.
the steel tubes ranged from 27.3 to 30.2 X10b pounds
per square inch and that for the aluminum-alloy tubes
varied from 9.79 to 10.81X10® pounds per square inch.
In both groups the range of variation was close to 10
percent.
Elongations over a 2-inch gage length were deter¬
mined by means of dividers; they varied from 11.5 to
32 percent for the steel tubes (table V) and from 17 to
34 percent for the aluminum-alloy tubes (table VI).
The specimens that broke at the jaws were not consid¬
ered in obtaining these limits.
Tables V and VI also give the tensile strength of
each specimen. This value ranged from 88,400 to
132,900 pounds per square inch for the steel tubes and
from 62,800 to 67,000 pounds per square inch for the
aluminum-alloy tubes.
strength, high yield strength, low elongation, low ratio
of tensile strength to yield strength tend to occur to¬
gether and high tensile strength is associated with low
yield strength, high elongation, etc. However, no
quantitative relation could be found between the results
for materials in the two groups.
Not nearly so marked a differentiation into two groups
was apparent for the aluminum-alloy tubes. The ratio
of tensile strength to yield strength varied through a
much smaller range, namely, from 1.27 to 1.49. Figure
2(a) shows three specimens with a relatively sharp knee
near the yield stress (P0, Jo, M0) and three with a rela¬
tively rounded knee (U0, s0, x0). There was again a
rough tendency for low tensile strength to occur to¬
gether with high yield strength, low elongation and low
ratio of tensile strength to yield strength.
518
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 2.— Stress-strain curves of 17ST aluminum-alloy tubes. Tensile specimens Po, Jo, Mo, with relatively sharp knee near the yield strength were cut from the same three
lengths of tubing as shear specimens P2, Ji, M2, respectively; similarly tensile specimens Uo, so, xo, with relatively rounded knee near the yield strength were cut from the same
three lengths as shear specimens CJ2, si, xi, respectively. The ratio of tensile strength to yield strength in tension is shown as a number on each tensile stress-strain curve.
TORSION TESTS
CALCULATION OF SHEAR STRESSES
Figure 3 shows the method of mounting the specimen
for test in the torsion machine. The ends of the tube
were reinforced by two steel plugs of proper diameter
and were then clamped solidly between wedge-shaped
jaws A; they were free to move in an axial direction
throughout the test. Specimens not over 20 inches in
length were tested in the 13,000 pound-inch pendulum-
type machine shown in figure 3 and the longer tubes
were tested in a 60,000 pound-inch lever-type machine.
The method of measuring the angle of twist under
load is also shown in figure 3. The fixture consists of
two rings B fastened to the specimen at points 25
Figure 3.— Torsion testing machine with 17ST aluminum-alloy tube in position after
test to failure.
centimeters (9.84 inches) apart by three screws C.
Each ring carries a pair of aluminum radial arms D,
one pair carrying the scales E and the other the pointers
F. Readings were taken on both scales and averages
were used to compensate for any effect due to bending
of the tube under load.
The torsion tests give the relation between the torque
M transmitted by the tube and the angle of twist per
unit length 6 produced by that torque. The stress-
strain curves in shear were computed from these torque-
twist curves in the following manner.
The relation between the shear stress r and the
torque M in a twisted circular tube is given by the
equation:
M\Q) -2-k ( Tr2dr (2)
J T\
where r is the radial distance from the axis of the tube.
ru radius of the inner wall.
r2, radius of the outer wall,
r, shear stress at a distance r from the axis.
The relation between this shear stress and the shear
strain y = rd,
T=f{y)=J(rd) (3)
may be found by substituting (3) in (2) and differenti¬
ating both sides with respect to d. (See reference 5,
p. 128.) This gives the differential equation:
r23j(r26) —rtfind) 6 °^+3 ilf) (4)
where r2d, r^d are the shear strains at the outside and
the inside wall of the tube, respectively. All quantities
in this equation are given by the dimensions of the
tube and the torque-twist curve except the stresses
f(r2d) and /(r^). The stress j(r2d) can, therefore, be
calculated from equation (4) provided j{rx0) is known;
this suggests a method of step-by-step solution begin¬
ning with the end of the elastic range in which
is known. Practically, this method of computation is
laborious and is not warranted by the accuracy of the
data for tubes as thin as those tested in the present
TORSION TESTS OF TUBES
519
investigation. It is entirely sufficient in these cases to
use approximate methods based upon arbitrary sim¬
plifying assumptions.
A number of such methods have been used, all of
them serving the purpose equally well. For this in¬
vestigation the method chosen was to calculate the
stress and strain in the mean fiber:
r = K(ri+r2)=^~
on the assumption that both stresses and strains in¬
crease linearly with distance from the axis of the tube,
as they do in the elastic case. This calculation gave
Mr 2 M
1
t
Iv ttDH 1 — 2-j^-f 2 yD
Q- *
i=lr=-2V~D
(S)
where D=2r2 is the outside diameter of the tube and
t=r2—ri is its wall thickness. Even for the thickest
tubes tested ^^=0.1192^ the stresses so calculated
could not differ by more than 14 percent from any stress
existing in the wall. The stresses at the mean fiber
calculated from (5) could not be in error by more than
1.5 percent for tubes up to -^=0.12. This value is the
percentage difference in the mean fiber stress for a given
twisting moment M calculated, on the one hand, by the
extreme assumption of elastic twist corresponding to
the first equation (5) and, on the other hand, bv the
extreme assumption of pure plastic shear (uniform
shearing stress throughout).
Figures 1(b) and 2(b) show a number of stress-strain
curves in shear derived from the moment-twist curve,
with the help of (5).
The accuracy of the approximation (5) is brought out
further by a comparison of exact and approximate analy¬
ses for a relatively thick ^^=0.0562^ steel tube and for
one of the thickest aluminum-alloy tubes ^-^=0.1192y-
The exact and the approximate stress-strain curves for
these two tubes are shown in figures 4 and 5. In each
figure the two curves coincide within 1 percent for the
most part and differ at no point by more than 2 percent.
Their yield strengths in shear defined by the intersec¬
tion of the sloping line with the stress-strain curve agree
within a fraction of 1 percent.
The yield strengths obtained from the torsion tests
with the help of equation (5) are listed in table VII for
the steel tubes and in table VIII for the aluminum-
alloy tubes.
Figure 6 shows four chromium- molybdenum steel
tubes and four 17ST aluminum-alloy tubes after com¬
pletion of the torsion test. The twist gages D (fig. 3)
were kept on the tubes until they failed either with a
loud snap by two-lobe buckling (specimens Pi, Bi fig. 6)
or until the knee of the torque-twist curve had been
well passed. In the latter case the torque increased
slowly with increasing twist beyond the point at which
the gages had been removed, until failure occurred
either by gradual two-lobe buckling (Qb ffi), by helical
Figure 4. — Shear stress-strain curve for specimen Ji (chromium-molybdenum, t/D=
0.0562) calculated from torque-twist curve.
A. Approximate method: Assume linear stress distribution across section as in
elastic case, calculate stresses and strains at mean fiber from
2 M
1
D D2
-VO-h)
recursion font
/2\ 3 / 1 T „ dM , „„ 3
~(z>) hbrL de +3MJ+( 2 )t
B. Exact method: Solve the recursion formula
TD0
"o
(V>
28
.c 24
o-
o
C) 16
12
v
o
to
6
4
O
•
“D —
-<y—
V
f- e°"
^ /
-
p
/
-
/
A
/
//
>
L
- //
/
o
+
Calculated
//
by a
PPro
exac
ximah
t
? met
hod
t
2 4 6 8 10 12 14 16 18 20x10 '3
She or s fr oin, in./ in.
Figure 5.— Shear stress-strain curve for specimen Aai (17ST, t/D = 0.1192) calculated
from torque-twist curve.
deformation of the axis of the tube (L5, S2) or, as in the
case of some of the aluminum-alloy tubes, by a sudden
fracture (TO ; specimen J5 (fig. 6) wTould probably have
failed by fracture if it had not developed a slight two-
lobe buckle after twisting plastically through a large
angle.
520
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ANALYSIS OF RESULTS
DISCUSSION OF TYPKS OF FAILURE
Observation of the failure of thin circular tubes in
torsion has shown that three different limiting types of
failure are of particular significance in engineering
design :
1. Two-lobe buckling of the tube wall.
2. Helical deformation of the axis of the tube.
3. Plastic yielding of the material.
The first two types are caused by elastic instability of
the twisted tube and do not necessarily involve perma¬
nent deformation of the material. They have been
treated theoretically by Schwerin (reference 6).
Schwerin’s formulas for the buckling strength of
-kE U( t it2 \
T 1 — /x L\l~D+ZD2" 7 (7)
where L is the length of the tube.
3. If plastic yielding is assumed to progress under
a constant and uniformly distributed stress in shear:
r = constant (g)
the value of the constant being equal to the stress at
which the stress-strain curve in shear becomes hori¬
zontal.
The conditions of perfect symmetry and homogeneity
on which equations (6) and (7) are based are not
realized in practice. Nor will the conditions underlying
(8), i. e., yielding under constant stress independent
Iigi re 6. Appearance of four chromium-molybdenuru steel tubes (P:, Qi, L5, J5) and four 17ST aluminum-alloy tubes (Bj, Ji, S2, TO after completion of torsion
test. Pi, Bi failed by sudden two-lobe buckling; Qi, Ji failed by gradual two-lobe buckling; L5, S2 failed by helical deformation of the axis; Ti failed by fracture;
J5 twisted plastically through a large angle and then failed by a slight two-lobe buckle.
long tubes may be written in terms of the ratio t/D
of wall thickness to outside diameter in the following
form:
1. For two-lobe buckling
T —
0.656 E
1-V
1 +2.4-^ -f-
(6)
where r is the critical shear stress at the mean fiber;
E, Young’s modulus; and n, Poisson’s ratio of the mate¬
rial. Terms involving (Jj) are neglected in the paren¬
theses since they are small for tubes in which such
elastic failure can take place.
2. For buckling of the axis of the tube into a helix
Schwerin derived the formula
of strain, be true for most materials. The equations
(6), (7), and (8) represent, therefore, only approxima¬
tions of practical cases. The degree of approximation
lor the cases of elastic buckling has been investigated
fully in an excellent paper by L. H. Donnell. (See
reference 7.) Donnell found that the experimental
value of critical shear stress for tubes was roughly 75
percent of the calculated critical stress.
Although equations (6), (7), and (8) are only rough
approximations of practical cases, they give a general
idea of the effect of different variables upon the tor¬
sional strength and upon the type of failure. If they
were accurate representations of the behavior of tubes,
the stress at failure and the type of failure could be
predicted by computations of r in each of the equations
TORSION TESTS OF TUBES
(6), (7), and (8). The conditions at failure would be
those for which r is smallest. An analysis of this sort
was made for all the tubes tested. Young’s modulus
E and Poisson’s ratio n were taken equal to the average
value given in (12) and (13) on page (11) below. The
values of n, E, t, D, and L being known, the critical
shear stresses given by equations (6) and (7) were
calculated.
The resulting tabulation of values of r as given by
equations (6) and (7) always showed higher values for
helical twisting than for two-lobe buckling. The value
of t for two-lobe buckling lay above the yield strength
in shear for 55 out of the 63 steel tubes and for 90 out
of the 102 aluminum-alloy tubes. The yield strength in
shear was taken as the stress at which the secant modulus
of the stress-strain curve in shear was % times the initial
modulus for the steel tubes and % times the initial
modulus for the aluminum-alloy tubes. More informa¬
tion concerning the factors % and % is given later.
For the remaining 8 of the steel tubes and for 3 of
the aluminum-alloy tubes the theoretical shear stress
for two-lobe buckling lay between that at which the
secant modulus of the stress-strain curve in shear
deviated by 2 percent from its initial value and the
yield strength in shear as just defined. For the re¬
maining 9 of the aluminum-alloy tubes it lay below
the stress at which the secant modulus deviated 2 per¬
cent from its initial value.
It would not be correct to conclude from this analysis
that the shear stress had passed beyond the yield
strength in most of the tubes tested before failure took
place. That statement would be true only if the critical
shear stress for two-lobe buckling could be calculated
from (6) up to the yield stress in shear. The critical
shear stress is considerably lower than that given by
(6) if the stress-strain curve deviates gradually from
Hooke’s law in approaching the yield strength. How-
over, the analysis did show that considerable yielding
must have preceded failure in all but 8 of the steel
tubes and all but 12 of the aluminum-alloy tubes. For
only 9 of the aluminum-alloy tubes did the analysis
predict failure by elastic two-lobe buckling.
It is noteworthy that none of the tidies fell into the
category of failure by helical twisting. This result
does not exclude this type of failure as a practical possi¬
bility. It only indicates that none of the tubes used
in the present investigation (maximum length/diameter
ratio, L]D = 80) were sufficiently long to deform into a
helix before failing either by two-lobe buckling or by
plastic failure. *
Inspection of the tubes after failure (see fig. 6 and
tables VII and VIII) indicated that helical twisting did
actually occur in some of the thick-wall long tidies and
also that in the majority of the tubes the final failure
was one of two-lobe buckling. The observed helical
failures and also many of the two-lobe failures must have
occurred after the yield strength of the material had
been reached; i. e., they must be considered as a con¬
521
sequence of the yielding of the material rather than the
primary cause of failure.
The conclusion that helical failure, with its depend¬
ence on length, must have been secondary is confirmed
by a comparison of the shear stress at failure for the 60-
inch tubes with that for the 20-incli tubes as given in
tables VII and VIII. Only the tubes failing elastically
show a consistent tendency toward lower strengths
with increase in length. However, this tendency does
not indicate the occurrence of helical failure even for
the tubes failing elastically. The lowering in strength
of the elastic tubes may be explained by the effect of
length on the stress producing two-lobe buckling.
If plastic failure and two-lobe failure alone controlled
the strength of the tubes, it should be possible to de¬
scribe the strength of these tubes in terms of the vari¬
ables determining these types of failure. The maxi¬
mum median-fiber shear stress in the plastic failure of a
thin tube depends primarily on the ultimate strength
in shear of the material. In a tube that buckles
elastically the maximum median-fiber shear stress will,
according to equation (6), vary with the ratio t/D. In
the intermediate case of plastic buckling both t/D and
the shape of the stress-strain curve in shear beyond the
proportional limit are important factors.
No simple relation was found to describe accurately
the stress-strain curves of the tubes in shear beyond the
proportional limit. An approximate idea of the stress-
strain curve may be obtained from a knowledge of both
the yield strength in shear Tyieid and the ultimate
strength in shear tuU. The ratio of ultimate strength in
shear to yield strength in shear may be taken as a mea¬
sure of the rise in the stress-strain curve beyond the yield
point. If this ratio is close to 1 .0, the stress-strain curve
beyond the yield point will be nearly horizontal while a
ratio of 1.4 indicates a considerable rise in stress beyond
the yield point; in one case the stress-strain curve will
have a sharp knee near the yield point while in the other
that knee will be well rounded.
RELATION RETWEEN STRESS-STRAIN CURVES IN SHEAR AND
STRESS-STRAIN CURVES IN TENSION
There is still one difficulty in choosing Tvieid, tuU as
the two variables that, in addition to the variable t/D,
affect the strength of the present group of steel and
aluminum-alloy tubes. Neither of these quantities is
ordinarily known and both can be determined from
torsion tests only when the specimen has sufficiently
thick walls so that failure occurs by yielding without
any buckling. The properties of the material that are
generally known are the yield strength in tension,
< TVieia , and the ultimate strength in tension, auit. It
would he possible to substitute these two tensile prop¬
erties for the two shear properties of the material if a
simple relation of sufficient accuracy could be found
connecting the two sets of properties.
The existence of such a relation, particularly for the
chromium-molybdenum steel tubes, is indicated by the
522
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
similarity in shape of stress-strain curves in tension and
in shear of specimens cut from the same tube (see
figs. 1 and 2.) Theoretical considerations (reference 5,
p. 204) indicate that the stress-strain curve in shear
may be computed from the stress-strain curve in
tension by simply multiplying tensile strains by 1.5
and dividing tensile stresses by ^3.
The applicability of this relation to the steel tubes
was tested by using it to compute for several tubes the
stress-strain curves in shear from their tensile stress-
strain curves. The measured stress-strain curves in
shear and those calculated from the tension tests were
found to agree fairly well over their entire range. In
most cases it was noticed, however, that the calculated
stress-strain curve lay a small distance to the right of
the observed curve. A closer degree of coincidence
could have been obtained by choosing a value less than
1.5 for the factor by which tensile strains must be
multiplied to obtain shear strains. This deviation
from the theoretical values is not surprising, since the
O
OX
oo
8
o
o
R
8
—
— ft
.8
o
6
0
. Q
o
4
VewA
yic ld)s
®o
CO
$
o o
cr
(->
/9 E
/s a
D
o
±
tyield
£ yield
Ave
rage
>; 1
+
— t—
-H-
£
fc— +-
*
+ .
.±
\ -
+
+
+
*
++
+
f +
*
+
_ t_
1
±
+
+
:
1.0 UO 1.20 1.30 1.40 1.50 1.60
a ult
(6y:eld)5/!>s
Figure 7.— Ratios of yield strengths and yield strains in shear and in tension for
chromium-molybdenum steel tubes.
theoretical ratios -y’3 and 1.5 have a sound basis only
for an idealized stress-strain curve with an infinitely
sharp knee at the yield point and no rise in stress beyond
that point. For the same reason one would expect
the foregoing ratios not to hold for the aluminum-alloy
tubes in which the ratio of ultimate strength to yield
strength was not 1, but lay between 1.3 and 1.5.
An estimate of the optimum “factors of affinity”
crfr and y/e connecting stress-strain curves in tension
and in shear was obtained by plotting the ratios of
yield stresses and yield strains — ■ iel-> for each one
T yield e yield.
of the tubes tested using — — as abscissa to bring out
the variation of the two ratios of affinity with the change
in shape of the stress-strain curve beyond the yield
strength. (See fig. 7 for steel tubes and fig. 8 for alumi¬
num-alloy tubes.)
<?.<?
2.0
re
J.6
1.4
1.2
LO 1
1.26
o
Oo
0 §
p,
O
A\
/era
9e;
O
O c
1
00*5
0
o
o
- ft
o
(
§
o
6/S E
o
(■
yxcldj
/9 G
o
^ c
o
ro
D
o
X?
n,'<
d
+
+
- -±~
+
+
+
+
^ yiel
J +
+
+
-'N
1
verage-..
+ ;
-± ^
+
5
*+
+•
1.30
134
>.38
1.42
1.46 /.50
jit
(Gyi eld)s,
Figure 8— Ratios of yield strengths and yield strains in shear and in tension for
17ST aluminum-alloy tubes.
The yield strength used in these computations was
taken as that stress on the stress-strain curve at which
the secant modulus was % the elastic modulus for the
steel tubes and the stress at which it was % of the elastic
modulus for the aluminum-alloy tubes. The factors
% and % were chosen to give the same value for the
tensile yield strength of material just passing Navy
Specifications 44Tl8a and 44T21 (tables I and II) as
the yield strength laid down in these specifications
(0.2 percent offset), provided the material has a Young’s
modulus of 30X10f' pounds per square inch for the steel
tubes and one of 10 X 10s pounds per square inch for the
aluminum-alloy tubes. The tensile yield strengths
computed upon both definitions are listed in tables
\ and VI. The averages at the bottom of these tables
show that the % E yield strength is 2 percent higher,
on the average, for the chromium-molybdenum steel
tubes and that the % E yield strength agrees, on the
average, within a fraction of 1 percent with the 0.2
percent offset yield strength for the aluminum-alloy
tubes. The chief advantage of the % E and % E yield
strengths over the 0.2 percent yield strength is that it
will bring the elastic portion of the stress-strain curves
in tension into coincidence with the elastic portion of
the stress-strain curves in shear if the ordinates and
abscissas of the tensile stress-strain curve are multiplied
by the factors Tyield 7yield
Oyield tyield
respectively.
For the steel tubes (fig. 7) the ratio - scattered
T yield
within ±11 percent about an average value of 1.73
while the ratio ~1-- scattered through the same per-
tyield
centage range about an average value of 1.41. There
TORSION TESTS OF TUBES
523
is a systematic deviation from these average values
that becomes a maximum for tubes having - — --=1.3
& yield
approximately. The theoretical affinity ratios -yj3
and 1.5 are fair approximations for the stress-strain
curves approaching the idealized shape — ult =1.0.
Gyield
For the aluminum-alloy tubes (fig. 8) the picture is
quite different; the ratio ----- lies between 1.3 and 1.5.
1 & yield
It is not surprising, therefore, that the average affinity
ratios are nowhere near the theoretical values ^3 and
1.5; they are closer to 2 and 1 .3. The maximum scatter
to each side of these average values is of the order of
±11 percent.
60
%
&
<o
\40
$
o
o
o
V.'
$*>
£
to
O' 4 8/2 16' 20 x /O'3
Strain, in. /in.
Figure 9. — Comparison of stress-strain curves in shear of chromium-molybdenum
steel tubes Fo (1.38 X 0.038 in.) with curve obtained from tensile stress-strain curve
by multiplying stresses by 1/V 3 and strains by 1.4.
V ^
V (
V 2
V
□
V
V V
VoS
v
?<& °
0
boTi
>
o
B
> F
o F
i, Tc
2 >
5 .
rom
rsior
tens
r
7 specimer
7 L =/
L =/
9in.
9 in.
□ F
v F
L =-
i/e specimen Fc
15 in.
$
i
4 8/2 /6’ 20 x 10-
Strain, in. /in.
60
Q
C>
•O
C>
o
o
N'
§20
C
V)
0
Figure 10. — Comparison of stress-strain curves in shear of chromium-molybdenum
steel tubes Lo (1.5 X 0.12 in.) with curve obtained from tensile stress-strain curve by
multiplying stresses by 1/V 3 and strains by 1.4.
The usefulness of these approximate affinity rela¬
tions in predicting the shear stress-strain curve from the
tensile stress-strain curve is brought out by figures 9
and 10 for a group of steel tubes and by figures 11 and
12 for a group of aluminum-alloy tubes. These figures
show the stress-strain curves in shear as computed from
those in tension by multiplying tensile strains by 1.4
for the steel tubes and by 1.3 for the aluminum-alloy
tubes and dividing the tensile stresses by -^3 and 2,
respectively. The stress-strain curves in shear as
obtained directly from the torque-twist curves are
shown for comparison. The calculated curves ap¬
fT°
o ° °
+ X
A A
O O
x x
A
°+x ‘
A A
%
A
o
A
D Of
X
* A
A
.xacr^--
P
X)
i
.... &
t
+ L
x u
Torsion
//
spec
/
imen
L = /
L =/
9 in.
9 in.
*
a
X
A
-A
A L
oFr
‘0/77 /
//
ensi/t
//
3 N
I
L = 4
Lq
?5/n.
F
+
A
+
4 8/2/6 20x10
Strain, in. /in
proached those obtained from the test data satisfac¬
torily; i. e., within the limits of variations of the differ¬
ent torsion tests, except in the neighborhood of the
knee, where the stresses deviated as much as 15 percent
for the aluminum-alloy tubes Mj, M2, M0 (fig. 11).
The greater deviation from affinity for the aluminum-
alloy tubes as compared with the steel tubes is also
brought out by a comparison of figure 2 with
figure 1.
30
6.
CF
$
o
C5
to' /O
to
tb
C
x
cn
0
Figure 11. — Comparison of stress-strain curves in shear of 17ST aluminum-alloy
tubes Mo (2X0.11 in.) with curve obtained from tensile stress-strain curve by multi¬
plying stresses by 0.5 and strains by 1.3.
o
o
O
XF
X
X
4*
c
, *
c
9
£>
o *
Hr
U
o *
o'
2 _
O
Ok
?
o *
fc
+ M,
X Ma
S3
Tor
•om
-si or
//
tern
_
> specim
tl
'He spec
_ 1 _
en 1
L
:ime/
>2L
=6C
7 M0
1 in.
/ in.
_
J _ _ 1 _ I _ I _ L _ I _ I _ J _ L
2 4 6 8 /Ox/O'3
Strain, in. /in.
40
Cr
$
Q>
O
to
<0
<u
c
to
30
20
/O
+ < o
—
Tor
om
si or
tern
~~i
spi
~i/e _
ecim
u
spec
en L
L
imet
m2i
, = 6G
7 y0
~n.
f n.
s. + +
. +
+o
+ C
t>A
i-
*
<
o +
4
*0-
P+
* O
\
- 0
O
4 6 8
Strain, in. /in.
/O
!2x/0 '
Figure 12.— Comparison of stress-strain curves in shear of 17ST aluminum-alloy
tubes yo (1X0.09 in.) with curve obtained from tensile stress-strain curve by multi¬
plying stresses by 0.5 and strains by 1.3.
VARIATION OF STRENGTH OF TUBBS WITH DIMENSIONS AND
PHYSICAL PROPERTIES
Variation of stresses at failure. — It has been stated
that the tubes tested failed either by plastic torsion,
two-lobe buckling, or a failure intermediate between
these and that the strength of the tube should there¬
fore depend on the variables determining these three
types of failure. For a tube of given metal, i. e., given
elastic constants, the length of which is in the range
where its effect is negligible, these variables are the
wall thickness over diameter ratio t/D, and at least two
variables describing the plastic properties in shear of
the tube material; e. g., the yield point in shear, TvUld
and the ultimate strength in shear, ruU. In the previous
section it was shown that the shear properties and
tensile properties of the tube material were roughly
affine. The last two variables may therefore be re¬
placed by the corresponding tensile properties, i. e.,
(TVieid and <ruU. In general, then, one would expect that
524
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the maximum shearing stress of the tubes would follow
a relation of the type:
■M
j a
yield) ®ult
(9)
It is necessary to reduce the number of independent
variables from 3 to 2 in order to represent the results as
a family of curves on a sheet of paper. This reduction
may be accomplished by trying various relations be¬
tween Tmax and one of the independent variables and
then choosing the one that gives the most consistent
behavior for the experimental points. After a number
tubes (fig. 13) show a large scatter throughout the range
tested. This result would be expected from the con¬
siderable variation in the ratio and the values of
O yield
Cult itself (table V). The points for the aluminum-
alloy tubes (fig. 14) fall close to a common curve except
for the very thin tubes, which failed by elastic buckling.
Figure 14 clearly shows a segregation into the three
types of failure that were observed; i. e., failure by elas¬
tic two-lobe buckling on the extreme left, failure by a
combination of yielding in shear and buckling in the
middle, failure in pure shear on the extreme right.
The two extreme types of failure are understood fairly
Figure 13. — Variation of ratio of shear stress at failure to tensile
yield strength with t/D for chromium-molybdenum steel tubes.
= 15.27 1(— - A +0.981.
d D \(T yield J
V3
Straight lines in central region calculated from:
of trials the most consistent behavior for the steel
tubes was found by plotting:
* jimiA (io)
Cyield O' i /ield/
The factor ^3 was chosen to make the ordinates close
to 1 for most of the tubes.
For the aluminum-alloy tubes it appeared preferable
to plot:
9 T max jl ^ ault \ (ii)
Cult \D O yield/
The corresponding plots using t/D as abscissa and the
term on the left as ordinate are shown in figures 13 and
14 for the two groups of tubes. The points for the steel
well. The theoretical shearing stress at failure for a
long tube failing elastically is given by equation (6);
for tubes of finite length, it can either be derived from
Schwerin’s theory (reference 6) or it can be read off di¬
rectly from the curves computed by Donnell (reference
7). (The three curves shown for elastic two-lobe buck¬
ling in figs. 13 and 14 correspond to minimum, average,
and maximum values of avUU and ouU, respectively, as
measured for the tubes tested.)
Figures 13 and 14 show that no more than 7 of the
steel tubes and no more than 20 of the aluminum-alloy
tubes can be considered as having failed by elastic
buckling; this number includes the tubes lying in the
transition region between elastic failure and combined
failure as well as those definitely to the left of it. The
TORSION TESTS OF TUBES
525
Figure 14. — Variation of ratio of shear stress at failure to tensile strength with t/D for 17ST aluminum-alloy tubes. Straight line in central region calculated from:
9— =8.96-^+0.501.
b Toil D
approximate analysis in an earlier section of this paper
had predicted that 8 of the steel tubes and 11 of the
aluminum-alloy tubes should have fallen into this cate¬
gory. The agreement, though not close, is sufficient
considering the uncertainty of the assumptions made,
especially those relative to the limit above which
combined failure must be expected.
In every case of elastic buckling the long tubes failed
at a lower stress than the short ones, the difference
exceeding 30 percent in some cases. Schwerin’s for¬
mula for long tubes (equation (6)) is not sufficient,
therefore, to describe the strength of the short tubes
failing elastically. An adequate comparison with the
theory must include the effect of length as considered
in general by Schwerin (reference 6) and in detail by
Donnell (reference 7). Donnell has shown that the
effect of length L, thickness t, and diameter I) on the
strength in torsion of an elastic tube may be repre¬
sented on a single curve by plotting
as a function of
B=
_r L
E t
i m
WD3
Figure 15 shows the curves derived by Donnell for
tubes with hinged edges and with clamped edges to¬
gether with Schwerin’s curve for infinitely long tubes.
The individual points represent the observed values of
computed from the observed shear stress at
failure and the dimensions of the tube and the following
elastic constants: for chromium-molybdenum steel
tubes,
E—28, 600,000 pounds per square inch, ^=0-235, (12)
for 17ST aluminum-alloy tubes,
El—2 10,430,000 pounds per square inch, m=0-319. (13)
10.0
5.0
x Steel -Donnell. a Aluminum alloy 17 ST. NBS.
o Chromium- molybdenum steel. NBS.
— Donnell's "exact'1 solution. - Schwerin (p=O.S).
Two-iobe buckling
55T-.
f
=
w
T
three -
i i- i ; . i
'obe
buckling
Clomped edges
H/nged edges
05 JO
.50 LOO
1_ LH
/F/F IP
• 4 rt
.. tli
i.
50 100
Figure 15. — Comparison of observed shear stress at failure of tubes that failed by
plastic buckling with theoretical values given by Donnell and Schwerin.
The Young’s moduli represent average values of the
modulus measured in the tension test (tables \ and
VI). The values for Poisson’s ratio represent an aver¬
age of values calculated for each size ol tube from the
well-known relation This relation is strictly
true only for perfectly isotropic material obeying
Hooke’s Law. The relatively low value of n for the
steel tubes may be due partly to lack of isotropy of the
material. It did not seem worth while to investigate
this in view of the small effect of a change in p on the
critical stress of a thin tube as given by figure 15. The
526
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
points for the steel tubes are scattered over the same
region as those obtained by Donnell in tests on steel
tubes buckling with two lobes (crosses); they are
on the average about 26 percent below the curve for a
tube with hinged edges. The points for the aluminum-
alloy tubes are somewhat higher, scattering through a
range of about ±25 percent about the curve with hinged
edges. A few points fell into the border region between
two-lobe and three-lobe failure. Examination of the
corresponding tubes indicated a failure which may have
started with three lobes but which ended with two lobes
as the deformation increased. No definite reason can
be assigned for the greater strengths of the aluminum-
alloy tubes; possibly the closer tolerances within which
the tubes are manufactured permit them to develop
more nearly the full theoretical strength of the ideal
tube. All of the tubes except one showed strengths
greater than that given by Schwerin’s formula for
infinitely long tubes. Donnell’s curve for hinged
edges may, therefore, be taken as a fair estimate of the
probable strength of the tubes failing elastically while
Schwerin’s fornmla may be used to give a lower limit
of their strength.
Failure in plastic shear may be expected when the
shear stress reaches a value equal to the ultimate shear
strength, tuU, of the material. In the case of the
steel tubes (fig. 13) this assumption leads to a family of
horizontal straight lines having the ordinate
A 3r _ -yf^Tuu (Tuit
Gyield Quit Gyield
It is seen, after drawing the curves corresponding to
elastic failure for a long tube as given by equation (6)
and the horizontal straight lines corresponding to
failure by plastic shear, that most of the points fall
into the intermediate region. For the aluminum-alloy
tubes the individual points seem to fall about a common
straight line increasing with the t/D ratio. The points
for the steel tubes in figure 13 show too great a scatter
to suggest the type of variation *witli t/D at a glance;
however, it appears, after segregating the points into
groups with nearly constant ratio c Tult/(rvield that a
linear increase with t/D is the simplest variation that
gives an approximate fit. It remains to find an em¬
pirical relation between the stress ratio at failure and
the ratio (ruU/avieid. A number of formulas were tried
and the best fit was obtained with a formula of the
type:
v/3 r t
— =an
& yield -Ls
Vult
Gyle Id
i)+4
(16)
where a and 6 are constants. Evaluating these con¬
stants by least squares gave a = 15.27 and 6=0.981 so
that the stress ratio at failure of the chromium-molybde¬
num steel tubes buckling plastically may be expressed
by the empirical formula:
=15.27 _i)+0.981, (°-O2<B<O O0
Gyield LJ\(JvUU / (L/D< 80). (17)
The stress ratios calculated from this formula are
plotted against the observed stress ratios in figure 16.
The points scatter about 5 percent to either side of the
Only 2 of the 63 steel tubes tested fell into the region of
failure in pure shear. These two were insufficient to
establish a value for the ratio Tuit/<ruu- In the absence
of adequate test data it was decided to assume this
ratio to be the same as that of the yield strengths:
Tuit== Gun 0,577 (Tun (14)
This assumption is believed to be conservative since the
corresponding ratio of ultimate stresses for the alumi¬
num-alloy tubes was found to be about 10 percent
higher; i. e., 0.64. Converting equation (14) into the
ordinates used in figure 13 gives the family of horizontal
lines:
Tult _ &utt
Gyield Gyield
In the case of the aluminum-alloy tubes (fig. 14) 18
of the points fall into the region of plastic shear. They
scatter about a common horizontal line with the ordi¬
nate
2— = 1.28 (15)
*uU
For the aluminum-alloy tubes, therefore, the ultimate
strength in plastic shear is about 64 percent of the ulti¬
mate strength in tension.
Figure 16.— Comparison of calculated and observed stress ratios for chromium-
molybdenum steel tubes.
line of exact agreement. The corresponding empirical
formula for the plastic buckling of the aluminum-alloy
tubes was also evaluated with the help of least squares;
it may be written -as:
TORSION TESTS OF TUBES
527
-^-=4.48^+0.2506, (+022<-^<0.085,^ < 6o)- (18)
The lower limit of p=0.022 corresponds to the cut-off
of the empirical formula by Schwerin’s curve for long
tubes. Data on torsion tests of short tubes kindly
.70
U
(b
V.
5
.60
.50
.40
0 on
o .30
I 'v*
.20
JO
0
JO
.20
30
T
Cfu/t
/
+
/
A A
Kj / O/
+ -
4$
.40 .50 .60 . 70
observed
Figure 17. — Comparison of calculated and observed stress ratios for 17ST aluminum-
alloy tubes:
— =4.48 4,+0.2506
Tull V
for, 0.022< -D < 0.085.
supplied by the Aluminum Company of America in¬
dicate that the cut-off for short tubes can be moved
to smaller values of jy The tests made by the Aluminum
Company of America (Physical Test Report Xo. 31-40)
on 13 17ST tubes having a jj ratio ranging from 0.0095
to 0.02 and an ^—4.8, indicate that the straight line
The individual points scatter about 4 percent to either
side of the line of exact agreement.
Design charts for twisting moment producing fail¬
ure. — Designers are usually more interested in expres¬
sing the torsional strength of a tube in terms of torque
at failure rather than in terms of the mean fiber stress r
at failure. The value of r had originally been derived
from M by relation (5), so that r and M are connected
by the formula:
M
ttD 3 t
2 D
Formulas for M for the three types of failure may be
obtained from equation (19) by substituting for r
the value obtained from Donnell’s work (fig. 15) for the
case of elastic failure, from equations (17) and (18) for
the case of combined failure, and from equations (14)
and (15) for the case of plastic failure.
Elastic failure by two-lobe buckling depends, accord¬
ing to Donnell, on the length as well as on the wall-
thickness ratio t/D of the tube. For long tubes (fig.
15) the length effect is small, however, and the actual
strength of the tube will be only a few percent
greater than that given by Schwerin’s formula (6) in
which the length does not enter.
Substituting equations (6), (17), (14), and (12) in
equation (19) gives the following formulas for the
twisting torque at failure of the chromium-molybdenum
steel tubes: two-lobe buckling failure of a long tube:
M
3.11X10 '(£)•"(! +„4) (20)
D <J yield & yield
(0<p<0.024)
combined plastic failure and buckling
M
IP
-=0.908
G yield
GX
1-++2+)
15.27
t / O’?/ 1 1 _
D V & yield
+ 0.981 (o.015>^ >0.092) (21)
failure in pure shear:
M
-0.908^1 — 2^+2^)^
II O’ yield H
0.068<p<0.100)
(22)
(18) may be extended to the left down to j^=0.09 at
which point it is cut off by Donnell’s curve (see fig. 15)
for jf=4.8. Tests on 23 further tubes with ^=7 and
with yj ranging from 0.018 to 0.099 were found to scatter
uniformly about the straight lines given by (18) and
(15). The stress ratios calculated from formula (18)
are compared with the observed stress ratios in figure 17.
The ranges of t/D for which each one of these formulas
holds overlap because the boundary between the differ¬
ent types of failure depends on ayieu and <suU in addition
to t/D. The proper type of formula to use in any given
case is the one that gives the lowest twisting moment M.
In the special case of a material for which Gull Gyield)
it is seen that combined failure according to equation
(21) should always occur in preference to failure in
pure shear, the torque for combined failure being about
2 percent less than that for pure shear. Actually the
2 percent variation is not significant ; the experimental
scatter of points would produce an uncertainty of this
528
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
order in the fitting of the empirical relation (17) by
least squares. For material having a stress-strain
curve such that cruit=^vuid equations (21) and (22)
should coincide since a tube of such material would not
be able to carry more than the yield stress in torsion of
the material.
The equations (20), (21), and (22) cannot be ex¬
pressed in Cartesian coordinates as a single curve or
even as a family of curves because they contain the
four variables
M
t &ull
D3
G yield D Gyigid
show them as a single curve in a nomographic chart
connecting the first three variables, <jvuu must be
-> and a
yield •
In order to
expressed as a function of— ^
G yield
of a type form;
G yield
Co
Gull
^\Gyield
')■
-Cl
(23)
which converts equation (20) into the same type form
as equation (21). Evaluating c0 and C\ to give the best
fit to the observed values of the tensile yield strengths
plotted as a function of
for (23):
Gull
G yield
gave the following relation
106
' yield -
6 62(_?uu _A_|_9 79
\Gyield /
(24)
Figure 18 shows the nomogram that was derived from
equations (21) and (22) after substituting equation (24)
in (20). Two examples illustrate the use of this
nomogram.
1. Find the wall thickness of a 2-inch chromium-
molybdenum steel tube 4 feet long that will fail when
subjected to a torque of 2,500 lb. -ft. The tensile
yield strength of the tube material is 80,000 pounds
per square inch and its tensile ultimate strength is
100,000 pounds per square inch.
Answer. The tube falls within the range of dimen¬
sions and properties of those tested so that figure 18
may be applied to compute its wall thickness.
G ull
G yield
100000
80000
= 1.25
M _ 2500X12
D^Gyieia 23 (80000)
0.0469
Connecting these points on the nomogram (dotted
line, fig. 18) gives:
*
D
= 0.0487, *=2X0.0487=0. 0974 inch.
Failure by combined plastic shear and buckling may
be expected.
2. Find the wall thickness of a 1 K-inch chromium-
molybdenum steel tube 5 feet long that will fail when
subjected to a torque of 600 lb.-ft. The tensile yield
strength of the tube material is 75,000 pounds per
square inch and its tensile ultimate strength is 95,000
pounds per square inch.
Answer. The tube falls within the range of dimen¬
sions and properties of those tested so that figure 18
may be applied to compute it.
auu _95,000
Gyield 75,000
M
DA Gyie Id
600X12
1.53 X 75,000
0.0284
Connecting these points on the nomogram (dotted
line, fig. 18) gives two intersections as follows:
*
D
= 0.0229, ^=0.0302.
The first value corresponds to two-lobe buckling as a
long tube and the second, to combined failure. A
heavier tube is required to resist combined failure than
to resist buckling; hence combined failure is more
likely to occur. The wall thickness must be chosen as
*=1. 5X0.0302 = 0.0453 inch.
Frequently material is required to satisfy certain
specifications for minimum yield strength and tensile
strength.
Design curves for such material may easily be derived
either from equations (20), (21), and (22) or from
figure 18 by the substitution of the specified values of
c Tuii and Gyieid. Figure 19 shows a design chart for
determining the size of chromium-molybdenum steel
tubes 19 to 60 inches in length that just meet the mini¬
mum requirements of Navy Specifications 44T18 and
44T18a (table I).
The material of the tube specified in problem 2
just meets Navy Specification 44T18a. The curve of
figure 19 can, therefore, be applied directly to solve
problem 2.
M 600X12
1.53
7,200
3.375
2,130 lb./sq. in.
The ordinate ^=2,130 intersects curve B at ^=0.03.
A vertical through the point of intersection extending
into the lower half of the chart intersects the inclined
line for D= 1.5 inch at a value of *=0.045 inch. This
solution coincides with the one obtained from the nomo¬
gram of figure 18.
Design charts for the aluminum-alloy tubes may be
obtained by substituting the expressions for critical
stress given by equations (6), (18), and (15) into equa¬
tion (19). If, in addition, the values given in equation
(13) for the elastic constants E and are substituted,
the following three equations are obtained for the
torque at failure.
For elastic two-lobe buckling of a long tube according
to Schwerin:
M
D3
Gull
i.2xi oy t y
Gull \DJ
1 4-0.4^
0<g<0.02
(25)
TORSION TESTS OF TUBES
529
1.6 —
1.5 —
1.4 —
(fylt
(fyield
1.2 —
/./ —
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
530
lb./sq. in., <rv,v;i=75,000 lb./sq. in.).
lor combined plastic failure and two-lobe buckling:
ingly, be described with the help of the three variables
M
Do
b=0-394(B)(1 + 15'95- 33J^)’
0.02<— <0.088^
for failure in pure shear:
M
= 1 .005^- Y 1 -2^+2 ~
D3ouU \DJ\ D D 2
(o.088<^<0.12
(26)
(27)
I he strength of the aluminum-alloy tubes can, accord -
yv — > (Tun, and L- Only the two variables yr- anc^ n
Lrouit D J Do uii
are needed if curves of (25) are plotted for given values
of ouU as in figure 14. This procedure results in figure
20. A simple example will illustrate the use of these
curves.
Find the wall thickness of a 2-inch 17ST aluminum-
alloy tube 5 feet long that will fail when subjected to a
torque of 2,000 lb. -ft. The tensile strength of the tube
material is 68,000 pounds per square inch.
Answer. — The tube falls within the range of dimen¬
sions and properties of those tested so that figure 20
may be applied to compute it.
TORSION TESTS OF TUBES
531
M 2,000X12
Ddault 23 X 68,000
0.044]
According to figure 20, this corresponds to
•^=0.061, *=0.061X2 = 0.122 inch.
The wall thickness of the tube that may be expected
to fail under about 2,000 Ib.-ft. torque would be 0.122
inch.
A design chart similar to figure 19 may be derived
from figure 20 for aluminum-alloy material required to
satisfy certain specifications for minimum tensile
strength. Figure 21 shows such a chart for 17ST tubing
complying with Navy Specification 44T21 (table II);
the upper half of the figure was constructed from figure
20 by substituting 55,000 pounds per square inch for
while the lower half is a set of straight lines cor¬
responding to commercially available diameters of 17ST
tubing. The following example illustrates the use of
figure 21.
Find the wall thickness of a 2-inch 17ST aluminum-
alloy tube 5 feet long that will fail when subjected to
a torque of 1,000 lb.-ft. The material of the tube shall
just meet Navy Specification 44T21.
The tube falls within the range of dimensions and
properties of those tested so that figure 21 may be
applied to compute it.
M
£>3
1000X12
23
1,500
It is seen that by following the dotted line in figure
21 that this value corresponds to a wall thickness of
*=0.086 inch in a tube 2 inches in diameter.
National Bureau op Standards,
W ashington, D. C., February 1937.
REFERENCES
1. Otey, N. S.: Torsional Strength of Nickel Steel and Dural¬
umin Tubing as Affected by the Ratio of Diameter to Gage
Thickness. T. N. No. 189, N. A. C. A., 1924.
2. The Allowable Stress in Tubes Subjected to Torsion. A. C.
I. C. No. 641, Materiel Division, Army Air Corps, 1929.
3. Templin, R. L., and Moore, R. L.: Specimens for Torsion
Tests of Metals. A. S. T. M. Proc., Part II, 30, 1930,
pp. 534-543.
4. Fuller, Forrest B.: The Torsional Strength of Solid and
Hollow Cylindrical Sections of Heat-Treated Alloy Steel.
Jour. Aero. Sci., vol. Ill, no. 7, May 1936, pp. 248-251.
5. Nadai, A.: Plasticity. McGraw-Hill Book Co., Inc., 1931.
6. Schwerin, E.: Die Torsionsstabilitat des dunnwandigen
Rohres. Z. f. a. M. M., vol. V, no. 3, June 1925, pp.
235-243.
7. Donnell, L. H.: Stability of Thin- Walled Tubes Under Tor¬
sion. T. R. No. 479, N. A. C. A., 1933.
532
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 21.— Design chart for torsional strength of 17ST aluminum-alloy tubes 19-60 inches long satisfying Navy Specification 44T21 (Vui, =55.000 lb./sq. in.).
TORSION TESTS OF TUBES
533
TABLE V.— TENSILE AND HARDNESS PROPERTIES OF CHROMIUM-MOLYBDENUM STEEL TUBES
Speci¬
men
Nominal size
(in.)
Yield strength
Tensile
strength
(lb./sq. in.)
Elonga¬
tion in 2
inches
(percent)
Vickers numbers *>
Young's
modulus
(lb./sq. in.)
Tensile
strength
Yield
strength
0.002 «
(lb./sq. in.)
5/9 E
(lb./sq. in.)
Left
end
Right
end
Ao
MX0.Q28
84, 000
84, 300
97, 400
23.0
209
224
29.9X106
« 1. 16
Bo
1 X .035
89, 000
91,000
101, 000
18.0
216
214
28.8
1. 14
Co
VAX .049
93, 000
93, 500
102, 500
12.5
224
213
29.0
1. 10
Do
1J4X .058
99, 000
100, 000
110, 700
18.5
249
240
29.1
1.12
Eo
2 X .065
108, 000
109, 500
114,800
18.5
264
253
28.7
1.06
Fo
1%X .035
81, 000
84, 000
118, 700
17.2
263
264
28.8
1.46
Go
VAX .035
69, 200
69, 000
107, 300
28.5
260
260
29.0
1.55
Ho
VAX .049
78, 600
79, 400
88, 400
17.0
214
204
28.5
1. 12
Io
lAX .065
67, 700
67, 700
105, 300
32.0
206
214
28.6
1. 56
Jo
1HX .083
82,200
85, 500
114, 300
24.0
262
263
28.8
1.39
Ko
VAX .095
110, 000
110, 500
113,300
16.8
243
242
28.8
1.03
Lo
VAX . 120
96, 000
97, 000
106, 700
26.0
236
232
28.5
1.11
Mo
VAX .049
90, 500
91, 100
96, 600
16.0
241
266
27.3
1.07
No
VAX .049
96, 800
103, 600
132, 900
19.0
296
311
27.6
1.37
Oo
VAX .035
93, 000
93, 300
100, 300
14.0
240
274
27.5
1.08
Po
VAX .035
105, 000
105, 300
109, 700
16.0
283
262
27.6
1.04
Qo
2 X .035
99, 100
101, 000
109, 200
11.5
264
245
27.6
1. 10
Ro
VAX .035
95, 200
95, 900
101, 700
14.0
254
248
29.0
1.07
So
VAX .035
87, 800
88, 200
98, 200
16.0
252
239
28.4
1.12
To
VAX .035
93, 800
95, 500
107. 400
17.0
245
232
28.2
1. 14
Uo
1 AX .049
103, 800
105, 300
122, 000
15.0
272
270
28.8
1. 18
Vo
2 AX .032
75, 000
73, 000
122, 500
24.0
281
270
30.2
1.63
Average (22 speci-
mens) _ . . .
90, 800
92,900
108, 200
18.8
249
247
28.6
1.208
“ Stress at which strain exceeds
1 Vickers numbers for 10-kg weight.
c Based on 0.002 yield strength.
by 0.002, in./in.
TABLE VI.— TENSILE AND HARDNESS PROPERTIES OF 17ST ALUMINUM-ALLOY TUBES
Speci¬
men
Nomina! size
(in.)
Yield strength
Tensile
strength
(lb./sq. in.)
Elonga¬
tion in 2
inches
(per¬
cent)
Vickers numbers b
Young’s
modulus
(lb./sq. in.)
Tensile
strength
Yield
strength
0.002 o
(lb./sq. in.)
2/3 E
(lb./sq. in.)
Left
end
Right
end
lo
1 XO. 018
46, 600
46, 700
63, 400
24.0
127
125
10. 27X10«
Cl. 36
mo
1 X .020
47, 200
47, 300
63, 600
22.0
134
133
10. 18
1.34
no
1 X .022
48, 900
49, 000
65, 400
25.0
134
134
10. 13
1.34
oo
1 X . 025
49, 000
49, 100
65, 200
24.0
133
133
10. 34
1.33
Po
1 X .028
46, 400
46, 400
64, 800
25.0
134
136
10. 43
1.40
qo
1 X .032
45, 300
45, 400
65, 400
17.0
134
135
10.31
1.44
so
1 X .042
46, 500
46, 500
65, 900
24.0
137
134
10.41
1.42
to
1 X .049
46, 600
46, 600
66, 300
27.0
135
135
10. 34
1.42
uo
1 X . 058
45, 600
45, 500
66, 000
27.0
137
135
10.48
1. 45
VO
1 X .065
44, 300
44, 100
65, 800
29.0
135
135
10. 48
1.49
Wo
1 X .072
45, 800
45, 600
65, 900
29.0
135
134
10. 54
1.44
Xo
1 X . 083
45, 500
45, 500
65, 300
29.0
135
135
10. 37
1.44
yo
1 X .095
45, 300
45, 300
65, 300
28.0
137
137
10.35
1.44
zo
1 X . 109
47, 400
47, 400
65, 000
28.0
137
138
10.46
1.37
Aao
1 X . 120
47, 400
47, 300
65, 800
28.0
140
140
10. 56
1.39
Uo
l^X .022
46, 900
47, 100
65, 900
18.0
134
132
10. 30
1.40
Vo
1AX .025
47, 300
47, 400
64, 200
21.0
136
137
10. 42
1.36
Wo
1 AX .028
49, 400
49, 500
67, 000
25.0
137
137
10.51
1.35
Xo
1AX .032
48, 000
48, 100
65, 600
25.5
135
134
10. 05
1.36
Yo
1AX .035
50, 200
50. 300
66, 200
27.0
142
142
10. 40
1.32
Zo
VAX .042
47, 200
47, 300
66, 200
23.5
134
137
10. 35
1.40
ao
lAX .049
46, 600
46, 600
65, 900
27.0
135
135
10. 17
1.41
bo
VAX .058
45, 800
45, 700
65, 800
31.0
137
135
10. 66
1.44
Co
lAX .065
46, 400
46, 400
64,000
28.0
134
131
10.41
1.38
do
1AX .072
44, 400
44, 500
63, 200
28.0
140
138
9. 79
1.42
eo
VAX -083
46, 500
46, 600
63,900
28.0
136
137
10. 29
1.37
fo
1HX .095
47, 200
47, 200
65, 200
25.5
138
138
10. 46
1.38
go
lAX . 109
49, 700
49, 800
66, 200
25.0
137
135
10. 36
1.33
ho
1AX -120
47, 600
47, 600
67, 000
30.0
137
138
10. 59
1.41
io
1AX .134
47, 500
47, 500
66, 600
30.0
136
137
10. 48
1.40
jo
1MX .148
47, 900
47, 900
66, 400
31.0
135
136
10.59
1.39
ko
l^X .165
47, 400
47, 300
66, 100
31.0
138
139
10. 77
1.40
Ao
2 X .022
47, 400
47, 400
63, 800
d 16. 5
133
132
10. 48
1.35
Bo
2 X .025
49, 400
49, 400
62, 800
MO.O
134
132
10.65
1.27
Co
2 X .028
48, 400
48,500
64, 700
d 11. 0
134
134
10. 49
1.33
Do
2 X .032
48, 300
48, 400
64, 500
23.0
132
131
10. 38
1.33
Eo
2 X .035
48,900
49, 000
65, 400
24.0
134
131
10.50
1.33
Fo
2 X .042
49, 600
49, 500
6-1, 100
23.0
135
132
10. 75
1.30
Go
2 X . 049
50, 000
49, 900
65,200
22.5
134
133
10. 75
1.31
Io
2 X .065
46, 100
46,000
65, 100
30.0
134
131
10.61
1.42
Jo
2 X .072
48, 600
48, 700
66, 200
27.0
136
133
10. 32
1.36
Ko
2 X .083
47, 400
47, 200
66,000
29.0
134
134
10.81
1. 40
Lo
2 X .095
47,900
47, 800
65, 100
30.0
133
133
10. 73
1.36
Mo
2 X • 109
49, 700
49, 800
65, 100
29.0
133
134
10.40
1.31
No
2 X .120
46, 700
46, 700
65, 800
29.0
134
133
10. 53
1.41
Oo
2 X . 134
47, 100
47, 100
64, 000
28.0
133
131
10. 56
1.36
Po
2 X . 148
48, 000
48, 000
66, 000
28.0
133
134
10.29
1.38
Qo
2 X • 165
48. 800
48, 900
65, 400
30.0
137
134
10. 37
1.34
Ro
2 X .180
48, 500
48, 500
65, 600
31.0
137
134
10. 12
1.35
So
2 X . 203
48, 000
48, 000
66, 100
30.0
135
135
10.64
1.38
To
2 X .220
48, 300
48, 300
65, 900
34.0
133
133
10. 46
1.36
Ave
ir
rage (51 spec-
nens) _
47, 470
47, 480
65, 320
26.0
135
134
10.43
| 1.377
• Stress at which strain exceeds by 0.002 in./in.
& Vickers number for 10-kg weight.
« Based on 2/3 E yield strength.
d Broke at end of plug.
534
REPORT NO. 601— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE VIE— ^RESULTS OF TORSION TESTS OF CHROMIUM-MOLYBDENUM STEEL TUBES
Speci¬
men
Length
L (in.)
Outside
diameter
D (in.)
Thickness
t (in.)
LID
t ID
Yield
strength
in shear
by 5/9 G
method
(lb./sq. in.)
Mean fiber
shear stress
at failure
(lb./sq. in.)
Shear
modulus
(lb./sq. in.)
Final type
of failure 0
A,
19
0. 750
0. 0304
25.3
0. 04055
48, 600
50, 600
11. 55X10 6
2 lobes.
A2
19
. 750
.0303
25.3
. 04040
47, 900
50, 400
11. 50
Do.
A 5
60
.751
. C302
79.9
. 04020
49, 500
51,100
12. 05
Do.
B,
19
1.001
. 0381
19.0
. 03807
54, 900
57, 000
11. 55
Do.
Bj
19
1.001
.0380
19. 0
. 03795
56,000
57, 300
11.80
Do.
B,
19
1.001
. 0380
19.0
. 03795
57, 400
57, 700
11.36
Do.
c,
19
1. 128
.0479
16.9
.04245
54, 300
56, 400
11.80
Do.
c2
19
1. 127
.0480
16.9
. 04255
54, 400
56, 700
11.86
Do.
c»
60
1. 127
.0480
53. 2
. 04255
54, 500
57, 700
11.86
DO.
Di
19
1. 503
. 0580
12. 6
. 03860
59, 800
61, 500
11.75
Do.
Dj
19
1. 503
.0580
12.6
. 03860
59, 700
61, 800
11.75
Do.
Da
19
1.503
.0581
12.6
.03866
58, 000
61, 400
11.97
Do.
D«
19
1.503
.0581
12.6
. 03866
59, 000
60, 800
11.70
Do.
1>5
48
1.503
.0581
31.9
. 03866
58. 500
59, 800
11.52
Do.
E,
19
2. 004
.0652
9.5
. 03255
6C, 100
60, 900
11.30
Do.
e2
19
2. 004
.0652
9.5
. 03255
57, 500
59, 100
11.62
Do.
Ea
19
2.004
.0653
9.5
. 03258
60, 000
60, 300
11.45
Do.
Es
48
2.005
. 0652
24.0
. 03255
59, 100
59, 900
11.52
Do.
Fi
19
1.377
. 0382
13.8
. 02775
47, 000
53, 400
11.08
Do.
F2
19
1.377
.0382
13.8
. 02775
45, 300
53, 300
11.23
Do.
Fs
45
1. 385
.0381
32.7
. 02753
46, 100
53, 000
11.30
Do.
Oi
19
1. 498
. 0349
12.7
. 02330
39, 500
46, 000
11. 17
Do.
02
19
1.499
.0349
12.7
. 02326
40, 500
45, 900
10. 86
Do.
Os
45
1.498
. 0349
30. 1
. 02330
43, 800
47, 200
11.83
Do.
Hi
19
1. 510
.0528
12.6
. 03500
47, 700
50, 500
11.76
Do.
h2
19
1.511
. 0527
12.6
. 03486
47, 400
49, 800
11.42
Do.
I.
19
1.510
. 0685
12.6
. 04540
40, 000
54, 300
11.42
Do.
I2
19
1.510
.0687
12.6
. 04550
38, 000
52, 200
11.42
Do.
Ji
19
1. 503
.0845
12.6
.0562
47, 000
65, 700
11.90
Do.
J2
19
1.503
.0845
12.6
.0562
47, 100
65, 500
11.83
Do.
Js
47
1. 503
.0845
31.4
. 0562
47, 500
65, 100
11.32
Do.
K,
19
1.502
.0926
12.6
.0617
63, 500
68, 600
11.90
Do.
k2
19
1.503
.0925
12.6
. 0616
63, 100
68, 800
11.73
Do.
Ei
19
1.500
. 1259
12.7
. 0840
54, 500
62, 900
12.00
Do.
l2
19
1.499
. 1258
12.7
. 0840
53,000
61, 000
12. 05
Do.
LS
45
1.500
. 1258
30. 2
. 0839
51,500
59, 400
11.30
Helix.
Mi
19
1. 630
. 0495
11.6
. 03035
54, 500
55. 800
11. 55
2 lobes.
M2
19
1.631
.0495
11.6
. 03033
54, 500
57, 400
11.72
Do.
Ni
19
1 753
.0509
10.8
. 02905
56, 300
62, 600
11. 26
Do.
N2
19
1. 752
. 0509
10.8
. 02907
57, 000
61,700
11. 26
Do.
Ns
45
1. 752
.0507
26. 1
. 02895
54, 300
81, 500
11.33
Do.
Oi
19'
1.626
. 0359
11.7
. 02206
54, 500
54, 600
11.60
Do.
o2
19
1. 625
. 0358
11. 7
. 02202
55, 400
11.72
Do.
03
60
1.628
. 0357
36.8
. 02196
b 56, 600
56. 000
11.55
Do.
Pi
19
1.751
.0356
10.8
.02030
59, 000
11. 62
Do.
p2
19
1. 752
. 0354
10.8
. 02022
57, 900
12.23
Do.
Pa
60
1. 751
. 0354
34. 2
. 02022
56, 000
11.65
Do.
Qi
19
2. 005
. 0361
9.5
. C1801
56, 400
11.30
Do.
Q»
60
1.998
.0360
30.0
. 01801
53, 100
11. 10
Do.
Hi
19
1. 124
.0316
16.9
. 02815
‘ 57, 200
57, 000
11.55
Do.
r2
19
1. 124
.0317
16.9
. 02822
» 59, 100
58, 900
11.83
Do.
Ra
60
1. 124
.0317
53.4
. 02822
61, 000
11.69
Do.
s,
19
1.250
.0338
15. 2
. 02706
52, 500
53, 000
11.83
Do.
S2
19
1. 251
. 0338
15. 2
. C2700
52, 800
52, 800
11.70
Do.
Tj
19
1.503
. 0352
12.6
. 02342
55, 000
55, 200
11.73
Do.
Tj
19
1. 503
.0352
12.6
. 02342
54, 800
54, 900
11.66
Do.
T3
60
1.503
.0352
39.9
. 02342
52, 900
11. 60
Do.
u,
19
1.506
.0501
12.6
. 03339
59, 000
61.700
11.76
Do.
u2
19
1.506
.0501
12.6
.03330 |
59, 100
61,600
11.50
Do.
U3
60
1.506
.0501
39.8
. 03330
59, 600
61, 900
11.80
Do.
V,
19
2.500
.0341
7. 6
. 01364
41, 100
41, 300
11. 16
Do.
V2
19
2. 506
. 0336
7.6
.01340
40, 500
40, 500
10. 80
Do.
Vs
60
2. 504
.0340
24.0
. 013.58
—
29,500
10. 45
Do.
Average (63 specimens) _ _
52, 780
56, 550
11.57
0 Type'of failure as indicated by inspection of tube after removal from test fixture.
6 Extrapolated value.
TORSION TESTS OF TUBES
TABLE
VIII.— RESULTS OF TORSION TESTS OF 17ST ALUMINUM-ALLOY TUBES
Speci¬
men
Length
L (in.)
Outside
diametet
D (in.)
Thickness
t (in.)
LID
HD
Yield
strength
2/3 O
(lb./sq. in.)
Mean fiber
shear stress
at failure
(lb./sq. in.)
Shear
modulus
(lb./sq. in.)
Final type of failure 0
i.
20
0.9997
0. 0188
20.0
0. 01880
21,000
3.86X106
2 lobes.
i*
60
1. 0005
.0187
60.0
. 01869
IP, 400
3. 86
Do.
m:
20
. 9994
.0199
20.0
.01991
21,900
21, 900
3. 89
Do.
m2
60
1. 0003
.0198
60.0
.01979
20, 500
3. 89
Do.
m
20
1. 0024
.0224
19.9
. 02235
23, 000
23, 100
3. 86
Do.
02
60
1. 0021
.0224
59. 8
. 02235
23,400
3.86
Do.
Oj
20
1.0016
.0252
19.9
. 02516
23, 000
23, 400
3. 88
Do.
02
60
1, 0017
.0257
59.8
. 02566
25, 200
3. 88
Do.
Pi
20
1. 0002
.0283
20.0
. 02829
21,200
23, 600
3.92
Do.
P2
60
1.0006
.0285
60. 0
.02848
22, 600
24, 200
4.00
Do.
Ql
20
1. 0028
.0324
19.9
.03231
22, 5C0
24, 900
4.00
Do.
<42
60
1. 0024
. 0325
59.8
. 03242
23, 500
26, 000
3. 92
Do.
Si
20
1.0031
. 0422
19.9
. 04207
23, 500
27, 900
3.96
Do.
S2
60
1. 0018
. 0423
59.8
. 04222
24, 800
29, 200
4.08
Do.
tj
20
1. 0007
.0498
20.0
. 01977
23, 700
30, 400
4. 00
Do.
t2
60
1.0013
.0498
59. 9
. 04974
24, 600
31,300
4. 05
Do.
Ul
20
1. 0020
. 0590
20.0
. 05888
23, 800
33, 700
3.97
Do.
U2
60
1.0027
.0588
59.8
. 05864
24, 100
33, 700
3.97
Do.
Vi
20
1. 0020
. 0637
20.0
. 06357
23, 000
34, 000
3. 95
Do.
V2
60
1. 0024
.0637
59.8
. 06355
24, 300
35, 200
3. 94
Do.
Wi
20
1. 0006
.0718
20.0
.07176
24, 000
36, 800
4.00
Do.
W2
60
1. 0004
.0717
60. 0
. 07167
25, 400
38, 600
4.00
Do.
Xl
20
.9994
,0832
20.0
.08325
23, 600
40. 000
3. 97
Helix and 2 lobes.
X2
60
.9998
.0832
60. 0
. 08322
25, 000
41, 200
3.97
Do.
yi
20
. 9975
.0938
20.0
. 09403
23, 700
41, 400
3.97
Helix.
Y2
60
.9984
.0942
60. 1
. 09435
24, 300
42, 400
3.97
Helix and 2 lobes.
Zi
20
.9965
. 1076
20. 1
. 10797
23, 000
41, 100
3.99
Helix.
Z2
60
.9971
. 1074
60.2
. 10771
24, 000
41,900
3. 99
Do.
Aai
20
1. 0001
. 1192
20.0
. 11919
23, 000
41, 300
3.97
Do.
A 02
60
1. 0005
. 1188
60.0
. 11874
24, 100
42, 400
3.97
Do.
Ui
20
1. 4955
. 0224
13. 4
. 01498
20, 100
3. 96
2 lobes.
U2
60
1. 5000
.0227
40.0
.01513
ie; 900
3. 96
Do.
V,
20
1. 4996
.0244
13.3
.01627
20, 700
3.94
Do.
v2
60
1. 5003
.0244
40.0
.01626
18, 500
3. 94
Do.
w.
20
1. 5066
.0285
13.3
. 01892
23, 500
4.00
Do.
w2
60
1. 5055
.0285
39.9
.01893
22, 000
3.94
Do.
X,
20
1. 5035
. 0330
13.3
.02195
22, 800
23, 600
3.96
Do.
Xo
60
1. 5C33
.0330
39.9
. 02195
22, 200
22, 800
3. 96
Do.
Yi
20
1.4997
.0354
13.3
. 02360
23, 500
24, 400
3. 97
Do.
y2
60
1.5018
.0354
39.9
. 02357
24, 800
3.97
Do.
Z 1
20
1.5017
.0436
13.3
. 02903
22, 500
25. 100
3.88
Do.
z2
CO
1. 5022
. 0435
39.9
.02896
23, 100
24, 100
3.93
Do.
ai
20
1. 5001
.0491
13.3
. 03273
23, 000
26, 400
3.92
Do.
a2
60
1. 5006
.0497
40.0
.03312
23, 600
26, 100
3.97
Dc.
b,
20
1. 5031
. 0585
13.3
. 03892
23, 600
27, 000
3.94
Do.
b2
60
1.5035
.0585
39.9
.03891
24, 200
27, 700
3.94
Do.
Cl
20
1. 4995
. 0634
13.3
.04228
22, 100
27, 700
3. 95
Do.
C2
60
1. 5000
.0636
40.0
. 04240
22, 600
27, 400
3. 97
Do.
di
20
1.4988
.0719
13.4
. 04797
22, 50C
29, 600
3. 97
Do.
d2
60
1.4980
. 0721
40. 1
. 04813
23, 200
30, 500
3.99
Do.
ei
20
1. 5002
.0837
13.3
. 05579
22, 000
31, 900
3.94
Do.
e2
60
1. 5007
.0837
40.0
. 05577
22, 900
31, 700
3. 98
Do.
f.
20
1. 5019
. 0956
13.3
. 06365
22, 400
33. 900
3. 93
Do.
f2
60
1.5015
. 0955
39.9
. 06360
23, 000
34, 000
3. 93
Do.
gi
20
1. 5004
. 1107
13.3
. 07378
24, 000
39, 300
3. 95
Do.
g2
60
1.4996
. 1107
40.0
. 07382
24, 600
37, 700
3. 97
Helix and 2 lobes.
hi
20
1. 4988
.1192
13.4
. 07953
23, 300
40, 600
4.02
2 lobes.
h2
60
1.4992
. 1195
40.0
. 07971
23, 400
40, 600
4. CO
Helix and 2 lobes.
ii
20
1. 5020
. 1337
13.3
. 08901
23, 500
42, 900
3. 97
Do.
i2
60
1.5014
. 1337
39.9
. 08905
23, 700
41, 900
4. 00
Do.
jl
20
1. 4991
. 1461
13.3
. 09746
23, 500
42, 700
3.96
Fracture— slight helix.
h
60
1. 4997
.1466
40.0
. 09775
23, 800
42, 800
3. 98
Helix.
k,
20
1. 5010
. 1658
13.3
. 11046
23, 000
42, 700
3. 97
Do.
k2
60
1.5010
. 1659
39.9
. 11053
22, 900
41, 500
3.93
Do.
Ai
20
2. 0035
. 0202
10.0
. 01008
16. 000
3.86
2 lobes.
A 2
60
2 0029
0202
30 0
.01009
12, 200
3. 86
Do.
B,
20
2. 0058
.0255
10.0
.01271
19, 700
3.95
Do.
b2
60
2. 0037
.0254
30.0
. 01268
15, 000
3. 95
Do.
Cl
20
2. 0047
.0274
10.0
. 01367
21,200
3.97
Do.
C2
60
2. 0048
.0274
29.9
. 01367
16, 500
3. 97
Do.
D,
20
2. 0061
.0314
10.0
. 01565
_
21, 800
3. 95
Do.
D2
60
2. 0044
.0315
29.9
.01572
19, 000
3. 95
Do.
Ei
20
2. 0054
.0359
10.0
.01790
23, 300
23, 300
3.95
Do.
e2
60
2. 0033
.0361
29.9
. 01802
20, 200
3. 95
Do.
Fi
20
2. 0020
.0426
10.0
. 02128
23, 700
24, 600
3. 99
Do.
f2
60
2. 0020
.0426
29.9
. 02128
23, 200
3. 99
Do.
Gi
20
2. 0053
.0509
10.0
. 02538
23, 800
25, 100
3.97
Do.
O2
60
2. 0035
.0510
29.9
. 02546
24, 600
24, 700
3. 97
Do.
Ii
20
2. 0010
. 0668
10.0
. 03338
22, 900
26, 100
3. 92
Do.
I2
60
1. 9998
. 0670
30. 0
.03350
23, 300
25, 700
3.92
Do.
Ji
20
1. 9988
. 0716
10.0
. 03582
22, COO
26, 900
3.95
Do.
J2
60
1.9988
.0716
30. 0
. 03582
23, 000
27, 000
3. 95
Do.
Ki
20
2. 0012
.0833
10.0
. 04162
22, 700
28, 100
3.97
Do.
k2
60
2. 0013
.0838
30.0
. 04187
22, 800
27, 700
3. 97
Do.
Li
20
2. 0012
.0952
10.0
. 04757
23, 200
30, 700
3. 98
Do.
l2
00
2. 0009
.0952
30.0
. 04758
23, 300
29, 500
3.98
Do.
Mi
20
2. 0002
. 1110
10. 0
. 05549
24, 700
33. 900
3. 97
Do.
M2
60
1.9988
.1109
30.0
. 05548
24, 600
33, 200
3. 97
Do.
N,
20
2. 0027
. 1206
10.0
. 06022
22, 500
35, 000
4.01
Do.
k2
60
2. 0026
. 1209
29.9
. 06037
22, 500
34, 400
4.01
Do.
Oi
20
1.9952
. 1316
10.0
. 06596
22, 400
36, 700
3. 96
Do.
02
60
1. 9988
. 1326
30.0
. 06634
22, 500
34, 700
3.96
Do.
Pi
20
2. 0027
. 1487
10.0
. 07425
24, 000
40, 200
3.99
Helix and 2 lobes.
P2
60
2. 0027
. 1496
29.9
. 07470
24, 000
39, 600
3. 99
Helix.
Qi
20
1.9974
. 1662
10. 0
. 08321
23, 500
41, 600
3.97
2 lobes.
Q2
60
1.9971
. 1654
30.0
. 08282
23, 300
40, 300
3. 97
Helix.
Ri
20
1. 9980
. 1816
10.0
. 09089
22, 500
42, 200
3. 99
2 lobes.
r<2
60
1. 9978
. 1816
30.0
. 09090
22,500
41,500
3.99
Helix and 2 lobes.
Si
20
2. 0018
.2039
10.0
. 10186
22, 600
41, 400
3. 97
Fracture, slight helix.
s2
60
2. 0027
.2040
29.9
. 10186
22, 400
42, 200
3. 97
Helix.
Ti
20
1. 9994
.2195
10.0
. 10983
23, 500
43, 000
4. 00
Fracture.
t2
60
1.9989
.2206
30.0
. 11036
23. 400
42. 400
4.00
Helix.
A
verage (102
specimens).
- - -
23.310
30. 380
3. 96
1
0 Type of failure as indicated by inspection of tube after removal from test fixture.
3854S— 38 - 35
Hi
REPORT No. 602
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
By Joseph A. Shortal
SUMMARY
The slot-lip ailerons developed by the N. A. C. A. con¬
sist oj a jlap-type spoiler with an adjoining continuously
open slot. The ailerons were developed in an investiga¬
tion oj the delayed response, or lag, oj spoiler-type lateral
controls. Tests oj these slot-lip ailerons were made on
wing models in the 7- by 10-joot wind tunnel, on a Fair-
child 22 airplane in the jull-scale wind tunnel and in
flight, and on the Weick Wl-A airplane injlight.
The tests showed that, although the slot-lip ailerons did
not have the lag normally associated with plain spoilers,
they were rather slow in developing the full amount oj
rolling moment and therejore imparted a sluggish motion
to the roll oj the airplane. The tests in the jull-scale
tunnel showed that the drag due to the open slot was
excessive, but later tests in the 7- by 10-joot tunnel revealed
that this drag could be somewhat reduced by modijying the
slot shape.
In spite oj their disadvantages, the N. A. C. A. slot-
lip ailerons exhibited certain characteristics that are
desirable for airplanes in which sajety and simplicity oj
operation are considered oj greater importance than high
perjormance and a great degree oj maneuverability. The
slot-lip ailerons permit the use oj a jull-span jlap; the
slot may extend the angle-oj -attack range with stability
in roll; and the ratios oj yawing moment to rolling moment
are such as to be particularly satisjactory jor the two-
control operation oj an airplane.
INTRODUCTION
Since the high wing loadings of many modern air¬
planes have necessitated the use of landing flaps to
reduce the landing speed, considerable interest has been
displayed in lateral-control devices with which a flap
covering the entire wing span can be used. The spoiler
type of control, located near the midchord, permits the
free use of the trailing edge of the wing for full-span
flaps. Wind-tunnel tests (reference 1) of wing models
indicated that spoilers had desirable control charac¬
teristics, but flight tests (reference 2) revealed con¬
siderable lag between the control movement and the
beginning of the wing motion in the desired direction.
The slot-lip aileron, which consists of a spoiler with an
adjoining continuously open slot, has been developed
during the attempt to find a control device with the
desirable characteristics of the spoiler and without its
undesirable lag.
This lag, or the delay of the response motion of the
airplane after a control movement, with various spoil¬
ers and spoiler-aileron combinations, was measured in
the flight tests of reference 2. It was noticed that the
pilots failed to detect any lag less than 0.10 second.
This value, in seconds, seems to be an upper limit to
the lag and is of particular interest. In the interpre¬
tation of model tests and the application of the results
to airplanes, it seems that the lag should be expressed
as the distance in wing chord lengths traveled by the
airplane after the control is moved. With the lag ex¬
pressed in this nondimensional form, the lag in seconds
may be computed for a particular airplane and speed
and compared with the 0.10-second limit, although this
time limit may depend upon the reaction of the pilot
and may vary with different pilots.
Another characteristic possessed by lateral-control
devices is that of “sluggishness.” The control may
cause the wing to move in the desired direction imme¬
diately, but the moment produced by the control may
not reach its maximum until the wing has traveled a,
considerable distance. As a result, the airplane motion
will appear rather sluggish. It seems that all control
devices are sluggish to a certain extent because the
change in lift is not effected immediately. In the
present report, sluggishness is defined as the distance in
chords traveled by the airplane from the time the con¬
trol is deflected until the maximum moment is produced.
At the start of the investigation the upper allowable
limit of sluggishness was not known but the tests have
indicated that the control was satisfactory if the
maximum moment was produced before the tested
airplane traveled four chord lengths. This value is
by no means fixed as it may be masked by such factors
as the moment of inertia of the airplane and the
indirect rolling moment induced by yawing motions.
The complete wind-tunnel and flight tests that have
been made by the N. A. C. A. to determine the practi¬
cability of slot-lip ailerons are reported herein. The
investigation was divided into the following phases:
1. An investigation in the 7- by 10-foot wind tunnel
of the lag characteristics of spoilers and slot-lip ailerons.
(See reference 3.)
2. The measurement in the 7- by 10-foot wind tunnel
of the lateral-control and stability characteristics of a
wing model equipped with slot-lip ailerons in several
chordwise locations.
537
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
538
3. The determination of the effect of slot-lip ailerons
on the lift and drag of a model wing and of an airplane.
4. A study in the 7- by 10-foot wind tunnel of the
effect of various slot shapes on the wing section drag
with a large-chord wing.
5. Flight tests of an airplane equipped with slot-lip
ailerons.
6. An analysis of the wind-tunnel and flight results
to obtain a quantitative comparison of the response
characteristics of slot-lip and ordinary ailerons.
LAG INVESTIGATION
The lag investigation was conducted in the open-jet
7- by 10-foot wind tunnel (reference 4). A Clark Y-15
wing of 4-foot chord and 8-foot span was hinged at one
end to the side of the tunnel as shown in figure 1. The
set-up thus simulated a 16-foot wing with one of the
tunnel vertical boundaries as an imaginary plane of
symmetry. The wing was restrained in roll by long-
elastic cords but was free to move to a new position of
equilibrium when a moment was applied by a control
device located at the free wing tip. A continuous record
of the control motion and the wing motion was obtained
by a recording instrument developed for flight tests.
The tests consisted of deflecting the ailerons various
amounts and recording the wing motion. The tunnel
was operated at an air speed of 80 miles per hour for 0°
angle of attack and at 40 miles per hour for 15° angle
of attack. The corresponding wing lift coefficients
were approximately 0.25 and 1.00.
RETRACTABLE SPOILERS
The retractable spoilers consisted of curved plates
that slid in and out of the wing as indicated in figure 2.
The spoiler chord and location are given as fractions
of the wing chord cw. The spoilers were of O.lOCw,
chord and were tested successively at different locations
between 0.1 hcw and 0.83<v Reference 2 had revealed
that a retractable spoiler located 0.15c„, had consider¬
able lag and reference 5, that a retractable spoiler
located 0.83c„, was satisfactory. The tests reported
in reference 6 indicated that the 0.30c„, location should
give the optimum rolling and yawing moments. It
was considered advisable, therefore, to investigate the
variation of lag with spoiler location for the entire
chordwise range. Some of the results are plotted in
figure 2.
The results from some typical lag records are plotted
in figure 3. It will be noticed that the retractable
spoiler at 0.1 5cw caused the wing to roll initially in the
wrong direction before rolling in the desired direction.
Included in the same figure for comparison is a response
curve obtained with a flat plate attached to the trailing
edge of the wing and deflected as an aileron ; this curve
is taken as representative of ordinary aileron action.
The considerable difference in the response of the wing
to these two devices is quite evident.
The results of figure 2 having indicated satisfactory
response time with a spoiler at 0.83^, tests were made
to determine the effect of a split flap on the spoiler
response. The curves of figure 4 show the time
Figure 2.— Effect of spoiler location on lag. The 7- by 10-foot tunnel; Cl, 1-0; air
speed, 40 m. p. h.
histories with and without a split flap deflected 60°
and indicate greater lag with the flap deflected.
Inasmuch as satisfactory operation had been obtained
in flight with combinations of ailerons and spoilers, it
was considered of interest to measure the lag obtained
Wing motion, <p , deg.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
539
Figure 4. — Time histories of wing motion with retractable spoiler at 0.83Cu, and with
a split flap. The 7- by 10-foot tunnel; Cl, 1.0; air Speed, 40 m. p. h.
Figure 5.— Time histories of wing motion with combinations of spoilers. The
7- by 10-foot tunnel; Cl, 1.0; air speed, 40 m. p. h.
540
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
with a combination of two retractable spoilers. A
representative time history is given in figure 5. The
addition of the 0.83cM spoiler counteracted the lag of
Hinge ox is
; Slot gap
Figure 6. — Effect of slot size on lag of retractable spoiler and slot at O.-Kic*. The
7- by 10-foot tunnel; Cl, 1.0; airspeed, 40 m. p. h.
the 0.30cw spoiler, but the response of the combination
was not so rapid as that of the rearward one alone nor
of the ordinary aileron.
It was believed that a slot adjoining the spoiler
would relieve the low pressure existing behind the
spoiler when it is first deflected. Lag measurements
were made of several widths of slot behind a retractable
spoiler located near 0.30cw. As shown in figure 6, a
slot with an upper gap of about 0.035cw reduced the
lag from about 8 chord lengths to less than 1 chord
length travel. The lower opening of the slot was later
reduced to about 0.06 cw and to the shape shown by the
dashed line without altering the response character¬
istics.
SLOT-UP AILERONS
Although the retractable spoilers with a slot would
probably give satisfactory control, the device appears
structurally undesirable. A simpler arrangement con¬
sisting of a slot with the upper portion, or lip, hinged for
control was given more consideration. This hinged lip
was designated a “slot-lip aileron.” Tests were made
of various combinations of sizes for the upper and lower
slot openings and with the aileron liinge-axis located
Figure 8.— Time histories of wing motion with slot-lip ailerons in various fore-and-
aft locations. The 7- by 10-foot tunnel; Cl, 1.0; air speed, 40 m. p. h.
0.1 0cw, 0.30 cw, and 0 .55cw back from the leading edge.
The slot sizes required to obtain an immediate response
following control movement were determined for each
location and the results are shown in figure 7. The
particular shape used was similar to that of a pre¬
viously developed low-drag slot. (See reference 7.)
The chord, ca, of the slot-lip aileron was 0.10 cw.
The wing motions obtained with the final slots for
each location of the slot-lip ailerons are compared with
the aileron curve in figure 8. The curves show imme¬
diate response in all cases although the final motion
builds up differently in each case.
The effect of the slot is clearly shown in figure 9 by
the time histories of the wing motion. With the slot
closed at the bottom, the wing moved in the wrong
direction as before with a lag of about 0.5 second. With
the upper slot opening sealed so that there was no slot
with the aileron neutral but a considerable opening
with the aileron deflected, the lag was reduced to about
0.3 second but was still unsatisfactorily large.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
541
With the final slot-lip ailerons showing satisfactory
lag characteristics, the hinge moments were measured.
Some modification of the aileron and slot was necessary
Figure 9. — Time histories of wing motion with slot-lip ailerons at 0.30cu,, showing
effect of the slot. The 7- by 10-foot tunnel; Cl, 1.0; air speed, 40 m. p. h.
which showed that the arrangement was not over¬
balanced at the start of control movement. The
arrangements tested are reported in more detail in
reference 3. The final hinge-moment curves are given
in figure 10 at lift coefficients of 0.25 and 1.0. The
hinge-moment tests were made with the wing used in
the lag tests and at an air speed of 60 miles per hour.
The hinge moments are given in the form of absolute
coefficients Ch based on the aileron chord ca and area
Sa back of the hinge,
~ hinge moment
k ~ qCaSa
ROLLING- AND YAWING-MOMENT TESTS
The lag investigation of slot-lip ailerons indicated
the possibilities of their providing improved lateral
control. A wing that had been used in the investi¬
gation reported in reference 8 was fitted with slot-lip
ailerons and the rolling and yawing moments produced
by these ailerons were measured. The effect of the
slot-lip ailerons on lateral control, on lateral stability,
and on lift and drag was determined with and without
a split flap.
APPARATUS AND TESTS
The model was mounted on the 6-component bal¬
ance of the open-throat 7- by 10-foot tunnel. (See
reference 4.) The three force and the three moment
components can be read independently and simulta¬
neously in the form of coefficients for a standard-size
model. The force-test tripod may be replaced by a
special mounting that permits the model to rotate
Figure 10.— Hinge-moment coefficients of slot-lip ailerons on the 4- by 8-foot wing in the 7- by 10-foot tunnel.
542
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
about the longitudinal wind axis passing through the
midspan quarter-chord point. This apparatus is
mounted on the balance and the rolling-moment
coefficients are read directly during forced rotation tests.
The model used in this part of the investigation was
the one with large rounded tips used for the tests re¬
ported in reference 8. A Clark Y wing section was
maintained throughout the span with no washout.
The basic chord of the wing was 10.66 inches, the span
was 60 inches, and the aspect ratio 6.0. A diagram of
shown by dashed lines were found necessary during
the tests and were made with wooden strips screwed
to the wing. The slot shape shown as (d) was designed
to reduce the drag of the slot by having the slot formed
between two airfoil-shape sections.
The standard test procedure was followed at a
dynamic pressure of 16.37 pounds per square foot
corresponding to an air speed of 80 miles per hour at
standard density. The Reynolds Number of the
tests was 609,000, based on the average wing chord of
10 inches.
The lift, the drag, and the pitching moment were
measured with the ailerons neutral; the roiling and the
yawing moments were measured with the ailerons de¬
flected various amounts. Tests were repeated with
the split flap deflected 60°. Some of the tests were
repeated with the wing yawed to determine the control
characteristics while sideslipping. Rotation tests were
made with the ailerons neutral when located in all
positions along the wing chord to determine the effect
of the slots on damping in roll. Rotation tests were
then made with the ailerons deflected when located
0.1 0c„, from the leading edge to determine the effect of
the deflected control on the damping.
KESULTS
(b) Slot-lip aileron at 0.30 Cu,.
■LOO"
1 -0.20"
(d) Slot-lip aileron at 0.55 c„ with special slot.
Figure 11. — Diagram of the Clark Y wing with slot-lip ailerons tested in the 7- by
10-foot tunnel.
the wing showing the ailerons and flap tested is given
in figure II. The split flap consisted of a sheet-steel
strip screwed to the wing at an angle of 60°. The
slot -lip ailerons were formed of brass with their upper
surfaces conforming to the upper contour of the wing.
The slot sizes and shapes were determined from the
lag investigation. The modifications to the slots
The results are given in figures 12 to 18. The co¬
efficients are obtained directly from the balance and
refer to the wind (or tunnel) axes. The results as given
have not been corrected for tunnel effects.
The results of the rotation tests are given in the form
of a damping coefficient
dC/
obtained from an aver¬
age of the results of rotation tests in both directions
at a rate of 0.05, where p' is the angular velocity
in roll and V is the air speed.
Ailerons neutral. — The curves of lift and drag with
flap and ailerons neutral are given in figure 12 (a) and
with flap deflected 60° in figure 12 (b). The shape of
the lift curves with flap neutral is somewhat affected
by the slots. The forward slot locations are more
effective than the rearward locations in delaying the
stall over the adjacent portion of the wing span. This
fact is revealed more clearly by the curves of damping
in roll in the same figures, which show that damping
is maintained to a higher angle of attack with the for¬
ward slots than with the rearward slots. The drag due
to the slot-lip ailerons will later be discussed in more
detail in connection with tests made at a larger value
of the Reynolds Number.
The effect of the slots on the manner in which the
wing stalled was studied by air-flow surveys with a fine
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
543
silk thread attached to a thin sting. The effectiveness
of the forwardly located slots is clearly shown in figure
13. The slot-lip ailerons were located in three different
positions with the flap neutral and deflected 60°, and
the wing was at an angle of attack of 22° (about 6° past
maximum lift). The stalled area of the wing is shown
by the shaded areas.
Effect of slot shape on control. — The slots first used
with the slot-lip ailerons in the present tests were
similar to the ones used in the lag investigation but
were later modified as shown by the dashed lines in
figure 1 1 . The rolling- and yawing-moment coefficients
obtained with the original and modified slots with the
slot-lip ailerons located at 0.10, 0.30, and 0.55^ from
the leading edge are given in figure 18(a) with the
right aileron deflected up 40° and the left aileron de¬
flected down 12°, flap 0°. The rolling moments with
the modified slot were superior to those with the original
slot in most cases. Consequently, complete data have
been given only for the tests with the modified slots.
The effect of a more drastic change in slot shape was
determined from tests of the slot-lip aileron shown in
38548—38 - 36
figure 11(d). In this case the slot was formed between
two airfoil-sliape sections, an arrangement that, it
was believed, would result in reduced drag. A com¬
parison of the relative control effectiveness of this
aileron and of the modified slot-lip aileron of figure 1 1 (c)
Aileron
Figure 13. — Effect of slot-lip ailerons on air flow above the stall. (Shaded area is
stalled.) Ailerons neutral; a, 22°.
Yawing-moment Rolling-moment Yawing-moment Rolling-moment Yawing-moment Rolling-moment
coefficient, Cn' coefficient, Ct‘ coefficient Cn' coefficient Cf coefficient Cn' coefficient, ; Cf
544
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 15.— Rolling- and yawing-moment coefficients due to slot-lip ailerons at 0.30c
Aileron deflection, 6a ,deg.
Figure 16— Rolling- and yawing-moment coefficients due to slot-lip ailerons at 0.55c u,.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
may be made from figures 16(a) and 17(a). Although
the aileron with the special slot gave higher rolling
moments above 20° deflection, the variation of this
moment with aileron deflection was not uniform.
With the flap deflected, the difference between the two
the effect of the slot on the rolling- and yawing-moment
coefficients. The ailerons as spoilers were deflected
upward 60° in all cases and were located at 0.10, 0.30,
and 0.55<v With the slots open the rolling moments
are appreciably higher below the stall but arc definitely
slot shapes was even greater, as may be seen by com¬
paring figures 16(b) and 17(b).
Comparison of slot-lip ailerons and spoilers. — A
direct comparison between slot-lip ailerons and plain
spoilers was made by testing the slot-lip ailerons in cer¬
tain conditions with the slot both open and completely
sealed. The results are given in figure 19 and show
lower above the stall. The yawing-moment coeffi¬
cients are lower with the slots open.
Effect of slot-lip aileron deflection. — For a satisfac¬
tory control device it is desirable that the curve of roll¬
ing moment against control deflection have no discon¬
tinuities. Owing to the importance of this requirement,
the results of all the slot-lip ailerons tested in this part
Yawing moment
coefficient, Cn! Rolling-moment coefficient ,
REPORT NO. 602 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
540
Figure 19.— Effect of slot-lip aileron location on rolling- and yawing-moment
coefficients, da up 60°; flap, 0°.
of the investigation have been plotted against aileron
deflection in figures 14 to 17. With the slot-lip ailerons
at the 0.10 cw location, the rolling moments are rela¬
tively low at 10° aileron deflection, particularly with
the flap deflected. With the ailerons at either 0.30c„
or 0 .55cw, however, the moments vary uniformly with
aileron deflection except with the flap deflected and the
aileron at 0.55(V With the special slot, the rolling
moments are low at 10° and 20° deflection but rise to
rather high values beyond 30° deflection. In most of
the cases given, the rolling moments with the slot-lip
aileron deflected downward are opposite in sign to the
moments with the ailerons deflected upward. This
characteristic allows the use of a differential aileron
linkage with some control obtained from the down¬
wardly deflected aileron.
Effect of flap deflection. — With the split flap de¬
flected 00°, the rolling moments produced by the slot-
lip ailerons were considerably higher at a given angle of
attack than with the flap neutral. Rolling- and yawing-
moment coefficients are given in figure 18(b) for the
slot-lip ailerons located at the three locations tested
with aileron deflection of 40° up, 12° down, with the
split flap deflected 60°. Large rolling moments were
given by the ailerons at the 0.1 0cw location at angles of
attack near the stall, but these moments rapidly dimin¬
ish as the angle of attack is reduced.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
547
A more conclusive comparison of the moments ob¬
tained with and without a flap may be made from fig¬
ure 20 with Cnf and C/ plotted against CL- With the
flap deflected 60° the rolling moments reached zero at
higher values of lift coefficient than with the flap re¬
tracted. These values of lift coefficient at which the
rolling-moment coefficients vanish are given in figure 21
for various aileron deflections. This characteristic lim¬
its the forward location of the ailerons because it is
necessary to have control maintained to the highest
speed at which the airplane will be flown with the flap
deflected. If the corresponding lift coefficient is 0.5,
the slot-lip aileron cannot be located farther forward
than 0.30cw and still give control.
Effect of deflected ailerons on damping in roll. —
With a wing rotating about the longitudinal axis, the
downgoing wing is at a higher angle of attack than the
center of the wing. If the curve of aileron rolling
Figure 21.— Lift coefficients at which rolling-moment coefficient vanishes when flap |
is deflected 60°.
moment against angle of attack has a positive slope,
the rolling moments obtained with the wing rotating
should be higher than those measured in static tests.
This increase in rolling effectiveness may be expressed
as a reduction in damping in roll. The reduction in
damping was checked by rotation tests made with slot-
lip ailerons at O.lOCu,, deflected 40° up, 10° down, and
with the split flap both neutral and deflected. The
measured values and an approximate curve for the
values for the intermediate locations have been included
in figure 22.
Choice of slot-lip aileron location. — In the discussion
of slot-lip aileron location, it has been shown that the
rolling moments are highest at angles of attack near
the stall with the forward location. With the aileron
in this location, control is not available at high speed
with a flap deflected. Control under these conditions
is only possible with the location at least as far from the
leading edge as 0.30c,f. Another interesting considera¬
tion is the yawing moment accompanying the rolling
moment. With ordinary ailerons the induced yawing
moment contributes practically the entire yawing mo¬
ment and the coefficient Cni is obtained from
ai=o.2o cLCi
for a rectangular wing of aspect ratio 6 with equal up-
and-down aileron deflection. (See reference 9.) In
Figure 22.— F.ffeet of slot-lip aileron location on damping in roll, up 40°.
figure 23 are plotted the ratios of yawing moments to
rolling moments for the slot-lip ailerons in the three
tested positions. Included in the same figure is the
theoretical ratio for equal up-and-down deflection of
ordinary ailerons. It will he seen that the slot-lip
ailerons produced a large profile yawing moment of the
same sign as the rolling moment, which was reduced by
Figure 23— Ratios of yawing moment to rolling moment for slot-lip ailerons.
the induced yawing moment until, at high lift coeffi¬
cients with the flap down, the yawing moment was
negative or adverse with the slot-lip aileron in the rear¬
ward location. It appears from reference 10 that, for
two-control operation of an airplane, an aileron giving-
rolling moments accompanied by yawing moments of
the same sign (favorable) and about one-fifth the magni¬
tude seems to be the most desirable, although the rate
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
548
of application of the control and the airplane character¬
istics influence the desirable ratio. With the slot-lip
Figure 24.— F.fTeet of slot-lip aileron location on A Cd, dCi./da, and Cl maz .
aileron at 0.30c„, the ratio of Cn'ICi varies from about
0.05 at maximum lift with the flap deflected to about
0.40 at high speed, flaps neutral. With the aileron in
the 0.55cw location, the ratio becomes negative at the
landing condition, whereas at the 0.10^ location the
ratio becomes excessively large at high speed. Consider¬
ation of lateral stability dictates a forward location; the
lowest drag is obtained with the rearward location.
The 0.30cw location would seem to be the most desirable
for a slot-lip aileron used as the sole means of lateral
control, except for the effect of the slots on the drag of
the wing.
LIFT AND DRAG EFFECTS DUE TO SLOT-LIP AILERONS
The effect of slot-lip ailerons on the lift and the draw
is of particular importance for high-performance air¬
planes. Previous tests have shown that at low angles
of attack practically all slots reduce the lift and increase
the drag. It has also been shown that a given size of
slot has less drag when located rearward on the wing
Aileron
1- by 10- ft. tunnel
Full-scale tunnel
location
10 "wing ! 48 "wing
66“ wing
0.20 cu
o
.45 "
A
—
.55 "
x 1 -
(a) Cl= 0. (b) Cl= 0.2.
Figure 26.— Scale effect on increment of drag due to 0.50 6/2 slot-lip ailerons.
than when located forward. In the present investiga¬
tion the slots were made as narrow as possible without
causing lag. Because the effect of the slots on the drag
was large, considerable attention was given to its meas¬
urement and to means for reducing it. The effect of
the slots on the drag was determined with slot-lip
ailerons on a small-scale wing model in the 7- by 10-
foot tunnel and on an actual airplane in the full-scale
tunnel. The airplane was equipped with slot-lip aile¬
rons in two locations, one (0.20cw) selected for its control
and stability characteristics and the other (0.45cw)
selected for its smaller effect on lift and drag.
TESTS IN THE 7- BY 10-FOOT TUNNEL
The tests of the small model in the 7- by 10-foot
tunnel mentioned in the last section are interesting
because they indicate certain trends. It would, how¬
ever, be misleading to attempt to predict the perform¬
ance of an airplane from the low-scale tests. The
values of increments of drag due to the slot-lip ailerons
have been computed for the slot-lip ailerons in the
three locations tested from polar curves plotted from
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
549
the data given in figures 12(a) and 12(b) and from
additional check tests. The average values of AOd
are given in figures 24, 25, and 26 and are compared with
values from other tests at large values of the Reynolds
66"
Figure 27. — Fairchild 22 airplane with slot-lip ailerons. The N. A. C. A. 2412 wing
section.
Number. The Reynolds Numbers given are the
effective Reynolds Number determined for each tunnel
from reference 11. The effects of slot-lip aileron
location on the slope of the lift curve dCL!da and on
maximum lift are shown in figure 24 and compared
with values from tests in the full-scale tunnel. Be¬
cause of the different test aspect ratios and different
Reynolds Numbers, the actual values do not agree but
the reductions in the values due to the slots are com¬
parable. The values at the 1.00cw location are taken
from the case with no slot or aileron.
TESTS IN THE FULL-SCALE TUNNEL
In order to determine the practicability of slot-lip
ailerons from actual flight tests and to determine their
drag at large scale, tests were made of a Fairchild 22
airplane equipped with a wing modified to permit the
installation of slot-lip ailerons with their hinge axes
at either 0.20 or 0A5cw positions. The F-22 airplane
is a two-place, externally braced, parasol-type mono-
Left Right
Stick position, deg.
Figure 28.— Slot-lip aileron deflections for Fairchild 22 airplane.
plane. A three-view drawing of the airplane as tested
in flight is shown in figure 27(a). Section drawings
of the wing showing the slot-lip ailerons in the two
positions on the N. A. C. A. 2412 wing used are shown
in figure 27(b) and (c). The allowable aileron mo¬
tions are shown in figure 28 for both positions. In the
tests in the full-scale tunnel the wing was mounted on
a slightly different fuselage for convenience.
The airplane with the horizontal tail surfaces and
propeller removed was mounted on the balance in the
full-scale tunnel as shown by figure 29. A description
of the wind tunnel and balances is given in reference 12.
The ailerons were locked in their neutral position and
lift, drag, and pitching moments were measured with
the slot-lip ailerons first in the 0.20 cw location, then in
the 0.4 5rw location, and finally without the slot-lip
ailerons. When the slot was not in use, the openings
550
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
were covered with metal plates shaped to conform to
the wing profile. A photograph (fig. 30) shows the
The tests were made with the flap both neutral and
deflected and covered a range of angles of attack from
— 8° to 24° at a tunnel air speed of about 56 miles per
hour. Scale-effect tests to determine the minimum
drag were made over a speed range from 30 to 120
miles per hour with the flap neutral.
All the results have been corrected for tare and wind-
tunnel effects. The lift, the drag, and the pitching-
moment coefficients are plotted in figure 31 against
angle of attack. The effect of the slot-lip ailerons
on the lift is clearly shown: The maximum lift and
o
.H
N
U
<v
-.4
2.0
Figure 29.— The Fairchild 22 airplane with slot-lip ailerons mounted for test in the
full-scale tunnel.
Figure 30. — View of the Fairchild 22 airplane wing showing details of slot.
wing with the slot open in the 0.45cw position and
with the front position slot covered by a metal plate.
the slope of the lift curve are reduced, but the stall is
somewhat delayed, as in the wing model tests. The
pitching-moment coefficients are only slightly affected
by the slot-lip ailerons. The effect of the flap on the
pitching moments is not conclusive since the horizontal
6, = 57
S/ot Up aileron
. located 0.20c
5/ot Up aileron
■ located 0.45 cu —
Slots sealed.
-.2
-4 0 4 8 /2/6 20
Angle of attack of thrust axis, dT ,deq
Figure 31.— Lift, drag, and pitching-moment coefficients of the Fairchild 22 airplane
with slot-lip ailerons. The full-scale tunnel; air speed, 56 m. p. h.; propeller and
horizontal tail surfaces removed; angle of wing setting, 4.4°.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
551
tail surface was not in place and the additional down-
wash at a given angle of attack with the flap deflected
would, no doubt, reduce the difference between the
results with flap neutral and flap deflected.
The effect of the slot-lip ailerons on drag is clearly
shown in figure 32, which is a plot of drag increment
Figure 32.— -Increase in drag due to slot-lip ailerons on the Fairchild 22 airplane in
the full-scale tunnel. Air speed, 56 m. p. h.
efficient is shown in figure 33(a) for minimum drag
and in figure 33(b) for drag at a lift coefficient of 0.2.
The effect of air speed or effective Reynolds Number
on the drag increment is shown in figure 26. The scale
effect is much greater at high lift coefficients than at the
minimum drag attitude. The points of figure 26 taken
from interpolated results of small-scale tests agree
fairly well with the large-scale tests. Figure 25, how¬
ever, shows poor agreement between large-scale and
small-scale tests at lift coefficients above 0.2.
The effect of the slot-lip ailerons as tested in the
full-scale tunnel on the Fairchild 22 airplane is more
clearly shown by computing the estimated performance
of the airplane. The following table gives the estimated
power-on performance characteristics based on the
tunnel results.
ESTIMATED PERFORMANCE OF F-22 AIRPLANE WITH
SLOT-LIP AILERONS IN TWO LOCATIONS
Slot
location
Vm i n (11
if = 0°
l. p. h.)
it = 56°
I mar
if = 0°
(m. p. h.)
Maximum
rate of
climb
(ft. /min.)
Maximum
angle of
climb
(deg.)
0. 20c* _
53.08
43. 75
122. 6
625.0
4.7 1
(». 45c _
52.91
44. 12
125. 0
675. 0
5. 7
No slot... ...
51.37
42. 75
129.4
772.5
6.3
ACh against lift coefficient for the slot-lip ailerons in
the two locations. With the particular shape of slot
used the drag increment increases appreciably with lift
coefficient. The effect of air speed on the drag co¬
slot-drag INVESTIGATION
An investigation of the drag of slots used with slot-lip
ailerons was conducted in the 7- by 10-foot wind tunnel.
A wing of N. A. C. A. 23012 section with a chord of
0 20 40 60 . 80
Air speed , m.p.h.
(a) Cz>m.n. (b) Cd at Cl= 0.2.
Figure 33.— Scale effect on drag coefficients of Fairchild 22 airplane with slct-lip ailerons tested in the full-scale tunnel.
IOO
120
552
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
4 feet and a span of 8 feet was mounted on the regular
balance between end planes that spanned the jet ver¬
tically as shown in figure 34. With an air speed of 80
miles per hour, the effective Reynolds Number was high
enough to overlap the Reynolds Number of the tests
i c 1 1 E 34. — The N. A. C. A. 23012 wing of 4-foot chord and 8-foot span with slots at
0.55c » mounted between end planes in the 7- by 10-foot tunnel.
in the full-scale tunnel. The full-span slots were all
located about 0.55 cw.
Tests were made of the wing with no slots, with
slot-lip ailerons of the type previously tested, and with
several modifications. The lift, the drag, and the pitch¬
ing-moment coefficients were obtained at an air speed of
80 miles per hour for all slots and at air speeds of 20,
40, and 60 miles per hour for certain conditions.
The results of the plain-wing tests at 80 miles per
hour corrected for tunnel effects are plotted in figure 35.
The values of the drag coefficient were corrected for
tares and for static-pressure gradient by the usual
methods and for deflection of the tunnel air stream by
the following equation from reference 13:
ACD,=0.25-hCr. 2
The pitching-moment coefficient at zero lift agreed
with the results from tests in the variable-density tun¬
nel, but the aerodynamic-center location was slightly
ahead of the location found in the variable-density
tunnel although it agreed with previous tests in the
7- by 10-foot tunnel of the same airfoil section. The
errors due to tunnel effects are eliminated by presenting
the results of the tests with various slots mainly in
terms of variation from the plain-wing tests.
The type of slot used with the previously tested slot-
lip ailerons was tested first for comparison. (See fig.
11(c).) The increments of drag obtained have been
plotted in figures 25 and 26 for comparison with the
previous tests. The increments as given are one-half
the measured increments for comparison with the other
one-half span slots. It will be seen (fig. 26) that the
increments agree with the previous tests in the 7- by
10-foot tunnel at low values of the Reynolds Number
at values of the lift coefficient of 0 and 0.2. There
appears to be a large favorable scale effect for the slot
location tested as compared with the tests of the more
forward locations in the full-scale tunnel. A direct
comparison is given in figure 25 of the drag increments
from partial-span slots. Differences in the low-scale
tests, which agree at zero lift but do not agree at other
lifts, are partly due to the additional induced drag
accompanying the distorted span load distribution of
the lift. In addition, the scale effect at high lift coeffi¬
cients differs from that at low lift coefficients. For this
reason, the low-scale tests are of little value in predict¬
ing the drag at high lift coefficients.
The results of the present tests are given in table I,
which shows: A diagram of each slot tested; increments
where c/h is the ratio of the wing chord to the height
of the jet. With the corrections applied, the profile
drag of the plain wing agrees with values obtained in
the variable-density tunnel at the same effective Rey¬
nolds Number. The accuracy of the equation in cor¬
recting for the air-stream deflection depends on the
nature of the spillage of air from the open test section
of the tunnel. In the 7- by 10-foot tunnel the exit
cone is of the same size as the entrance cone and part
of the deflected air stream at high lift coefficients flows
below the exit cone. In such a condition the theoretical
corrections do not hold. The theoretical correction for
angle of attack was insufficient to correct the results
to infinite aspect ratio, so an arbitrary correction was
applied to give a lift-curve slope of dCL/da0 of 0.101.
^ <D
Ao-s
-Jc.D'
£ P
/n't C
U ^
V U
-2 p
; Figure 35.— Aerodynamic characteristics of the 4- by 8-foot wing of N. A. C. A.
23012 section mounted between end planes in the 7- by 10-foot tunnel. Effective
Reynolds Number, 4,090,000; aerodynamic-center location: ahead of quarter-chord
I point 0.030c u,, above chord 0.084c„,.
of profile drag at CL— 0, 0.2, 0.4, and 0.5; slope of the
lift curve dCL/da0) shift of the angle of attack of zero
lift, Aalo; pitching-moment coefficient at zero lift,
Cm’, and the approximate aerodynamic-center location
in the fraction of cw from the quarter-chord point of the
wing. The values in the table are from the tests at
80 miles per hour. Only a few arrangements will be
discussed.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
553
The original slot 1 gave a rather low increment of
drag ACj>=0.0013 at zero lift hut gave a high incre¬
ment (A(V=0.0052) at CL = 0.5. With the surface
in the rear of the slot reduced in thickness to allow
smoother air flow, its in slot 5. the drag coefficient at
Cl—0. 5 increased to 0.0084 without appreciably affect¬
ing the drag at C'L= 0. The rounding of the slot en¬
trance so as to offer less resistance to the air. as in slot
II. reduced the drag coefficient at Cx— 0.5 to 0.0034 but
increased that at CL = 0 to 0.003S. It seemed, there¬
fore. that the sharp-edge entry was desirable for high¬
speed conditions and further attempts were made to
reduce the drag at CL= 0.5. Since the blunt shape of
slot 1 gave less drag than the pointed shape of slot 4.
slots 12 and 15 were tested, in which the lower opening
was variable in size and the rear face was extremely
blui * Then the slot was filled in. as in 16. and the
small opening ahead of the slot-lip aileron was sealed,
as in slot 1 S : the drag increments were reduced to 0.0033.
which is a substantial reduction from the original value
of 0.0052 at Ct== 0.5. If the slot size can be reduced as
in slot 21. the drag coefficient is reduced to 0.0028.
With the slot sealed on the bottom, as in slot 14. the
drag increment was only 0.001 1 : and when sealed only
at the top. as in slot 2". the drag increment was only
0.0008. With either surface sealed, however, the lateral
control obtained with the slot-lip aileron was no longer
satis ry because of lag. It therefore seems that,
although an appreciable reduction in drag due to the
original form of the slot-lip ailerons is obtainable, the
drag increments would still be considered excessive for
high- perf orm a nee a irpl a nes .
FLIGHT TESTS
After the wind-tunnel tests had indicated that the
slot-lip ailerons should give satisfactory lateral control, :
it seemed desirable to obtain flight tests of the device.
The pilots’ reactions to the aileron control as well as
instrument records of the airplane motion produced by
the ailerons were obtained. The airplane as tested in
flight with the slot-lip ailerons deflected in the 0.45cM
location is shown in figure 36. Four conditions were
investigated:
The hinge axis located at 0.20cw, flap neutral.
The hinge axis located at 0.20^, flap deflected.
The hinge axis located at 0A5cw, flap deflected.
The hinge axis located at 0A5cw, flap neutral.
METHODS
The flight tests consisted of three phases. First, the
angular velocity in roll and yaw and the control posi¬
tion were recorded on high-speed film during a maneu¬
ver in which the ailerons were fully deflected to deter¬
mine the response. Second, somewhat slower records
were obtained with the controls fully deflected at dif- I
ferent air speeds. Third, the control obtained with
partial aileron deflection at a given air speed was
determined. In addition, the force required to deflect
the ailerons under different conditions was measured.
Graphical differentiation of the angular-velocity records
gave the angular acceleration produced.
RESULTS
Time histories showing the response of the airplane
to the moment produced by the slot-lip ailerons in the
0.20c K location are given in figure 37 (a) with the flap
both neutral and deflected. It will be seen that the
wing starts to roll in the desired direction immediately
but is decidedly slow in attaining maximum angular
acceleration. Similar records with the ailerons in the
0.45c *. location are shown in figure 37(b). With the
ailerons in the rearward location, the maximum accel¬
eration is attained sooner than with them in the forward
location.
The effect of aileron deflection on angular velocity
and acceleration in roll and in yaw is shown in figure 38.
Fi'.CRE 36. — The Fairchild 22 airplane w::h si >i-lip ailerons as tested in flight.
For satisfactory operation the motions produced by
control deflection should not depart excessively from a
linear variation with deflection. With the flap neutral
this characteristic is obtained, but with the flap de¬
flected the control may be too weak for low aileron
deflections.
The variation of control effectiveness with air speed
is shown in figure 39. Normally, the angular velocity
and acceleration decrease with air speed but, with the
slot-lip aileron in the forward location with the flap
deflected, the velocity and acceleration decrease with
an increase of air speed. In fact, this characteristic
seems to be one that limits the forward location of the
slot-lip aileron. The slot-lip aileron should be so located
as to give good control up to the highest speed flown
with flap down. Reference to figure 21 will show the
lift coefficient at which control vanishes for various
aileron deflections and locations as determined from the
wind-tunnel tests.
The stick forces required for maximum deflection of
the slot-lip ailerons are given in the following table.
The pilots considered all the forces rather heavy and
the force of 19.8 pounds excessive with the flap de¬
flected and the aileron in the forward location.
554
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(aj Slot-lip ailerons at 0.20c (b) Slot-lip ailerons at 0.45c
Figure 37. — Time history of airplane motion with slot-lip ailerons on the Fairchild 22 airplane.
0 20 40 60 80 'DO
Percenioge maximum aileron def led ion
(a) Slot-lip ailerons at 0.20Cu..
(b) Slot-lip ailerons at 0.45c».
i igure 38. Variation of maximum rolling angular velocity and acceleration with aileron deflection for slot-lip ailerons on the Fairchild 22 airplane.
Aileron
location
Flap condition
Air speed
(ft. /sec.)
Stick force
(lb.)
0.20c w . .
Neutral . .
88
S 4 [
0.20c „ .
. do ..
132
10 s
0.20c „ _
Deflected _ .
71
14.5
0.20c tt. _
_ do . . . . . .
108
19. 8
0.45c „ _
Neutral
79
6 4
0.45c _ _
... do .
131
1 2 0 1
0.45c a _
Deflected
f>4
8 3 '
0.45c „ _
_ do _ _
83
8.8
The pilots reported that the control action was weak
for all flight conditions with the slot-lip ailerons and
that the sluggishness was definitely objectionable for
both locations, although less so at the rearward loca¬
tion. With the flaps deflected, the sluggishness was
worse than with them neutral. The actual magnitude
CD
of the sluggishness for the different conditions has been
computed and is discussed in the next section.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
555
ANALYSIS OF RESULTS
LAG AND SLUGGISHNESS
In the present analysis of wind-tunnel and flight
tests in which dynamic lift is produced, an attempt lias
been made to determine the sluggishness produced by
certain control devices. In the case of slot-lip ailerons
it is conceivable that the sluggishness might be greater
than with ordinary ailerons because the vortices shed
from the slot-lip ailerons located at midchord act on the
wing for a longer time. In addition, the wing travels a
greater distance before the final flow pattern, involving
separation over certain regions, is established.
60 80 100 120 140 160
Air speed, ft./ sec.
L0, the applied rolling moment.
pLp, the damping moment that depends on the
angular velocity in roll, p.
and <(>L the restraining moment due to the elastic
cords that depends on the angular deflection <£. The
coefficients Lp and L $ contain Ix, the moment of
inertia about the axis of rotation, so that L0 is expressed
as acceleration. The variations with time of the
angular deflection 4> and of the control deflection
were simultaneously recorded on the same film. The
values of the angular velocity p were determined by
graphical differentiation of the </> curves and the angular
Lift coefficient, CL
(a) Slot-lip aileron at 0.20c u>. (b) Slot-lip aileron at 0.45c ».
Figure 39. — Variation of maximum rolling angular velocity and acceleration with air speed for slot-lip ailerons on the Fairchild 22 airplane.
Wind-tunnel tests. — In the wind-tunnel tests of the
lag investigation a half-span wing was restrained in roll
by an elastic cord but was free to roll to a new position
of equilibrium after a rolling moment was applied by
certain control devices. (See fig. 1.) The equation of
motion of the wing thus restrained and acted upon may
be expressed by
dp
dt
— A>+ p>L„ T 4>L 0
where dp/dt is the rolling angular acceleration.
accelerations dp/dt were determined by graphical
differentiation of the p curves. The analysis consisted
of determining values of L0 from the determined values
of </>, p, and dp/dt by equation (1) and comparing the
values with those expected from the particular aileron
deflections. A typical curve of 8a and of against
time is shown in figure 40 with the computed values of
p and dp/dt for the wing motion due to a slot-lip aileron
located 0.30cw from the leading edge.
The values of L0 computed for the case shown in
figure 40 and the component parts of the moment are
(1)
556
REPORT NO. 602 NATIONAL ADVISORY COMMITTEE FOR A IRON A I I’ ICS
shown in figure 41. The static moment, L, curve luis
been included as a function of control deflection, as¬
suming the maximum static moment equal to the
Figure 40.— Time history of motion of wing with slot-lip ailerons at 0 40c,. The 7
by 10-foot tunnel.
Chord lengths traveled
f iguke 42.— Ratios of effective moment to static moment for various slot-lip aileron-
in the 7- by 10-foot tunnel.
maximum value of L0. Dividing L0 by the static
moment at any instant gives a measure of the sluggish¬
ness. Because the sluggishness varies directly as the
Figure 43. Analysis of aileron control with slot lip aileron at u IV '
0.827; air ftpeH, 08. S ft 'see.; flight test.
Aro-dT-' -r'.V,' - p'.V - 0 \> U-W-p'W-Vld SI ,
WIND-TUNNEL AND FLIGHT
TESTS OF SLOT-LIP AILERONS
7
wing chord and inversely as the air speed, the values
of time have been converted to the nondimensional
form of distance traveled in terms of chord lengths by
multiplying by Vjc. The sluggishness in terms of
IJL was computed for slot-lip ailerons in several
locations and for an attached aileron as shown in
figure 42.
Flight tests. — The method used in analyzing the
flight tests was essentially the same ns the one used with
the wind-tunnel tests. Flight records of simultaneous
values of rolling and yawing angular velocities and of
the control deflection were obtained. The angular
accelerations were graphically determined and, from
computed values of the resistance coefficients or deriva¬
tives, the moment acting on tin* airplane at each instant
was derived. The derivatives Lv, Lr, L a, Np, Nn and
Xa of the equations of motion
!/l U + pL»+rLt+0Lfi (rolling) (2)
dr . » » ,
A«-f pXp \ rXr+fiXfi (yawing) (3)
were determined for the particular cases as in reference
14, considering the effects on the derivatives of the
slot-lip ailerons and of the flap. The derivatives con¬
tain the proper values of Ix and /* so that L0 and X0
are expressed as accelerations.
The values of dpjdt and dr dt were determined by
graphical differentiation of the curves of p and r. |
Fi'jttt 44. -C«mp*rt*on of flight nod funnel measurement.* of jluggtshners of slot-lip
ailerons.
The values of the angle of sideslip 0 were determined
by summing the outward sideslip due to centrifugal
force and the inw ard sideslip due to the banked attitude, i
\\ ith positive r, the outward acceleration due to centrif¬
ugal force is
dr
dt
(£W"»
I he inward acceleration is
dr
dt
(j sin <f> (/(f)
w here </> is the angle of bank. Integrating,
v—gf<i><lt
or
(v)rW*«
Then the angle of sideslip is
0 (, )'(,•) • f ./V/'
I lie values of f rdt and f<f>dt were determined by graph¬
ical integration.
The values of L() and iY0 w ere determined from equa¬
tions (2) and (3). The interrelation of the various
l na RE 45. -Comparison of flight and tunnel measurements of sluggishness of
ordinary ailerons.
components for a typical case of a slot-lip aileron on
the F 22 airplane is shown in figure 43. All the values
are given in terms of acceleration. The values of L
and A are given in proportion to the aileron deflection
with maximum values equal to the maximum values
of />0 and .V0. -V measure of the sluggishness was taken
as the ratios of L L and XJX. The outlined procedure
was followed in analyzing the flight records for the
cases listed in the following table for the F-22 airplane.
Aileron
Location
if
(deg.)
Cl
V
(ft. /sec.)
P
C *—
Slot -lip. .
a 20c. .
0
0.85
97. 5
5.5
Do . . .
0.20c. _
50
1. 15
84. 0
5. 5
Do . .
0. 45c. .
0
. 83
98. 5
5. 5
Do , _ _
0 45c.— .
56
1. 14
84.0
5. 5
Narrow, ordinary .
T. K .
0
1.00
87.0
Do .
_ do _
56
1. 75
66. 5
Wide, ordinary. .
- do. .
0
1. 10
95.0
4 5
The ratios of Lq/L have been determined for each
tabulated case and are plotted in figures 44 and 45.
For comparison, the corresponding values found by
interpolation from the wind-tunnel tests have been
included in the same figures. The wind-tunnel tests,
however, were made only with the flap neutral.
Integrating,
558
REPORT NO. 002— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
DISCUSSION
With the ordinary ailerons (fig. 45) the full static
rolling moment was reached, for the average case,
after the airplane had traveled about 4 chord lengths.
In the case of the wide-ehord ailerons with the flap
down, the full moment was not produced until about
7 chord lengths had been traveled; with the narrow
aileron, flap neutral, substantially instantaneous re-
Figvre 46.— The Wl-A airplane with slot-lip ailerons and slotted flaps.
spouse was obtained. The accuracy of the method
used in determining the sluggishness depends largely
upon the accuracy with which the flight records of
aileron motion and airplane motion can be synchro¬
nized. The difference between the two extremes and
the average of between 3 and 4 chord lengths might
easily be attributed to errors in interpreting the flight
records. As the response to all the ordinary ailerons
tested was satisfactory to the pilots, it follows that any
device which gives a moment that is uniformly pro¬
duced and with the maximum in about 4 chord lengths
distance is satisfactory on this airplane. The wind-
tunnel tests of the ordinary aileron showed greater
sluggishness than did the flight tests.
With the slot-lip ailerons at 0.20 cw location (fig. 44)
the rolling moment is built up in a nonuniform manner,
the maximum being reached in about 10 chord lengths.
With the flap deflected, the moment actually lags for
6 chord lengths, the rolling motion of the airplane being
indirectly produced by the positive yawing moment
due to the ailerons. The wind-tunnel test gave a more
uniform curve but with the maximum reached at 12
chord lengths. The sluggishness of these ailerons is
considered excessive for the F-22 airplane. With the
slot-lip ailerons at 0A5cw, the moments built up uni¬
formly to a maximum in 8 chord lengths with flap
0° and in 14 chord lengths with flap deflected. The
tunnel test showed a maximum in about 10 chord
lengths with flap neutral. As in the case of the ordinary
ailerons, the wind-tunnel tests showed greater sluggish¬
ness than the flight tests. The sluggishness in flight
with the slot-lip aileron, flap neutral, was not appreci¬
ably greater than that with the wide-chord ordinary
aileron, flap deflected.
The yawing moments, as shown in figure 45, reach
their maximum fairly rapidly in all cases and may be
considered practically instantaneous.
The results of this analysis agree qualitatively with
the pilots’ reports of the action of the slot-lip ailerons
on the F-22 airplane. The pilots reported that the
slot-lip ailerons in either location were more sluggish
than ordinary ailerons and were worse with flap de¬
flected than with flap neutral. The 0.45cw location
was, however, better than the 0.20 cw location. In
addition to being sluggish, the aileron action was
reported to be very weak. In an effort to find an
explanation of this weak action, the moments deter¬
mined in the analysis have been converted to coeffi¬
cient form and are given in the following table with
corresponding coefficients obtained by interpolation
from the wind-tunnel force tests.
Aileron
location
Flap de¬
flection
Tunnel
Flight
Sf
(deg.)
Ci'
cv
So
(deg.)
Ci'
Cn'
Sa for
Ci'
(deg.)
S a for
cv
(deg.)
0.20c,,,--.
0
0. 0475
0.0105
-40
0. 0388
0. 0084
-33
-31
0.20c*-.
56
.0310
.0085
-40
.0199
. 0082
-29
-39
0.45c*.--
0
.0410
.0050
-40
. 0239
. 0032
-25
-32
0.45c
56
.0385
.0050
-40
.0219
.0033
-31
-32
The coefficients in flight are seen to be considerably
lower than the wind-tunnel values. One reasonable
explanation of this difference is that the ailerons in
flight may not have been deflected the indicated
40° because of structural flexure. In the last two
columns are given the necessary aileron deflections
corresponding to the moments produced. The effective
deflection was only about 32°.
Another determination of the sluggishness of slot-lip
ailerons has been made possible bv recent tests of the
Wl-A airplane made by the N. A. C. A. for the Bureau
of Air Commerce. The Wl-A airplane (fig. 46) has
slot-lip ailerons located 0.30<v (See fig. 47.) With
the stable three-wheel landing gear, the large dihedral
angle of the wings, and the slot-lip aileron so located as
to give a good ratio of yawing moment to rolling
moment, it was believed that the airplane could
be flown satisfactorily with adequate directional as
well as lateral control by means of the slot-lip
ailerons alone. The pilots reported that a good
degree of control was obtained with the slot-lip
ailerons with neither lag nor sluggishness in their
action. Successful flights were later made with the
rudder locked neutral, leaving only the slot-lip ailerons
WIND-TUNiNEL AND FLIGHT TESTS OF SLOT-UP AILERONS
559
for both directional and lateral control. The control was
Figure 48. — Time history of Wl-A airplane motion due to slot-lip ailerons.
Figure 49. — Analysis of flight test of Wl-A airplane with slot-lip ailerons at 0.30c«.
Sf, 0°; Cl, 0.55.
Aro=^ - r' AV - p’Np'-pNp Lo=~--p' L*-r' L/
equally good with the slotted flap deflected for landing.
Inasmuch as these results seemed to be in disagree¬
ment with the results of the tests of the F-22 airplane,
detailed records of the airplane motion following a
deflection of the slot-lip ailerons were made and are
given in figure 48. An analysis of the motions has been
made using estimated resistance derivatives and
moments of inertia for the Wl-A airplane. The
results of the analysis are given in figure 49. It will
be readily seen that an appreciable part of the rolling
angular velocity was indirectly obtained from the
large favorable yawing moment, as evidenced by the
large values of As in the previous analysis of
the F-22 tests, the values of Z0/-Z> and N0/N were com¬
puted and are given in figure 50 with the flap both
neutral and deflected. Comparison with figure 44
shows that the curve for L0/L with the flap neutral
lies between the curves from the F-22 tests of slot-lip
ailerons located at 0.20 cw and 0.45<v It therefore
Figure 50.— Sluggishness of slot-lip ailerons on Wl-A airplane.
seems that the apparent discrepancy between the
results of the F-22 tests and the Wl-A tests is explained
by the large dihedral of the Wl-A, which indirectly
contributed a large proportion of the roll.
With the special slotted flap of the A 1-A deflected
22%°, the sluggishness was appreciably less than that
for the F-22 with the split flap deflected 56°. In fact,
with the Wl-A airplane, the sluggishness was slightly
less with the flap deflected than with it retracted. It
seems, therefore, that the sluggishness may be critically
affected by the particular type of flap used.
CONCLUSIONS
1. For airplanes similar to the ones tested, the lag
with single retractable spoilers or ailerons varies with
the position along the wing chord from a negligible
value near the trailing edge to nearly 1 second for a
position near the leading edge. Unless the device is
located within 20 percent of the wing chord from the
trailing edge, the lag will be objectionably large (more
than 0.10 second).
2. With a proper combination of spoiler and slot,
such as the N. A. C. A. slot-lip aileron, the lag with
REPORT NO. 602— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
560
spoiler at any location may be reduced to a negligible
value although the sluggishness may be excessive.
This sluggishness may be in the order of 4 chord
lengths distance traveled by the airplane for ordinary
ailerons located at the trailing edge and about 12 chord
lengths for slot-lip ailerons located near the leading-
edge of the wing.
3. The added airplane drag with slot-lip ailerons is
considered excessive for high-performance airplanes,
being in the order of 10 percent of the wing drag at high
speed and about 35 percent of the wing profile drag
in the climbing attitude.
4. One advantage of the slots as used for the slot-
lip ailerons lies in the extension of the usable angle-of-
attack range of an airplane by delaying the stall of the
outer portions of the wing and thus maintaining damp¬
ing in roll. This effect becomes of small importance
when the slot is located farther back than 50 percent
of the wing chord.
5. For airplanes in which increased safety and sim¬
plicity of control is of more importance than high speed,
high rate of climb, and high maneuverability, the slot-
lip ailerons located between 30 and 40 percent of the
wing chord might be desirable, particularly when used
on an airplane having considerable dihedral.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., June 11, 1937.
REFERENCES
1. Weick, Fred E., and Shortal, Joseph A.: Wind-Tunnel
Research Comparing Lateral Control Devices, Particu¬
larly at High Angles of Attack. V — Spoilers and Ailerons
on Rectangular Wings. T. R. No. 439, N. A. C. A.. 1932.
2. Weick, Fred E., Soule, Hartley A., and Gough, Melvin N.:
A Flight Investigation of the Lateral Control Character¬
istics of Short, Wide Ailerons and Various Spoilers, with
Different Amounts of Wing Dihedral. T. R. No. 494,
N. A. C. A., 1934.
3. Weick, Fred E., and Shortal, Joseph A.: Development of the
N. A. C. A. Slot-Lip Aileron. T. N. No. 547, N. A. C. A.,
1935.
4. Harris, Thomas A.: The 7 by 10 Foot Wind Tunnel of the
National Advisory Committee for Aeronautics. T. R.
No. 412, N. A. C. A., 1931.
5. Soule, H. A., and McAvoy, W. H.: Flight Investigation of
Lateral Control Devices for Use with Full-Span Flaps.
T. R. No. 517, N. A. C. A., 1935.
6. Shortal, J. A.: Effect of Retractable-Spoiler Location on
Rolling- and Yawing-Moment Coefficients. T. N. No.
499, N. A. C. A., 1934.
7. Weick, Fred E., and Wenzinger, Carl J.: The Characteristics
of a Clark Y Wing Model Equipped with Several Forms
of Low-Drag Fixed Slots. T. R. No. 407, N. A. C. A.,
1932.
8. Weick, Fred E., and Shortal, Joseph A.: Wind-Tunnel Re¬
search Comparing Lateral Control Devices, Particularly
at High Angles of Attack. VIII. Straight and Skewed
Ailerons on Wings with Rounded Tips. T. N. No. 445,
N. A. C. A., 1933.
9. Pearson, H. A.: Theoretical Span Loading and Moments of
Tapered Wings Produced by Aileron Deflection. T. N.
No. 589, N. A. C. A., 1937.
10. Jones, Robert T.: A Study of the Two-Control Operation
of an Airplane. T. R. No. 579, N. A. C. A., 1936.
11. Platt, Robert C.: Turbulence Factors of N. A. C. A. Wind
Tunnels as Determined by Sphere Tests. T. R. No. 558,
N. A. C. A., 1936.
12. De France, Smith J.: The N. A. C. A. Full-Scale Wind Tun¬
nel. T. R. No. 459, N. A. C. A., 1933.
13. Glauert, H.: Wind Tunnel Interference on Wings, Bodies,
and Airscrews. R. & M. No. 1566, British A. R. C.,
1933.
14. Weick, Fred E., and Jones, Robert T.: The Effect of Lateral
Controls in Producing Motion of an Airplane as Com¬
puted from Wind-Tunnel Data. T. R. No. 570, N. A.
C. A., 1936.
WIND-TUNNEL AND FLIGHT TESTS OF SLOT-LIP AILERONS
561
TABLE I
SUMMARY OF DRAG INVESTIGATION OF VARIOUS SLOTS IN A 4- BY 8-FOOT N. A. C. A. 23012 WING IN THE 7-
BY 10-FOOT WIND TUNNEL
[Air speed, 80 m. p. h.]
Slot designation
A Cd for Cl=
dCh
da0
Aa,
Lo
c
m0
a. c. 1
0
0.2
0.4
0.5
0
0
0
0
0. 101
0
-0. 007
0.030
.0013
.0014
.0034
. 0052
.091
0
-.007
.030
.0014
.0016
.0038
.0052
.091
0
-.007
.030
.0018
.0026
. 0064
. 0085
.086
0
-.008
.034
.0014
. 0023
.0071
.0078
.084
-. i
-.007
.034
. 0016
0019
.0060
.0084
.084
-. l
-.007
. 034
.0018
.0023
.0061
.0090
.084
-. i
-.007
. 034 !
.0018
.0026
.0056
. 0093
.084
-. i
-.007
.034
.0020
.0018
.0055
.0071
.086
0
-.008
.034
.0043
.0058
. 0068
.0068
.095
.8
-.007
.015
.0041
. 0045
.0050
.0053
. 101
.9
-.007
. 000
.0038
.0038
.0037
.0034
.103
.9
-.011
.000
.0015
.0020
.0041
.0053
.086
0
-.007
.040
.0015
.0013
.0028
.0042
.092
0
-.008
.032
.0011
.0008
.0008
.0011
.100
-.1
-.008
.028
.0012
.0016
.0037
.0050
.086
0
-.007
.040
.0016
.0015
.0030
.0040
.090
-. 1
-.009
.036
.0015
.0019
.0035
. 0055
.092
-. 1
-.008
.036
.0016
.0013
.0022
.0033
.092
-. 1
-.009
.036
.0014
.0013
.0025
.0036
. 103
-.1
-.008
. 036 i
.0012
.0008
.0008
.0008
. 092
-. 1
-.008
. 026 j
.0012
.0010
0023
.0028
. 095
— . 1
-.008
.034 I
Values are approximate aerodynamic-center location in fractions of c» ahead of wing quarter-chord point.
REPORT No. 603
WIND-TUNNEL INVESTIGATION OF WINGS WITH ORDINARY AILERONS AND
FULL-SPAN EXTERNAL-AIRFOIL FLAPS
By Robert G. Platt and Joseph A. Shortal
SUMMARY
An investigation was carried out in the Ar. A. C. A.
7- by 10-foot wind tunnel of an N. A. C. A. 23012 airfoil
equipped, first, with a full-span N. A. C. A. 23012
external-airfoil flap having a chord 0.20 of the main airfoil
chord and with a full-span aileron with a chord 0.12 of
the main airfoil chord on the trailing edge of the main
airfoil and equipped , second, with a 0 .30-chord full-span
N. A. C. A. 23012 external-airfoil flap and a 0.13-chord
full-span aileron. The results are arranged in three
groups, the first two of which deal with the airfoil character¬
istics of the two airfoil-flap combinations and with the
lateral-control characteristics of the airfoil-flap-aileron
combinations. The third group of tests deals with several
means for balancing ailerons mounted on a special large-
chord N. A. C. A. 23012 airfoil model with and without
a 0.20-chord N. A. C. A. 23012 external-airfoil flap.
The tests included an ordinary aileron, a curtained-nose
balance, a Frise balance, and a tab.
The results obtained for the 0.30 cw flap verify the
conclusion made from previous tests of the 0.20 cw flap
combination, namely, that external-airfoil flaps applied
to the N. A. C. A. 230 airfoil sections give characteristics
more favorable to speed range, to low power requirements
in flight at high lift coefficients, and to low flap-operating
moments than do other types of flap in general use. The
ailerons can produce large rolling moments with relatively
small adverse yawing moments in flight conditions ranging
from high speed to minimum speed. The nose balance
and Frise balance were ineffective in reducing the stick
forces required for a given control effectiveness, but the
use of tabs in combination with a differential aileron
motion provided a means of obtaining desirable stick
forces throughout the flight range. The aerodynamic
advantages of this aileron-flap combination appear to
outweigh probable design difficulties.
INTRODUCTION
Improvement of airplane speed range and perform¬
ance by (lie use of trading-edge higb-lift devices has
been hampered by the necessary compromise between
obtaining the highest possible maximum lift coefficient
and the necessity of providing at least a minimum of
lateral control. The usual compromise has involved
the use of flaps over the central portion of the span with
ailerons attached to the tip portion. This procedure
results not only in the direct loss of possible maximum
lift over the unflapped area but may lead to an addi¬
tional hazard resulting from the tendency of partial-
span flaps of the conventional type to reduce, in some
cases, the degree of stability and control near the stall.
It is therefore generally recognized that the develop¬
ment of a lateral-control arrangement that can be used
in combination with a full-span flap offers definite
possibilities for improvements in speed range and
safety.
In most of the numerous attempts that have been
made to devise such an arrangement (for example,
references 1, 2, and 3) unforeseen difficulties have prac¬
tically canceled the anticipated improvement. In
some cases reductions of maximum lift or increases in
minimum drag have had to be accepted in order to
obtain the minimum acceptable lateral control; the
mechanical complications or operational difficulties of
other arrangements have prevented their satisfactory
application. At present no combination that makes
full use of the capabilities of high-lift devices and pro¬
vides satisfactory lateral control has found general
application to airplane design.
The investigation reported herein dealt with an
arrangement that, on preliminary study, indicated possi¬
bilities of meeting the foregoing requirements. The
arrangement consisted of a main airfoil on the trailing
edge of which were an external-airfoil flap and ailerons
forming the lip of the slot between the main airfoil and
the llap. This combination logically results from an
attempt to combine the desirable characteristics of tin'
slot-lip ailerons described in reference 3 with those of
the external-airfoil flaps described in reference 4.
These ailerons being structurally similar to ordinary
ailerons, relatively complicated mechanical and struc¬
tural arrangements are avoided and the main airfoil
contour is left unbroken when the ailerons are unde¬
flected, thus making available the full capabilities of
external-airfoil (laps for speed-range improvement and
reduction of power requirements in low-speed (light.
This wind-tunnel investigation was divided into
I liree general phases:
1. Measurement of the lift, drag, and pitching-
moment characteristics and the flap hinge moments of
an N. A. C. A. 23012 airfoil with N. A. C. A. 23012
564
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
external-airfoil flaps having chords (cf) that are 0.20
and 0.30 of the main airfoil chord (cw).
2. In addition to the characteristics measured in the
first phase, the measurement of the rolling- and yawing-
moment characteristics of the foregoing combinations
provided with ailerons having chords (ca) of 0.12 and
0.13 of the main airfoil chord and deflected various
amounts. (The aileron chord was made 10 percent of the
over-all airfoil chord in each case to permit the results
to be directly compared with the data of reference 3.)
3. Measurement of aileron hinge moments and lift
and drag increments of a wide-chord N. A. C. A. 23012
airfoil with and without a 0.20 cw external-airfoil flap.
Various types of aileron balance were tested.
(a) N. A. C. A. 23012 airfoil with 0.20 cw N. A. C. A. 23012 external-airfoil flap and
0.12 cw ordinary ailerons.
(h) N. A. C. A. 23012 airfoil with 0.30 cw N. A. C. A. 23012 external-airfoil flap and
0.13 Cw ordinary ailerons.
Figure 1. — xVilerons and flaps tested.
The results obtained have been studied with the
purpose of clarifying the fundamental phenomena in¬
volved in the operation of the general type of device
tested. They further provide the information neces¬
sary for comparison of the particular arrangement
tested with other devices intended to accomplish the
same purpose. Certain difficulties that may be en¬
countered in flight applications of the device are pointed
out and some investigation of methods of overcoming
these difficulties is discussed.
APPARATUS AND METHODS
The investigation was carried out in the N. A. C. A.
i- by 10-foot open-throat wind tunnel (reference 5).
The models used in the first phase of the investigation
consisted of the following:
(1) A rectangular N. A. C. A. 23012 airfoil of 10-
inch chord and 60-inch span, constructed of laminated
mahogany.
(2) One 2-inch-chord and one 3-inch-chord dural¬
umin N. A. C. A. 23012 airfoil, each having a span of
60 inches. These small airfoils served as flaps.
The tests of the combination using the 2-inch-cbord
flap are described in reference 4; the data have been
included in this report for completeness. Exactly
similar methods were adopted for the tests of the
combination using the 3-inch-chord flap; surveys were
made to determine the effect of flap position and angle,
a desirable flap-hinge-axis location was selected from
contours similar to those in reference 4, and force tests
were made to determine the characteristics of the
finally selected arrangement at various flap angles.
In order to avoid section inaccuracies during the final
force tests, these tests were completed before ailerons
were built into the trailing edge of the main airfoil.
For the second phase of the investigation the trailing
edge of the main airfoil was cut off and ailerons extend¬
ing across the full 60-inch span of the airfoil were in¬
stalled. For the tests with the 2-inch flap the chord
of the ailerons (back of the hinge) was 1.2 inches; for
the tests with the 3-inch flap it was 1.3 inches. The
1.2-inch -chord ailerons were made of the wooden sec¬
tion taken from the trailing edge of the main airfoil
but difficulty in maintaining accurate settings of these
ailerons indicated the desirability of using duralumin
for the wider-chord ailerons. The settings of the 1.3-
inch ailerons were probably somewhat more accurate
than those of the 1.2-inch ailerons for this reason.
Figure 1 shows pertinent details of the models used.
Figure 2 is a photograph of the model with the 2-inch
flap and 1.2-incli ailerons. If the details relating to the
ailerons are disregarded, the figures show the condition
of the models in the first phase of the investigation.
A series of tests in which angle of attack, aileron
deflection, and flap angle were varied over the useful
Figure 2.— Model N. A. C. A. 23012 airfoil with 0.20 c„- N. A. C A. 23012 external-airfoil flap and 0.12 c,r ordinary aileron.
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS 565
ranges was made for each wing-flap-aileron combina¬
tion. The deflection of one half-span aileron was
varied from the selected maximum up to the maximum
down deflection. The effect of moving both ailerons
simultaneously may be obtained by the addition of the
effects produced by one aileron deflected to each of the
assumed settings, due account being taken of the signs
of moments and deflections. This method of obtain¬
ing rolling, yawing, and hinge moments of ailerons
deflected in various ways from the data for one aileron
is explained in detail in reference 2.
All tests involved in the first two phases were con¬
ducted according to standard force-test procedure in
the 7- by 10-foot tunnel (reference 5). The dynamic
pressure in the jet was maintained at 16.37 pounds per
square foot corresponding to a speed of 80 miles per
hour in standard air. The test Reynolds Number was
730,000 for the model with the 0.20 cw flap and 790,000
for the model with the 0.30 cw flap. The flow condi¬
tions correspond approximately to those that would
exist in free air at Reynolds Numbers of 1,000,000 and
1,100,000 respectively (reference 6).
Hinge moments of the flaps and ailerons were meas¬
ured in the usual manner. A calibrated torque rod,
attached to the surface under test and shielded from
the air stream, was turned by a pointer mounted next
to a graduated disk outside the jet. The difference of
the pointer deflections required to bring the surface to
the required deflection with the wind off and on was
read from the disk. This difference is proportional to
the aerodynamic moment about the hinge; the magni¬
tude of the hinge moment follows directly from the
known calibration of the rod.
The third phase of the investigation arose as the
result of analysis of the data alread}^ obtained, which
indicated that the ailerons would require excessive
operating moments under certain conditions. It was
therefore considered desirable to investigate the effec¬
tiveness of several methods of obtaining aileron bal¬
ance. In order to reproduce ailerons of practical sizes
with satisfactory accuracy, a special widc-chord model
was constructed to be mounted between end planes.
Although such an expedient does not reproduce full-
scale conditions, practical aileron details, such as clear¬
ances and hinges, can be reproduced. As will subse¬
quently be noted, leaks ahead of the aileron hinge
resulting from clearance between the wing and the
aileron have an appreciable effect on aileron charac¬
teristics and the clearance should therefore be accurately
controlled.
The wide-chord model consisted of a rectangular
N. A. C. A. 23012 airfoil having a chord of 4 feet and a
span of 8 feet, equipped with an aileron of 31 -inch span
and 5.76-inch chord back of the hinge, located centrally
along the span. The tests included the types of ailerons
shown in figure 3: An ordinary aileron, an aileron
with a nose balance shielded by curtains, an aileron
with a Frise nose, and an aileron with a tab. An
N. A. C. A. 23012 external-airfoil flap of 9.6-inch chord
and 8-foot span was provided. The section of this
model as tested was an accurate enlargement of that
used for the standard-size model tested with the 0.20
cw external-airfoil flap and 0.12 cw ailerons. The model,
complete with aileron and flap, was mounted between
large end planes in the jet of the 7- by 10-foot tunnel.
(See fig. 4.)
The regular force-test support, with two special struts
for angle-of-attack adjustment, was used to permit
measurement of the forces on the model. The aileron
hinge moments were measured by a torque-rod and
graduated-disk arrangement similar to that used for
the standard-size model. Values of lift and drag
increments due to aileron deflection and the variation
of aileron hinge moment with deflection were measured
Figure 3. — Various balanced ailerons tested on the wide-chord X. A. C. A. 23012
airfoil with and without a 0.20 c« N. A. C. A. 23012 external-airfoil flap.
at several angles of attack and flap angles. The tests
were repeated with the flap removed to determine the
effectiveness of the balancing means for narrow-chord
ordinary ailerons mounted on a plain wing.
The tests of the wide-chord model were made, in
general, at a dynamic pressure of 4.093 pounds per
square foot, corresponding to an air speed of 40 miles
per hour in standard air. The reduced speed was used
to avoid placing excessive loads on the balance parts
used as the model support. The effective Reynolds
Number in this case was of the order of 5,000,000 but it
should not be considered so accurate an index of flow
similarity as is usually the case in wind-tunnel testing.
566
REPORT NO. GC3— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 4.— The 4- by 8-foot model of the X. A. C. A. 23012 airfoil with an external -airfoil flap and an ordinary aileron, mounted between end planes in the 7- by
10-foot wind tunnel.
RESULTS
Application of results. — The precision of standard
force tests in the 7- by 10-foot tunnel is discussed in
references 2 and 5. The results as corrected are
considered applicable to flight conditions with normal
engineering accuracy at the previously stated values of
the effective Reynolds Number. These values are too
small to be directly usable in most cases but, with the
aid of reference 7, a number of the characteristics of
the present airfoils may be inferred for larger values of
the Reynolds Number.
The conditions under which the ailerons on the wide-
chord airfoil were tested were far removed from those
for which theoretical wind-tunnel corrections may be
applied ; they therefore do not appear susceptible of
accurate interpretation in terms of fundamental param¬
eters. The ideal conditions in this respect were dis¬
regarded in favor of obtaining a reasonably accurate
reproduction of the full-size ailerons themselves, includ¬
ing the end effects, to facilitate accurate comparison of
the various ailerons tested. Consequently, any ap¬
plication to flight characteristics must be considered
qualitative in nature. For comparison of the ailerons
among themselves, however, the accuracy is probably
much better than that usually obtained in standard
small-scale tests, owing to the relatively large magnitude
of the forces acting on the large model. The effectiveness
of the data subsequently presented in showing consistent
differences between the ailerons serves as an indication
of the accuracy with which the values were measured.
Presentation and analysis of results. — The data
obtained in the tests have been reduced to nondimen-
sional coefficient form and are presented in a series of
standard plots. The usual N. A. C. A. absolute
coefficients are used throughout, except for a few
symbols that have not been standardized. In the
computation of the standard airfoil coefficients, the
nominal area has been taken as the sum of the individual
areas of the nonretracting surfaces (see references 2
and 4); the chord lengths have been similarly treated.
The nonstandard coefficients are:
Cnv induced yawing-moment coefficient.
(7„0, profile yawing-moment coefficient.
Ch, hinge-moment coefficient based on the dimensions
of the surface whose hinge moment is being
measured. ^Thus, C
L, the increment of lift coefficient produced by a
specified deflection of the aileron on the wide-
chord model.
A CD, the increment of drag corresponding to A CL.
<5, angular deflection of the chord line of an auxiliary
surface from the chord line of the surface to
which it is attached, having the same sign
convention as angle of attack.
The following subscripts serve to identify the various
parts of the complete wing model:
w, of the main airfoil.
/, of the flap.
a, of the aileron.
t, of the tab.
The results of the first phase of the investigation
consist entirely of lift, drag, pitching-moment, and flap
hinge-moment data relating to the two high-lift arrange¬
ments tested. Data for the plain N. A. C. A. 23012
airfoil used as the basic airfoil are shown in figure 5
together with data from another airfoil of the same
section. The data for the basic airfoil equipped with a
0.20 cw N. A. C. A. 23012 external-airfoil flap deflected
through various angles appear in figures G to 9.
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS 567
! Sto.
Up'r.
0
o
o
.0
Q
'o
o
-c
o
o
D
c
CD
23^
k
o
24 *
4
o
IS 60
0
20
40
o
•c
8 4/00
o
4 "c 120
QJ
<J
0 ^140
Q.
-4'S
- 8
o
1.25
25
5.0
7,5
10
15
20
25
30
40
50
60
-12
~ib
2.67
3.6 1
4 91
5.80
6.43
7.19
7 50
7.60
7.55
7. 14
6.4/
5.4 7
L'w 'r.
0 \
- 1.23
-1.71
-2 26
- 2.6 /
-2.92.
-3.50
-3.97
-4.28
-4.46
-4 48.
-4.17
-3.6 7
•*- t>
C ^
U O
Cj ^
D y
<u s-
0. o
20
/O
0
-70
r
*
U
c
—
—
Ij
4=
"1
T_
/ / u
20 40 60 80 ZOO
Percent of chord
m
ac above chord. 0./ /9c
ac from forward end
8(
9C
5.
IO(
7 3.01
/. 6 c
3-3/6
3 -1.33
3 .92 T-
3 (,/3)-/-(-
-. 70
43)
'
1
n n
j'
. .
.
— X-
r'l
*
t
\
L/D
CL
8
*
/
/
\
4
€
_
J
L
/ /
L
t. 8 .36
1.6
L4
1.2 .
,o
<u
o
.6 °
v:
.2
0
-.2
CJ
.32 c'
,<d
. ^ ■§
■ 28^ £
<b
: 24 -S’ 8
£ £
20
./elk.
0 n
./2* £
.08
.04
-8
l /e/. (ft/s ec). 1 17 3, Pres (st’nd. atm.):/ i "• 4
R N.:( Test) 609.000; Tested ■ L.M.A.L.
. Date. I/-20-35 & 6-4-36 \- g
Test. 3/79 AScB, 7 by tO ft. tunnel
Corrected for tunnel-wall effect.
-4 0 ~ 4 8 12 16 -~20 ~24 28
Angle of attack, a (degrees)
s.
(D
o
o
c
Qj
I
JO
09
.08
07
.06
.05
.04
03
.02
0/
0
-./
-.2
-.3
.4
+
Test
3/79 A,
n
0
ailerons
X
Test
3/79B,
ailerons
on
O
2
rev/ou
s
tests (T.
Ft. 5t
,4)
_
H
4
—
>5
y
1(C3
c
c
r
7
G
•—
- -
i— T“
/' .
T
a.c.
Air foil: N.A.C.,
A. 230/2, Test. 3/79 A&B
R.N.-.fEff.) 850.000
Results corrected to infinite A.n
: 1 1 J - i
43
. 44-
40.
co
CD
<b
U
o
A
28
0
U
8 5
4 u
o
Oo
V
cn
-8$
-!2
'46
Lift coefficient, CL
Figure 5. — The N. A. C. A. 23012 airfoil.
u
0
1-40
o
c-2 0
<D
28 u
0
*
24 < 20
.o
—
( fi.c.t.
—
—
t.Jj
i.
0
^20
Is
Ss
5
o
£
'<
u
s-
60
v
0
o
~k
c
4 u
u
QJ
0 Q-
-4 i
l
-8
-12
- 16
—
t:
"1
.
i
\
_
l//t
r.
.
P
.
Cl
-
V
A
/
\ —
,
r
—
\
/
/
J
4
\
/
4-
a
- 4-
r
U-
— i —
2.0
t.6
t.4
t.2
Airfoil • N.A.C..A. 23012
1 Size. 10' x60" Flap 2">60
1 Pres, (st'nd atm.) / 1
Tested: L.M.A.L. Date: 7-13-35 j
Vei(ft./sec.) 1/7.3 R N 730,000 -.4
. - Test aspect ratio, 5
_ | Results corrected to A R. 6
^ Test : 2831-a. 7 by 10 ft. tunnel
"1 Corrected for tunnel,- wat) effect.
0 4 3 /2 IS 20 24 28
Angle of attack, or (degrees)
q
J
...
—
—
■
h
•
-12
-/6
Main wing section _ _ _
Flap sect ion _ _
Main wing chord, cu •_ . . - -
Flap chord, c/ _ *
Datum chord, c=cw-\-c;.
Pivot aft of trailing edge of cu.. . . . - . ■ D32 cw
X. A. C. A. 23012
N. A. C. A. 23012
0. 833 c
O. 23 C,„ . 1607 c
. 0266 C
Airfoil: N.A.C.A. 230/2
Flap: N.A.C.A 230/2 Date: 7 /3-35
Test: 283/-a, 7 by /0 ft. tunnel
R.N.: (effective) /, 050, 000
Resu/ts corrected to infinite
aspect ratio.
.2 .4 .6 .8 t.O 12 t.4 t.6
Lift coefficient, C,.
Pivot below c» - - - - 0. 0f>4 cw
Pivot aft of flap leading edge. - - - --- ■ 25 <7
Pivot below cr.. ... - - - • cf
Flap displacement angle . . . - . .
(a. c.)0 from leading edge — ....
(a- C-A) above main wing chord..
Figure 6.— The N. A. C . A. 23012 airfoil with 0.20 cw N. A. C. A. external-airfoil flap. Flap angle, -3°. (See reference 4.)
0. 045 c
.0417 c
.0167 C
— 3°
. 245 c
.08 c
568
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
8 '*0
-12
~/6
T
t
\1
L/D
r
-j
—
—
c.p.
(a.
C.)0
r
i
—
C\
s'
/
—
-d -
C
Airfoil: N.A.C.A. 23012
Size: I0"x60" Flap: 2"x60"
Pres, (sf’nd. atm.): /
Tested: L M. A. L. Dote: 7-13-35
Vet. (ft. /sec.): tt 7. 3 R. N.: 730, 000
Test aspect ratio, 5
Results corrected to A.R. 6
Test: 383d, 7 by 10 ft. tunnel
Corrected for tunnel-wall effect. ,
4 0 4 8 13 16 20 34 28
Angle of attack , tv (degrees)
2.0
t.d
t.6
14
12
1.0
• o
C
.0)
.6 6 .
$
■4 o
u
.2$ .
0
-.2
-.4
-.6
.12
- - nr
.11
3
)
JO
.40
.09
.36
u
.32
c:
0)
0 .07
.28^
-c
£
o-06
*>
sn
u
o
ag
0)
*
u ~9> '
O t
/2& ^
.08
04
0
X
0)
O
o
c
tt)
e
i
.03
.02
.01
0
i
-.2
-.3
-.4
r 4
I
—
A
\
\
1
1
r>
■ -
2
■
J-
f
—
—
Airfoil: N.A.C.A. 330/2. Flap: N.A.C.A. 230/2
Test: 2834. 7 by 10 f t. tunnel
Date: 7-13-35 RN. fFff.) t ,050,000
Results corrected to infinite aspect ratio.
1.8
48
44
40
"•o'
DO ^
32 .1)
,0
28
.6
24 ■§
v
20 o
<D
a
16 §
.-8
/2.£
c
£
^ -i:
0
-4 o
-3?
Ch
c
X
-8
72
-16
O .2
.4 .6 .8 t.O
Lift coefficient, C:
i.Z 1.4 t.6
Figure 7.— The X. A. C. A. 23012 airfoil with 0.20c„, N. A
setting. The value of C
C. A. external-airfoil flap. Flap angle, 10°
(<t c •) o is computed about the aerodynamic center used for test 2831-a
The airfoil is the same as used for test 2831-a (fig. 6), except the flap
(See reference 4.)
Figure 8.— The X. A. C. A. 23012 airfoil with 0.20 cw N. A. C. A. 23012 external-airfoil flap. Flap angle 20°. The airfoil is the same as used for test 2831-a (fig. 0), except
the flap setting. The value of Cm (a.e.) 0 is computed about the aerodynamic center used for test 2831-a. (See reference 4.)
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL- AIRFOIL FLAPS 569
Figure 9.— The N. A. C. A. 23012 airfoil with 0.20 cw N. A. C. A. 23012 external-airfoil flap. Flap angle, 30°. The airfoil is the same as used for test 2831-a (fig 6),
except the flap setting. The value of Cm u,c.) # is computed about the aerodynamic center used for test 2831-a. (See reference 4.)
Alain wing section. . .
Flap section _ _ _
Over-all wing chord, c = c „>+c/.
Main wing chord, cw-- . .
Flap chord, c/ . . .
Datum chord, c=Cu>+c/.
N. A. C. A. 23012
N. A. C. A. 23012
0. 769 c
O. 30 Ctr .231c
Figure 10.— The N. A. C. A. 23012 airfoil with 0.30 c„
Pivot aft of trailing edge of c„- - -
Pivot below cw - - -
Pivot aft of flap leading edge -
Flap displacement angle -
a.c. from leading edge - - -
n.c. above main wing chord -
N. A. C. A. 23012 external -airfoil flap. Flap angle, -2°.
0.071 Cu
.049 c U-
.25 cf
0. 0546 <
. 0377 C
. 0577 C
— 2°
. 240 C
. 260 c
570
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure II .—The N. A. C. A. 23012 airfoil with 0.30 cw N. A. C. A. 23012 external-airfoil flap. Flap angle, 10°. The airfoil is the same as used for test 3240 (fig. 10),
except the flap setting. The value of Cn (a c<) is computed about the aerodynamic center used for test 3240
/ /
10
2.0
40
03
1.8
35
3
.03
1.6
32
• i?
.07
1.4
28
'sj
$
c
<0
o
06
1.2
24
.0)
CJ
u
iC
$
.05
1.0
Q
,<u
.o
20
<D
O
(J
I
04
.3$
46
bx
o
0
X
6
03
.6
o
42
£
ft
02
.4
03
Ol
.2
.04
; ;
-8 -4
Airfoil: N.A.C.A. 23012, Flop- 2 30 IB
Pres. (sf'nd. aim): / Size:/0"x60,3"x60 -.4
Vet. (ft. /sec ) 1/7.3. Dole: 6-1-36
Tested. L.M A R. N. ftest) 790, OOO . - $
Test. 3242, 7 by , O ft. lunnel
Corrected to aspect ratio 6 _
8
O
Q, .2
o
u
+.-3
c_
u
S - 4
—
•
ft.
•
—
<*>
—
CS.--5
=**
r
1
- — • -
K'n'(ac L
[JL
IF
48
\ 44
40
<0
36 JJ
o.
a>
32 ^
28
.o
24
x.
20 «
&
16 Q
<u
13 6
X
8 c
4%
o
- Oo
1'^
o
-8$
O
0 4 8 /2 (6 20 24 26
Angle of attack, (X (degrees)
Figure 12.— The N. A. C. A. 23012 airfoil with 0.30 c» N. A. C. A. 23012 external-airfoil flap. Flap angle, 20°. The airfoil is the same as used for test 3240 (fig. 10), except
Airfoil: N.A.C.A. 23012, F lap: N.A.C.A. 23012 ’2
Test 3242,7x10 ft. tunnel, R.N.:(Eff.) 1,100,000 ’
Resutts cor reded to infinite aspect ratio ®
? .4 .6 .8 10 1.2 1.4 76 18
Lift coefficient, CL
the flap setting. The value of Cm o is computed about the aerodynamic center used for test 3240.
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS 571
Figure 13.— The N. A. C. A. 23012 airfoil with 0.30 cw N. A. C. A. 23012 external-airfoil flap. Flap angle, 30°. The airfoil is the same as used for test 3240 (fig. 10), except
the flap setting. The value of CV. „ e0 o is computed about the aerodynamic center used for test 3240.
44
40
36 g
0)
32 ^
$
28
24
20'
S
o'
V
0
k
O
<D
16 §•
o
12%
x
x
a-s
t.
4^
<
0
0$
o
-8
c
-12
46
Figure 14.— The N. A. C. A. 23012 airfoil with 0.30 cv N. A. C. A. 23012 external-airfoil flap. Flap angle, 40°. The airfoil is the same as used for test 3240 (fig. 10), except
the flap setting. The value of Cm (o „ » is computed about the aerodynamic center used for test 3240.
Angle of attack for infinite aspect ro ho, cx0 (degrees)
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
572
The data for the basic airfoil equipped with a 0.30 cw
external-airfoil flap of N. x\. C. A. 23012 section appear
in figures 10 to 14. The variation of flap liinge-moment
coefficient with flap angle and angle of attack for each
flap is shown in figure 15. It will he noted that the geo¬
metric aspect ratios of the model with the 0.20 cw and
0.30 cw flaps were 5.0 and 4.61, respectively. For pur¬
poses of comparison the data have been corrected in the
usual manner (reference 2) for jet-boundary and plan-
form effects and are presented in the standard airfoil
plots for aspect ratios of 6 and infinity. Likewise,
the angles of attack shown for the flap hinge-moment
coefficient plots (fig. 15) refer to the conditions for a
wing of aspect ratio 6 in an infinite jet.
coefficients is neglected, the plotted values are directly
comparable with those obtained in previous lateral-
control investigations in the 7- by 10-foot tunnel. The
magnitude of the jet-boundary correction of yawing
moment is normally small, and the present results may,
therefore, be roughly compared with data obtained in
previous investigations without correction. For ac¬
curate comparison of yawing-moment data, however,
previous results should be corrected for the effect of the
jet boundaries on induced yawing moment by the
method given in the appendix.
The data in the figures have been selected from cross-
fairings against angle of attack in such a way as to show
the lateral-control characteristics at angles of attack
Figure 15. — Variation of flap hinge-moment coefficient with flap deflection, at several angles of attack.
The results of the second phase of the investigation
consist of rolling-moment, yawing-moment, and hinge-
moment coefficients, presented as functions of angular
deflection of the right aileron, the left aileron being held
neutral. The data for the basic model equipped with
the 0.20 cw external-airfoil flap and the 0.12 cw ailerons
appear in figures 16 to 19; those for the model with the
0.30 cw external-airfoil flap and 0.13 cw ailerons in
figures 20 to 23. For purposes of comparison the roll¬
ing- and yawing-moment coefficients have been cor¬
rected for jet-boundarv and aspect-ratio effects so that
the data as presented are representative of conditions
existing on a model of aspect ratio 6 in an infinite jet.
The method employed in making the corrections is
explained in an appendix to this report. Since the
effect of jet boundaries on measured rolling-moment
corresponding to lift coefficients of 0.2, 0.7, 1.2, and 1.8
with the ailerons neutral. The variation of lift coeffi¬
cient with aileron deflection at a given angle of attack
was neglected. The lift coefficients were selected as
representative of certain flight conditions: high speed,
maximum rate of climb, steep climb and approach
glide, and flight immediately before landing and after
take-off.
The plots of yawing-moment coefficient against roll¬
ing-moment coefficient may be regarded as analogous
to polar curves of lift and drag. As indicated in the
appendix, the theoretical induced yawing-moment co¬
efficients are shown in the figures. By this artifice
the figures are made to show the induced and profile
parts into which the measured yawing moment may be
divided.
573
WIND-TUNNEL INVESTIGATION OF WINGS WITH
AILERONS AND EXTERNAL-AIRFOIL FLAPS
(a) Variation of rolling-moment coefficient with deflec- (b) Variation of yawing-moment coefficient
tion of right aileron. Left aileron, 0°. with rolling-moment coefficient.
(c) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 16.— Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.12 cw ordinary aileron and 0.20 cw external-airfoil flap. Ci=0. 2.
(a) Variation of rolling-moment coefficient with deflec¬
tion of right aileron. Left aileron, 0°.
(b) Variation of yawing-moment coefficient with
rolling-moment coefficient.
(e) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 17.— Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.12 cw ordinary aileron and 0.20 cw external-airfoil flap. Cl=0. 7.
(a) Variation of rolling-moment coefficient with deflec- (b) Variation of yawing-moment coefficient with rolling- (c) Variation of aileron hinge-moment coefficient
tion of right aileron. Left aileron, 0°. moment coefficient. with aileron deflection.
Figure 18. — Rolling-, yawing-, and hinge-momeut coefficients of N. A. C. A. 23012 airfoil with 0.12 cw ordinary aileron and 0.20 cw external-airfoil flap. Ct = 1.2.
574
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(a) Variation of rolling-moment coefficient with deflec¬
tion of right aileron. Left aileron, 0°.
(b) Variation of yawing-moment coefficient with rolling-
moment coefficient.
(c) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 19— Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.12 cw ordinary aileron aDd 0 20 cu external-airfoil flap. C/,=1.8.
(a 1 Variation of rolling-moment coefficient with de- (b) Variation of yawing-moment coefficient with rolling-
flection of right aileron. Left aileron, 0°. moment coefficient.
(e) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 20— Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.13 c„ ordinary aileron and 0.30 external-airfoil flap. Ci = 0.2.
(a) Variation of rolling-moment coefficient with de- (b) Variation of yawing-moment coefficient with rolling-
flection of right aileron. Left aileron, 0°. moment coefficient.
(c) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 21. — Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.13 c« ordinary aileron and 0 30 cv external-airfoil flap. CY=0.7.
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS
O/O
(a) Variation of rolling-moment coefficient with (b Variation of yawing-moment coefficient with rolling-
deflection of right aileron. Left aileron, 0°. moment coefficient.
(c) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 22. — Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.13 cw ordinary aileron and 0.30 cw external-airfoil flap. CL— 1.2.
(a) Variation of rolling-moment coefficient with (bj Variation of yawing-moment coefficient with rolling-
deflection of right aileron. Left aileron, 0°. moment coefficient.
(c) Variation of aileron hinge-moment coefficient
with aileron deflection.
Figure 23.— Rolling-, yawing-, and hinge-moment coefficients of N. A. C. A. 23012 airfoil with 0.13 Cw ordinary aileron and 0.30 cw external-airfoil flap. Cl=1.S.
The data obtained in the third phase of the investi¬
gation are given in figures 24 to 31. The measured
values of lift and drag have been reduced to the form of
the lift and drag increments that result from a given
deflection of the aileron under test. The lift incre¬
ment produced by a deflected aileron on an airplane
wing is the direct source of the rolling moment obtained;
the drag increment likewise produces a corresponding
yawing moment. Thus, under comparable conditions
of wing lift coefficient and flap setting, the rolling and
yawing moments that one of the ailerons under test
would produce on an airplane wing are directly pro¬
portional to the measured lift and drag increments.
The factor of proportionality varies with wing plan
form but, for a given plan form, the factor remains
constant regardless of aileron deflection. The curves
of lift increment against aileron deflection and drag
increment against lift increment are therefore analo¬
gous in form to the rolling- and yawing-moment data
previously presented. Absolute values of hinge mo¬
ment as a function of aileron deflection are also given
these values are directly comparable with the data ob¬
tained for the standard model.
38548—38 - 38
576
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(a) Variation of aileron hinge-moment coefficient with aileron
deflection.
(b) Variation of lift-coefficient increment with aileron (c) Variation of drag-coefficient increment
deflection. with lift-coefficient increment.
Figure 24. — Characteristics of various balanced ailerons on X. A. C. A. 23012 airfoil with 0.20 c„ external-airfoil flap set at —3°. Ci= 0.2.
-40 -30 -20 -10 O 10 20 ~40 ~30 -20 -10 O ,0
6a , degrees 6a , degrees
-.05 O .05 JO J5
*CL
(a) Variation of aileron hinge-moment coefficient with aileron
deflection.
(b) Variation of lift-coefficient increment with aileron (c) Variation of drag-coefficient increment
deflection. with lift-coefficient increment.
Figure 25— Characteristics of various balanced ailerons on N. A. C. A. 23012 airfoil with 0.20 c w external-airfoil flap set at —3°. Cl= 0.7.
(a) \ ariation of aileron hinge-moment coefficient with (b) Variation of lift-coefficient increment with aileron (c) Variation of drag-coefficient increment with lift-
aileron deflection. deflection. coefficient increment.
Figure 26.— Characteristics of various balanced ailerons on N. A. C. A. 23012 airfoil with 0.20 cv external-airfoil flap set at 25°. Cl= 0.7.
The data for the wide-cliord model with the flap and
each of the first three ailerons tested (that is, the plain
aileron, the balanced aileron, and the Frise aileron)
have been cross-faired to obtain the values of the vari¬
ables at the same values of lift coefficient that were used
for the previous figures and are plotted in figures 24 to 27.
Similar data for the model with the same three ailerons
but without the flap are shown in figures 28 and 29.
No lift and drag measurements were made of the
model with the tabbed aileron because it could be
assumed that the aileron lift and drag increments at
small constant tab deflections were the same as those
for the ordinary aileron without a tab. Experience
coincides with flap theory in justifying this assumption
for the unstalled lift range although it cannot be ex¬
pected to hold at lift coefficients very near the stall.
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS
(a) Variation of aileron hinge-moment coefficient (b) Variation of lift-coefficient increment with aileron (c) Variation of drag-coefficient increment with
with aileron deflection. deflection. lift-coefficient increment.
Figure 27. — Characteristics of various balanced ailerons on N. A. C. A. 23012 airfoil with 0.20 c» external-airfoil flap set at 25°. <7/.= 1.2.
6a , degrees
(a) Variation of aileron hinge-moment coefficient
with aileron deflection.
(b) Variation of lift-coefficient increment with aileron
deflection.
(c) Variation of drag-coefficient increment with lift-
coefficient increment.
Figure 28. — Characteristics of various balanced ailerons on X, A. C. A. 23012 airfoil. Ci.=0.2.
(a) Variation of aileron hinge-moment coefficient (b) Variation of lift-coefficient increment with aileron (c) Variation of drag-coeflicient increment with lift-
with aileron deflection. deflection. coefficient increment,
Figure 29. — Characteristics of various balanced ailerons on X. A. C. A. 23012 airfoil. Cl — 0.7.
578
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Fig l'he 30.- Hinge-moment coefficients of a 0.12 cw ordinary aileron with 0.15c„ tab, mounted on an N. A. C. A. 23012 airfoil with and without a 0.20 c, external-airfoil flap.
Figure 31.— Variation of aileron floating angle with tab deflection; 0.12 cw ordinary aileron on an N. A. C. A. 23012 airfoil with and without a 0.20 cw external-airfoil flap.
An unconventional method, subsequently explained,
of using the tab to obtain aileron balance dictated the
method adopted for presenting the data for the model
with the tabbed aileron. In figure 30 the variation of
aileron hinge-moment coefficient with aileron deflection
is shown for a series of tab deflections at several condi¬
tions of angle of attack and flap angle. Figure 31 has
been replotted from the data of figure 30 to show the
variation of aileron floating angle with tab angle, the
data for the model both with and without the flap being
included. A drag test made at an air speed of 80 miles
per hour with the aileron neutral, the flap both removed
and set at the high-speed angle, and the model set at
0° angle of attack indicated that very small drag incre¬
ments would result from a 20° deflection of the tab.
The maximum increment of section profile-drag coeffi¬
cient obtained was 0.0002, which lies within the limits
of accuracy of the test.
DISCUSSION
As previously noted, the present investigation in one
of its phases extended the investigation of the N. A.
C. A. 23012 airfoil equipped with the N. A. C. A. 23012
external-airfoil flaps (reference 4) to include a flap
having a 0.30 cw chord. The methods used in selecting
a desirable location of the flap-hinge axis and in obtain¬
ing and presenting the results directly paralleled those
described in reference 4. Further, the data considered
most significant for the airfoil with the 0.20 cw flap
have been transferred directly into this report for
purposes of unity and completeness.
The discussion in reference 4 sets forth certain
advantages of the external-airfoil type of wing-flap
combination, principally in connection with its ability
to produce high lift coefficients with relatively small
increases of profile-drag coefficient. Figure 32 indicates
the relative value of the 0.20 cw and 0.30 cw flaps in
producing this effect. Tire curves are “envelope
polars,” obtained by fairing an envelope around the
polar curves for various settings of the flap. The
envelope polars thus show the minimum section profile-
drag coefficient that can be obtained at any lift coeffi¬
cient of which the wing-flap combination is capable.
The graph demonstrates that the characteristics of the
0.30 cw flap arrangement are at least as good as those of
the 0.20 cw flap arrangement and may be slightly better
in certain particulars other than the maximum lift
coefficient, in which the 0.30 cv flap is definitely superior.
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS 579
The better rounding of the polar for the 0.30 cw flap,
which gives it a slightly lower drag in the lift range
normally used in take-off and simultaneously would
permit a steeper gliding angle to be obtained at lift
coefficients near the maximum, is believed to result
from the different positioning of the hinge relative to the
flap. The use of a hinge location for the 0.20 cw flap
similar to that for the 0.30 cw might give a polar of more
nearly similar shape. The effect on the maximum lift
and minimum drag coefficients should not be adverse.
No direct experimental evidence on this point was
obtained, but comparison of the contour charts when
they were used for selection of the hinge axis of the
0.30 cw flap indicated the possibility.
It may be inferred from the observed variation of lift
coefficient with flap angle and angle of attack that an
airfoil and an external-airfoil flap act mutually to
suppress the tendency of the flow to separate from their
upper surfaces and thus delay stalling until a high lift
coefficient is reached. An important phase of this
action lies in the effect of the slot in producing a con¬
siderably higher speed of flow past the trailing edge of
the airfoil than would exist with the flap absent. It
therefore appears that ailerons placed on the trailing
edge of an airfoil equipped with an external-airfoil
flap are located in an especially effective position as
compared with those located on a plain airfoil. On an
ordinary airfoil it is known that the flow passes the
trailing edge with little more than the free-stream
velocity; in addition, the aileron may suffer from separa¬
tion at angles somewhat below the stall. Under com¬
parable conditions with the flap in action, it is apparent
that the flow past the aileron has been accelerated and
that the tendency to separation in this region has been
suppressed. It therefore appears that such an aileron
is in an excellent location for producing relatively large
rolling-moment coefficients when the combination is
developing a high lift coefficient. Reference to the
flap-load data of reference 4 further shows that the
flap carries very small forces when it is set for high
speed: As a first approximation with the flap thus set
the main airfoil may be considered an independent
airfoil without appendages. It can then be inferred
that deflection of the Hap from the high-speed to the
maximum-lift angle should cause a progressive increase
in the effectiveness of the ailerons.
The foregoing considerations serve to clarify in part
the variation of rolling-moment coefficient with flap
deflection shown in figures 16 to 23. It is evident that
as the flap is deflected the ailerons do gain considerably
in effectiveness at a given lift coefficient of the wing-flap
combination. The data reveal an additional simulta¬
neous effect that serves further to improve the aileron
effectiveness. As the aileron is deflected upward it
bends the flow upward and reduces the lift. At the
same time the size of the slot is considerably increased
and the flow, tending to follow the lower surface of the
aileron, encounters the flap at an increased angle of
attack. At a certain point in the aileron travel the
slot effectiveness has been reduced and the angle of
attack of the flap sufficiently increased to cause the
flap to stall, resulting in a further reduction in lift and
increase in drag.
Inspection of figures 16 to 23 shows that this effect
occurs at smaller aileron deflections as the flap ap¬
proaches the maximum-lift angle, where the slot size is
most critical. In figure 17, for example, the sharp rise
in the rolling-moment curve, which is associated with
the stalling of the flap, occurs at an aileron deflection
of about 12° up when the flap is down 10°, at 5° up
when the flap is down 20°, and so on. It is evident
that this effect, which further increases the rolling
moment and also reduces the adverse yawing moment,
likewise comes into action progressively as the flap is
deflected from the high-speed to the high-lift condition.
When the flap has passed the maximum lift angle (see
fig. 17, <5/=55°), the sudden increase of rolling moment
Lift coefficient, CL
Figure 32.— Envelope polars for X. A. C. A. 23012 airfoil with 0.20 cw and 0.30 c*
external-airfoil flaps. Effective Reynolds Number, approximately 1,000,000.
fails to appear because the flap is already stalled with
the aileron neutral.
In connection with the effect of the stalling of the
flap, it is noteworthy that the total lift of the flap is
not lost, a low pressure is still maintained over the (lap
upper surface, and its effect in suppressing separation
from the main airfoil is still active. Figure 14 shows
the effect of deflecting the flap beyond its angle for
maximum lift (5/=40° for the 0.30 cw flap), in which case
the flap stalled at a low angle of attack of the com¬
bination. Here the maximum lift coefficient was
reduced approximately 0.3 by the stalling of the flap.
As the maximum increase of CLmax produced by the
flap in this case is 0.9, it is clear that about two-thirds
of the flap effect remains after the flap has stalled. At
still larger deflections the slot is completely ineffective,
and it can be seen that the external-airfoil flap is then
equivalent to a split or Zap flap with a small gap
between it and the wing.
580
REPORT NO. G03— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Thus far the discussion has tended to bring out con¬
siderations favorable to combinations of airfoils, ex¬
ternal-airfoil flaps, and ailerons. Certain undesirable
consequences of the foregoing considerations must also
be recognized. It has been pointed out that ailerons
ot a given size on a wing with external-airfoil flaps can
produce more rolling moment than normal ailerons of
the same size on a plain wing. For application to
airplane design it might be concluded that satisfactory
control could be obtained with smaller ailerons by
using them in combination with an external-airfoil
flap. Such a conclusion is modified, however, bv
another important factor: The data (figs. 1G and 17)
show that the effect of the flap is not active near the
stalling lift coefficient with the flap at the high-speed
angle; thus, ailerons of reduced area would be rela¬
tively weak in this condition.
The location of the aileron in relatively high-speed
flow clearly must lead to increases of hinge moment as
well as of rolling moment. Comparison of the lift
increment per unit hinge moment of the present
ailerons (fig. 24) with that for ordinary ailerons (fig.
28) indicates that with the flap in the high-speed setting
the present ailerons are inferior. Since a large part of
airplane operation would involve use of the ailerons
with the flap at the high-speed setting, it seems desira¬
ble that the hinge moments of these ailerons be reduced
to values comparable with those of ordinary ailerons
for a given rolling moment. These considerations,
which were first apparent when the tests of the stand¬
ard model were compared with generally known char¬
acteristics of ordinary ailerons, led directly to the tests
of the various balanced ailerons on the wide-chord
model.
A study of some unpublished pressure-distribution
data for airfoils with external-airfoil flaps suggested
that a balance extending ahead of the aileron nose
might serve to reduce the aileron hinge moments.
Such a balance normally adds an appreciable amount
of drag, but the provision of “curtains” covering most
of the gap should eliminate the drag increment and still
permit the pressures to act on the balance area. The
arrangement finally selected, designated the “balanced
aileron” in figure 3, was provided with such a balance
and could be deflected between a 40° up and 15° down
angle without encountering the curtains. Ordinary
and Frise ailerons were included to provide a direct
comparison with the tests on the standard model and
with the action of a balance now in general use.
A slight reduction oi hinge moment per unit deflection
was obtained from the balanced aileron, but the lift
increment per unit deflection likewise decreased from
that obtained with the ordinary aileron, resulting in
no actual improvement. The loss of lift increment
suggests that there was more leakage between the bal¬
ance nose and the airfoil than existed in the case of the
plain aileron. This loss might be regained by the use
of some system for sealing the clearance and some
advantages thereby obtained. The present results
however, suggest that this form of balance does not
merit general application at the present time though
further development might render it very useful for
wings either with or without external-airfoil flaps.
The data obtained for the Frise aileron clearly illus¬
trate its action. As the aileron is deflected upward the
nose drops into the flow below the wing, and the
aileron “digs in,” giving a mild degree of overbalance.
As the nose becomes well extended, the upper surface
of the aileron is vented to the lower; the resulting flow
between the lower and upper surfaces markedly
reduced the effectiveness of the ailerons. Simultane¬
ously, the drag is increased by the disturbance to the
flow, which would produce a favorable yawing moment
such as has generally been observed in the use of Frise
ailerons. In spite of the favorable effect on yawing
moment, the Frise ailerons do not appear to be of
appreciable interest in the present connection on account
of their effect in reducing the maximum available
rolling moment and in having a tendency to over¬
balance in the initial stages of deflection.
Another method of reducing stick forces involves the
use of a differential linkage for aileron operation. (See
references 2 and 8.) The differential linkage interacts
with any tendency of the ailerons to float up from
neutral to produce a reduction in the stability of the
complete aileron system. In the tests reported in
reference 2 certain cases were found where the stability
became negative, i. e., the system was actually over¬
balanced. In this case the action is readily visualized:
The downgoing aileron reaches its maximum travel,
with the drive crank at dead center, before the upgoing
aileron has reached its natural upfloating angle. Thus,
the upgoing aileron is trying to deflect itself still farther
when the downgoing aileron can no longer exert a
restoring moment; the aerodynamic forces thus tend
to move the stick away from its neutral position.
When the upfloating angle of the ailerons is known, a
differential can be selected that will interact with the
upfloating tendency to produce a lesser reduction of
stability than that previously described. The stick
forces are thus reduced without producing overbalance
by a proper coordination of the differential linkage
with the aileron floating angle and the slope of the
curve of hinge moment with deflection.
Jones and Nerken (reference 8) have investigated
the properties of differential linkages and give formulas
and charts for the proper coordination of the important
factors. They have further suggested, in the case of
ailerons having a large variation of floating angle with
angle of attack, the use of a tab mounted on each
aileron to bias the aileron floating angle to a desirable
value. In the case of the present type of aileron, this
suggestion appears to be especially useful, since other
considerations militate against complete freedom of
WIND-TUNNEL INVESTIGATION OF WINGS WITH AILERONS AND EXTERNAL-AIRFOIL FLAPS 581
the designer in selecting a differential linkage suited
purely to the aileron characteristics. As the floating
angle of these ailerons varies with angle of attack and
flap angle, it would be desirable to have the differential
vary accordingly. This arrangement would not be
feasible, and the tab is therefore used to provide the
desired floating angle and thus avoid the necessity for
a varying differential. The desirability of preventing
the trailing edge of the downgoing aileron from passing
the leading edge of the flap indicates a linkage that
would reach dead center at a small downward aileron
deflection. This result, in turn, indicates that the
upgoing aileron deflection will not be large when the
downgoing aileron reaches dead center and that large
upfloating angles (over 20°, for example) will tend to
produce overbalance.
It is evident from the data for the standard model
(figs. 1G to 24) and from the foregoing discussion that
the ailerons operated by a differential linkage (which
apparently is vital to their successful application)
would be abnormally heavy in high-speed flight and
might become overbalanced in low-speed flight with the
flap down. The data of figure 31 show, however, that
throughout the normal-flight range the size of tab
tested is capable of bringing the aileron upfloating angle
within the desired range (15° to 20°).
It should be noted that in this application both tabs
are deflected the same amount in the same direction
and the tab deflection (with respect to the aileron chord
line) remains constant for a given setting of the flap
regardless of aileron deflection. It is apparent that
this is a highly unconventional application of a tab— ^
the tab merely serves to bias the aileron floating angle
and is not used to produce a moment about the aileron
hinge opposing the aileron hinge moment, which is the
normal use of tabs. The method presented in refer¬
ence 8, together with the data of figure 31, provides a
means of designing a lateral-control system having low
stick forces and using the ailerons with the external-
airfoil flap in the high-speed and liigh-lift settings.
In the intermediate range of flap settings (lor which
hinge moments were measured only on the tabbed
aileron) an additional difficulty in connection with the
use of the present ailerons became apparent. The
data for the tabbed aileron with the flap deflected 10
(fig. 30 (c)) show that “hysteresis” appears in the
variation of aileron hinge moment with deflection.
This effect is attributed to the phenomenon of flap
stalling: As the aileron moves away from the flap, the
flow leaves the flap upper surface, relieving the aileron
hinge moment and then, as the aileron returns, the flow
is restored at a different deflection, producing the
observed hysteresis. The appearance ol the phenome¬
non with the tab neutral indicates that it would appear
equally on an un tabbed aileron although no tests weie
made of the untabbed ailerons with the hap in the intei-
mediate angle range. The data in figure 30 (c) for the
tab 0°, flap 10° down, indicate the range in which the
hysteresis appears to be near 15° up aileron deflection,
corresponding approximately to the aileron deflection
at which the sharp rise of rolling moment took place
(see fig. 18 (a), 5/ = 10°) in the tests of the standard
model. It is anticipated that this discontinuous action,
which might affect the rolling moment as well as the
stick force, would be very disconcerting to a pilot.
Although no further investigation was undertaken at
the time, it is possible that scale effects and the use of
a gradually stalling airfoil section for the flap might
tend to smooth out the discontinuity.
Certain immediate possibilities of overcoming the
difficulty may deserve mention. Use of the flap in
only the high-speed and maximum-lift settings with
a rapid change between them should permit the pilot
to avoid the range in which the hysteresis appears.
On very large airplanes in which the ailerons might be
power-driven and no aileron “feel” would reach the
pilot’s control, the aileron deflection would be sus¬
ceptible of accurate control without reference to the
stick forces. In this case, the hysteresis should not be
an appreciable disadvantage. This consideration also
suggests the use of an irreversible operating mechanism
for smaller airplanes, in which case the hysteresis might
be noticeable but should not tend to produce disconcert¬
ing movements of the airplane. Such an arrangement
should also tend to suppress aileron flutter, some tendency
to which was noticed in the tests when the aileron trailing
edge closely approached the flap leading edge.
CONCLUDING REMARKS
The data obtained in the present investigation indi¬
cate the following generalizations. An N. A. C. A.
23012 airfoil equipped with a 0.30 cw N. A. C. A. 23012
external-airfoil flap, like the similar combination with
a 0.20 cw flap, gave characteristics favorable to speed
range, to low power requirements in flight at high lift
coefficients, and to low flap-operating moments. I he
aerodynamic qualities of the combination make it
especially suitable for the application of ailerons
mounted on the trailing edge of the main airfoil,
providing a means of lateral control consistent with
the use of full-span external-airfoil flaps. This possibil¬
ity gives the external-airfoil flap an advantage in
speed-range capabilities over such flaps as the ordinary
and simple split types, w hich, when used with ordinary
ailerons, sacrifice part of their span for the provision
of lateral control.
The results from the nanw-chord long-span ailerons
here investigated indicated large rolling-moment co¬
efficients at lift coefficients corresponding to flight
conditions ranging from high speed to minimum speed.
The adverse yawing moments tended to be somewhat
less than those of ordinary ailerons giving the same
rolling moment. In general, they agree with Munk’s
formula for induced yawing moment at low values of
the rolling moment; as the rolling moment is increased,
they tend to become more favorable.
582
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Three definite difficulties to be anticipated in the
application of the combination of ailerons with external-
airfoil flaps are indicated. First, the ailerons are
relatively weak in producing rolling moment when the
wing is near the stalling angle of attack with the flap
in the high-speed setting. Second, the variation of
aileron hinge moment with angle of attack and flap
setting is such as to cause relatively large stick forces
in the high-speed range and to cause overbalance near
the stall with the flap in the high-lift setting. Third,
a discontinuity of hinge moment, and possibly of
rolling moment, occurs as the ailerons are deflected
with the flap in the intermediate-angle range. The
investigation indicated that nose balances and Frise
balances were ineffective in reducing the stick forces
required for a given control effectiveness in the high¬
speed condition. The use of a tab to bias the aileron
floating angle together with a differential aileron motion
provides a means of obtaining reduced stick forces in
the high-speed condition and of avoiding overbalance
in the higli-lift condition. Further research and
application to experimental designs should serve to
determine the importance of the anticipated difficulties
in actual use and should establish more clearly the
merit of the combination of ailerons and external-airfoil
flaps for airplane-design application.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics
Langley Field, Va., March 12, 1937.
APPENDIX
effect of jet boundaries and aspect ratio on
MEASURED ROLLING- AND YAWING-MOMENT CO¬
EFFICIENTS
As previously noted in the text, the use of standard
airfoils for tests of airfoils with external-airfoil flaps
in the 7- by 10-foot tunnel led to the use of geometric
aspect ratios of 5.0 and 4.61 for the combinations tested
in the present investigation. Although main airfoils
of larger aspect ratio could have been constructed,
considerations of model deflection, comparison of plain-
airfoil test data, and economy dictated the method
adopted. It was recognized, however, that the varia¬
tion of lift-curve slope and of induced drag with aspect
ratio would result in measured rolling- and yawing-
moment coefficients not directly comparable with data
from tests of airfoils of aspect ratio 6. Corrections
based on present knowledge of induced-flow phenomena
were therefore devised to permit such comparisons.
CORRECTION OF ROLLING-MOMENT COEFFICIENT
Pearson (reference 9) has carried out a general
solution of the lift distribution for wings with ailerons,
from which he obtained an equation for the rolling
moment
L=2qb2(kb)F2
where § is the dynamic pressure.
b, the wing span.
5, the aileron deflection.
and F2, a factor (presented in chart form) depending
on plan form, aspect ratio, and ratio of total
aileron span to total wing span.
The factor k is a section characteristic for an airfoil
with a flap or aileron and is equal to the change of
angle of attack equivalent to a given aileron deflection
divided by the given aileron deflection. This value
may also be expressed as the ratio of the section lift-
curve slopes
do 1 IdCj
db I da0
(The lower-case letters repre¬
sent airfoil section characteristics; thus cx is the section
lift coefficient, CL the wing lift coefficient, and Cx the
wing rolling-moment coefficient.) The equation thus
represents the total rolling moment as the rolling
moment to be expected from the change of airfoil sec¬
tion when the aileron is deflected, reduced by a factor
to allow for the induced rolling moment resulting from
wing plan-form effect.
Computing the rolling-moment coefficient from Pear¬
son’s formula, the equation
Cl=2A(k8)F2
is obtained, where A is the aspect ratio. By the use of
this relation and the designation of the values appro¬
priate to two different aspect ratios as subscript Ax
and subscript A2) it is possible to obtain a factor for
the rolling-moment coefficient measured for a wing of
A=AX to express the rolling-moment coefficient for a
wing of A~A2 under otherwise identical conditions,
as follows:
X
(kb)
XW)
A1
But it has been pointed out that k depends only on
the airfoil section characteristics and therefore does not
change with A. Thus, at a given value of aileron
deflection
and
(kb)Al=(kb)A2
AJd
CA2-Cia1xa1F
‘■Ac
Factors for the particular values of A in question
were calculated from the formula using values of F2
obtained from the reference and cross-plotted against
A. The final correction formulas used were as follows:
for the airfoil with the 0.20 cw flap and 0.12 cw ailerons
C,4=6=1.08(7,
and for the airfoil with the 0.30 cw flap and 0.13 c,r
ailerons
G,=,= 1.12 C,t
The subscript m signifies the value measured in the
wind tunnel.
The error produced by the jet boundaries in the
measured rolling-moment coefficient has been estimated
from the formula of reference 10; it amounts to less
than 1 percent of the measured coefficient and is con¬
servative for prediction of flight rolling moments.
This correction is consequently considered negligible.
CORRECTION OF YAWING-MOMENT COEFFICIENT
Munk (reference 11) expressed the induced yawing-
moment coefficient of a wing with ailerons having equal
up-and-down deflections as
on '
C„i= —~rXCL
7r/i
(It should be noted that there is a disagreement of sign
with the original published formula; the sign has been
changed to agree with the standard N. A. C. A. sign
convention for moments.) This formula may be used
to compute the change of Cni resulting from a given
change of aspect ratio; this computation is directly
583
584
REPORT NO. 603— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
analogous to the well-known one for the change of
induced drag coefficient with aspect ratio.
The jet-boundary effect on the induced yawing-
moment coefficient results from the change in local wind
direction (ait, the standard angle-of-attack correction)
with respect to the model resulting from the limited
extent of the air stream. Through this effect the
rolling-moment vector is rotated through the angle
<xit, resulting in a component in the yawing-moment
direction
@nit—<*itXCi
The jet-boundary correction factor for the 7- by 10-
foot tunnel is equal to 0.1 Go in the formula ait -KffL.
(See reference 2.)
The total induced yawing-moment coefficient of a
model in the 7- by 10-foot tunnel may then be ex¬
pressed as
C
, _ [SO,
" ~ It A.
xcL
o.i6s|xo.xn]
or
* lmXt L(7rAm Td-lOo-^)
The profile yawing-moment coefficient is then
( 3 , „
Cn* — Cnm + CimX CL( ~ f 0 . 1 65 ^ )
For xl=6
but
where
cni=-clA=5xcLxi
CiA^=fiCtm
67T
„ a2fu
j8= -42
4 f1
the rolling-moment coefficient correction factor pre¬
viously developed. Thus for A = 6
3/3
0n*A- 6~ ClmXCLX^ r
and since
C —C A-C
^".4=6 n0~ "iA=Q
,-S . 3 3/3'
=6 — Cnm + Cim X C /.( 0.165^
irAm Gtt.
Inserting appropriate values the following correction
formulas were derived. For the airfoil with the 0.20
cw flap and 0.12 cw ailerons
CnA^=cnm+ommxCiinxcL
For the airfoil with the 0.30 cw flap and 0.13 cw ailerons
CnA_ 6= cnm + 0.04 1 8 X Clm x CL
In conclusion it should be noted that the foregoing
corrections, which have been applied to all the rolling-
and yawing-moment coefficients presented in this report,
include the standard assumptions of induced flow and
jet-boundary correction theory. They should therefore
be regarded as first approximations rather than as
rigorous expressions of the corrections that should be
applied.
REFERENCES
1. Soule, H. A., and McAvoy, W. H.: Flight Investigation of
Lateral Control Devices for Use with Full-Span Flaps.
T. R. No. 517, N. A. C. A., 1935.
2. Platt, Robert C.: Aerodynamic Characteristics of Wings
with Cambered External-Airfoil Flaps, Including Lateral
Control with a Full-Span Flap. T. R. No. 541, N. A. C. A.,
1935.
3. Shortal, Joseph A.: Wind-Tunnel and Flight Tests of Slot-
Lip Ailerons. T. R. No. 602, N. A. C. A., 1937.
4. Platt, Robert C., and Abbott, Ira H.: Aerodynamic Charac¬
teristics of N. A. C. A. 23012 and 23021 Airfoils with 20-
Percent-Chord External-Airfoil Flaps of N. A. C. A.
23012 Section. T. R. No. 573, N. A. C. A., 1936.
5. Harris, Thomas A.: The 7 by 10 Foot Wind Tunnel of the
National Advisory Committee for Aeronautics. T. R.
No. 412, N. A. C. A., 1931.
6. Platt, Robert C.: Turbulence Factors of N. A. C. A. Wind
Tunnels as Determined by Sphere Tests. T. R. No. 558,
N. A. C. A., 1936.
7. Jacobs, Eastman N., and Sherman, Albert.: Airfoil Section
Characteristics as Affected by Variations of the Reynolds
Number. T. R. No. 586, N. A. C. A., 1937.
8. Jones, Robert T., and Nerken, Albert I.: The Reduction of
Aileron Operating Force by Differential Linkage. T. N.
No. 586, N. A. C. A., 1936.
9. Pearson, H. A.: Theoretical Span Loading and Moments
of Tapered Wings Produced by Aileron Deflection.
T. N. No. 589, N. A. C. A., 1937.
10. Biot, M.: Korrecktur fur das Quermoment von Tragflugeln
bei Untersuchungen im Windkanal mit Kreisquerschnitt.
Z. F. M., 24. Jahrgang, Nr. 15, 14. August 1933, S. 410-411.
11. Munk, Max M.: A New Relation between the Induced
Yawing Moment and the Rolling Moment of an Airfoil
in Straight Motion. T. R. No. 197, N. A. C. A., 1924. .
REPORT No. 604
PRESSURE-DISTRIBUTION MEASUREMENTS AT LARGE ANGLES OF PITCH ON FINS
OF DIFFERENT SPAN-CHORD RATIO ON A 1, 40-SCALE MODEL OF THE U. S.
AIRSHIP “AKRON”
By James G. McHugh
SUMMARY
Pressure-distribution measurements on a 'jo-scale model
of the U. S. airship “Akron” were conducted in the
N. A. C. A. 20-foot mind tunnel.
The measurements were made on the starboard jin oj
each of jour sets oj horizontal tail surfaces , all oj approxi¬
mately the same area but differing in span-chord ratio, for
jive angles of pitch varying from 11.6° to 34°, for four
elevator angles, and at air speeds ranging from 56 to 77
miles per hour. Pressures were also measured at 13
stations along the rear half oj the port side of the hull at one
elevator setting for the same five angles of pitch and at an
air speed oj approximately 91 miles per hour.
The maximum pressures recorded on the leading edge oj
the jins, for pitch angles up to 20°, were approximately the
same for all jins tested regardless oj span-chord ratio. At
angles of pitch above 20° the maximum jin pressures in¬
creased with decreasing span-chord ratio. A negative
pressure oj 13 times the dynamic pressure oj the undis¬
turbed air stream was measured on the jin of lowest span-
chord ratio at a pitch angle oj 34°. The pitching moment
contributed by the after portion of the hull increased with
pitch until, at the maximum angles tested, it was approxi¬
mately equal to the moment contributed by the jins. The
normal force on the jin and the moment oj forces about the
fin root were determined. The results indicate that,
ignoring the effect on drag, it would be advantageous f rom
structural considerations to use a fin of lower span-chord
ratio than that used on the “Akron.”
INTRODUCTION
The task of obtaining load measurements on a full-
scale airship in free flight is difficult and, consequently,
only a small amount of reliable flight data on airship
loads is available. Many wind-tunnel tests of scale
models have been made but, since the scale of an airship
model for wind-tunnel tests must of necessity be very
small, the results obtained are in some cases of ques¬
tionable value.
The results of previous pressure-distribution measure¬
ments on the hull and fins of a relatively large (bo-
scale) model of the U. S. airship Akron fitted with
fins of the type used on the full-scale airship and tested
at angles of pitch from 0° to 18° are presented in
reference 1. Although such a range of angles of pitch
would not be exceeded under normal operating condi¬
tions, it appears possible that much larger angles of
pitch might be encountered in severe gusts. No
Figure. 1— The Bo-scale model of the Akron mounted in the 20-foot wind tunnel.
information concerning the magnitude of fin loads and
pressures encountered at larger pitch angles has been
available, but the results of reference 1 indicated that a
high concentration of load near the tip would be
obtained.
At the request of the Bureau of Aeronautics, Navy
Department, the investigation herein reported was
made to obtain information concerning loads at high
angles of pitch and to determine good fin proportions.
The bo-scale airship model used in the investigation
reported in reference 1 was tested through a range of
pitch angles from 12° to 34° with the object of deter¬
mining: (1) The effect of span-chord ratio on the aero¬
dynamic forces acting on the fins of airships; (2) the
effect of slots between the fin and the hull on pressure
distribution over the fin; and (3) the effect of changes
585
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
586
in fin span-cliord ratio on pressure distribution over the
hull.
It is believed that the relatively large scale of the
model here used, the high pitch angles included, and the
fact that simultaneous measurements of pressure were
made on both surfaces of an entire tin greatly enhance
the value of these results.
APPARATUS AND TESTS
The airship model used in these tests is described in
detail in reference 1. The method of mounting it in
the wind tunnel is shown in figure 1 and is essentially
ends of the copper tubes in such manner that they pro¬
truded through the inboard edge, gluing the two halves
of the fin together. The ends of the copper tubing
projecting through the fin surfaces were ground flush,
thereby forming a smooth pressure orifice.
Four sets of horizontal tail surfaces, designated
Mark II fin, fin 3, fin 3-A, and fin 4 (figs. 3 to 7), all of
approximately the same area but of different span-
chord ratios, were tested. The Mark II fin was the
type used on the Akron. Fins 3 and 4 were basically
similar but their span-chord ratios were changed bv
cutting areas off the inboard edge and adding an equiva-
(a) Typical sections in direction B-B et
stations 14 and 16 showing radial loca¬
tions of orifices in hull. Orifice mark¬
ed X at station 16 only.
(b) Typical sections in direction B-B at
stations 15 and 17 showing radial loca¬
tions of orifices in hull.
(c) Typical sections in direction B-B at
stations 18, 19, 20, and 21 showing radi¬
al locations of orifices in hull. Two
orifices marked X at stations 18, 20,
and 21 only. Three orifices marked
Y at station 18 only.
(d) Typical sections in direction B-B at
stations 22, 23, 24 , 25, and 26 showing
radial locations of orifices in hull.
Two orifices marked X at stations 22
and 23 only.
Figure 2.— Locations of orifices for the pressure measurement on a Mo-scale model of the Akron.
as described in reference 2, with the exception that for
these tests the model was suspended feet above the
center line of the tunnel. The tests were made in the
N. A. C. A. 20-foot wind tunnel (reference 3).
In order to determine the effect of different fins on
the pressure distribution over the rear part of the hull,
162 pressure orifices distributed among 13 stations on
the port side of the model were used. The location of
the stations and the distribution of the orifices around
the hull are shown in figure 2. Principal dimensions of
the hull and fins are given in table I.
The fins were of laminated wood. Pressure orifices
were installed by splitting the fins at their plane of
symmetry, drilling small holes at the point where
pressures were to be measured, inserting short lengths
of %2-incli (inside diameter) copper tubing therein
until they protruded a minute distance beyond the
outer surface of the fin, and then, after alining the free
lent area at the forward part of the fin in such manner
that the position of the elevator axis, the edge shape,
and the radius of the tip plan form remained constant for
all fins. Fin 3-A was similar to fin 3 except for a
change in the plan form of the forward part of the fin.
An additional type of fin wTas obtained by altering the
Mark II fin so as to form a slot between the inboard
edge of the fin and the hull of the ship. Two slot widths
(% inch and % inch) were used. The longitudinal
location of the slot on the fin, which corresponded to a
location between frame 0 and frame 17. 5 of the full-
scale airship, is shown by dotted lines in figure 3.
Figure 8 shows the fin with slot mounted for tests.
Pressure orifices were installed in pairs on fins
Mark II, 3, and 4. One orifice of each pair opened on
the upper surface and the other, on the lower surface
of the fin. In the case of fin 3-A, pressure orifices
were installed only on the upper surface. On all the
587
PRESSURE-DISTRIBUTION
MEASUREMENTS ON FINS OF U. S. AIRSHIP “AKRON”
fins the pressure orifices were located to facilitate
fairing of the pressure diagram; the locations are
shown in figures 3 to 6.
Two multiple- tube photographic recording manom¬
eters, each composed of a circular bank of 100 glass
tubes, were mounted on pivots inside the model and
were free to swing about a horizontal axis at right
angles to the longitudinal axis of the ship, thus allowing
the manometers to remain level for any angle of pitch.
The manometers were electrically operated by remote
control from the test chamber floor. Photostat paper
was automatically drawn around the outer circum¬
ference of the bank of tubes, and exposure was made
by flashing a lamp at the center of the bank of tubes.
Two simultaneous records, one for each manometer,
gave for one pitch angle a complete diagram of the
pressure distribution over both surfaces of a fin. Two
PRESSURE MEASUREMENTS ON FINS
[No pressure-distribution measurements were taken on the elevators]
Fin
F. levator angle
(deg.)
Nominal
pitch angle
(deg.)
Approxi¬
mate
velocity
(m. p. fa.)
Mark II > . .
0, 10, 20
12, 18, 24, 30, 36
69
Mark II _
20
18, 30
77
Mark 1 1, 9£-inch slot - - .
20
12, 18, 24, 30
77
Mark II, ?4-inch slot--
20
12, 18, 24.30
77
:i -
-15. 0, 10,20
12, 18, 24, 30, 36
74
3-A _
-15,0, 10,20
12, 18, 24, 30, 36
56
4 _ _
-15,0, 10, 20
12, 18, 24, 30, 36
56
1 With counterbalances.
ACCURACY
The sources of error that affect the pressure-dis¬
tribution measurements are:
(1) Errors in measurements of the manometer de¬
flection.
Elevator AB C D EFGH.I Elation.
Figure 3. — Dimensions and orifice locations. Mark II fin; Mo-scale model of the Akron; slot locations are shown in dotted lines; all dimensions given in inches.
sets of pressure measurements were made at each pitch
angle and an average of the two records was used in
plotting the pressure diagram. In order to provide a
reference line on the pressure records, six of the glass
tubes spaced equidistantly around the manometer
were connected to the reference pressure, which for
these tests was the static pressure in the test chamber.
With the exception of the Mark II fin, which was
tested with and without elevator counterbalances, all
fins were tested without counterbalances. In all cases
the control car was installed on the hull of the model.
All pressure-distribution measurements were made on
the starboard fin and for all fins tested the vertical fins
were of the Mark II type with rudder neutral and the
airship at 0° yaw.
The tests herein reported are listed in the following
table:
PRESSURE MEASUREMENTS ON HULL
Fin
Elevator
angle
(deg.)
Nominal
pitch angle
(deg.)
Approxi¬
mate
velocity
(m. p. h.)
Mark II _
20
12, 18, 24. 30, 36
91
3 _
20
12, 18,24. 30. 36
91
4 _ _ _ _
20
12, 18, 24, 30, 36
91
(2) Oscillation of the manometers.
(3) Fluctuation in velocity and direction of the air
stream.
(4) Shrinkage of the photostat paper.
The error due to (1) is considered to be small. The
errors due to (1), (2), and (3) are of the order of ±2
percent for low pitch angles. At high pitch angles
the error is considerably greater, as shown by compari¬
son of check tests. The errors from (4) were found, in
general, to be less than 1 percent for all cases.
RESULTS
The great amount of data derived from these tests
makes it impractical to present them in their entirety.
Consequently, only the portion required for the final
analysis of the results is presented.
Final results of the pressure measurements are pre¬
sented in terms of dynamic pressure q of the air stream.
All pressures are referred to the test-chamber pressure,
and no correction has been made for the difference
between the static pressure in the air stream and the
reference pressure. Application of this correction
would have no effect on the integrated values of normal
force on the fins. Pressures were measured on both the
upper and lower surfaces of the fins (except for fin
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
t i&i re 5. Dimensions and orifice locations. Fin 3- A ; Do-scale model of the Akron; all dimensions given in inches.
589
PRESSURE-DISTRIBUTION
MEASUREMENTS ON FINS OF U. S.
AIRSHIP “AKRON”
Mark II fin
Figure 7.— Thn fins on which pressure-distribution measurements were made.
590
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 8.— Mark II fin
3-A) and the effect of the static-pressure correction
would be to shift the position of the pressure diagram
without causing any change in the included area. The
influence of the static-pressure correction on the point
pressures would have been small. A static-pressure
survey of the tunnel, made in the absence of the model,
showed that the maximum difference between the
static pressure in the test chamber and the static
Figure 9. — Variation of air-stream angle in region of starboard fin with measured
pitch of model.
pressure in the region of the air stream through which
pressure measurements were made was of the order of
0.005 q.
A preliminary comparison of the results of these
tests with those reported in reference 1 showed poor
agreement. Since the only essential difference in the
set-ups was the location of the model above the center
line of the air stream, 3K feet for the present tests and
pith %-inch slot, mounted for tests.
I foot for the tests reported in reference 1, the lack of
agreement was thought to be due to the fact that the
flow characteristics of the air stream were different at
the two model locations. A stream-angle survey of
the air stream confirmed this belief. Figure 9 shows
the variation with pitch of the model of the stream
angles at the tail of the model. The results have been
corrected to take account of the pitch angle in the air
stream. No correction has been made to take account
of the yaw angle in the air stream.
It is desired to call attention at this time to the fact
that the pressures on the upper surfaces of the fins
were much greater than had been anticipated. Con¬
sequently, at high pitch angles, for the first of the tests
made, some of the negative pressures near the tip of the
fin were so great that the liquid in the manometer tubes
rose above the height of the photostat paper on which
the magnitude of the pressures was to be recorded, and
consequently no determination could be made of the
maximum pressures. In cases where only a few
pressures were indeterminate, judgment was used in
fairing in the pressure diagrams. In cases where
several pressures were indeterminate, the tests in
question were repeated at a lower air speed. Even¬
tually all efforts to obtain tests at a high air speed were
abandoned and, during the latter part of the program,
tests were made at an air speed low enough to insure
that all pressures obtained would be recorded on the
photostat paper.
In certain cases at high pitch angles where check
readings were taken at intervals of approximately 1
591
PRESSURE-DISTRIBUTION
MEASUREMENTS ON FINS OF U. S. AIRSHIP ' AKRON”
minute, a great difference in pressures was recorded.
This difference indicated that at extremely high pitch
angles (0=22° to 34°) the forces on the model were
fluctuating rapidly, probably owing to instability of
the air flow. At times the model was observed to
undergo violent spasmodic quivers. This motion was
probably due in part to the fluctuation of aerodynamic
forces on the tail of the model
Definitions of the terms used in this report follow:
6, pitch angle.
oe, elevator angle.
a>, hull orifice location, measured from keel in
degrees.
/r normal force on fins
N’ ~ qS~
<7, dynamic pressure (1/2 pi72),
p, mass density of the air.
V, air speed.
S, area of fin.
, , . (maximum span of fin) 2
Fin span-chord ratio, - j t- —
1 ’ area ol fin
observed point pressure.
PRESSURE-DISTRIBUTION MEASUREMENTS ON THE FINS
The magnitude of the maximum pressures and the
manner in which the pressure varies over all the (ins
are illustrated in figures 10 to 15. Large-scale pressure
plots of p/q against fin width were made and the
pressure diagrams thus formed were graphically inte¬
grated to determine the normal force per unit length at
each station along the fin. Similarly, the spanwise
location of the center of pressure at each longitudinal
station on the fin was determined. The values of the
normal force per unit length of fin and the moment of
that force about the fin root are given in tables II to
VII for each station on the fin at which pressure-dis¬
tribution measurements were made. In order to show
the variation of normal force on the fin, there are
included, for the various fins tested, typical plots of
normal force per unit length against length ol fin for
the condition of 5C=20° (figs. 16 to 22). Also included,
for the same fins and elevator positions, are charts
showing the variation along the fin chord of the moment
of the forces on the fin about the fin root (figs. 23 to 27).
P,
592
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figl-ke 12. Pressure distribution on horizontal fin of the ‘io-scale model of the Akron at various pitch angles. Mark II fin (counterbalances removed); ?i-inch
slot; 5e=20°.
Figure 13.— Pressure distribution on horizontal fin of the ‘io-scale model of the Akron at various pitch angles. Fin 3; se=20°.
Figure 14.— Pressure distribution on upper surface of horizontal fin of the ‘io-scale model of the Akron at various pitch angles. Fin 3-A ; 5, =20°.
593
PRESSURE-DISTRIBUTION
MEASUREMENTS ON FINS OF U. S. AIRSHIP “AKRON”
Curves showing the variation of normal-force coeffi¬
cient with pitch angle for various elevator settings are
given for the three types of fin tested in figures 28, 29,
and 30. Figure 28 also compares the results of these
tests of the Mark II fin with those reported in refer¬
ence 1.
The chordwise location of the center of pressure on
the fin was determined from the plots of normal force
per unit length against fin length. Values of (normal
force)/# and the location of the center of pressure of
fin forces are presented in table VIII.
the projected distance of that point on the horizontal
radius of the section. The area of the pressure diagram
thus formed gave the transverse force per unit length
at the particular station in question.
The integrated values of / from station 14 aft were
plotted against distance from the how of the model.
The effect at six angles of pitch of different fins on the
transverse force on the hull is shown in figures 34, 35,
and 36. There are tabulated in table IX: (1) the total
transverse force over the rear portion of the hull,
which was obtained from graphical integration of the
Figures 31, 32, and 33 show the variation with pitch
angle of the maximum point pressure at each station
at which pressure-distribution measurements were
made.
PRESSURE-DISTRIBUTION MEASUREMENTS ON THE HULL
The value of the transverse force per unit length at
any station on the hull is given by the expression
dF C2*
where F is the total transverse force per unit length.
x, the distance from the nose of the hull meas¬
ured along the longitudinal axis,
r, the radius of the hull.
p, the pressure on the section at a point whose
angular distance from the keel is co.
A graphical solution of this equation was obtained by
plotting the pressure at each point on the hull against
areas under the curves shown in figures 34, 35, and 36;
(2) the moment about the center of buoyancy of the
transverse forces on the rear portion of the hull; (3)
the normal force on the various fins that were used on
the model when the hull pressures were measured;
(4) the moment of the fin force about the center
of buoyancy; and (5) the total moment of the
combined hull and fin forces about the center of
buoyancy.
Figure 37 shows the effects of the different fins on
the moment, about the center of buoyancy, of the
transverse aerodynamic forces acting on the fins and
on the rear portion of the hull.
In order to facilitate the application of model test
results to a full-scale airship, there is included in table
X the location of the structural frames on the Akron
and their corresponding location on the ho-scale
model.
594
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 16— Normal force per unit length on fin of the Mo-scale model of the Akron.
Mark II fin (with counterbalances); 5„=20°.
Figure 17— Normal force per unit length on fin of the Mo-scale model of the Akron.
Mark II fin (counterbalances removed); 8C=20°.
Figure 18— Normal force per unit length on fin of the Mo-scale model of the Akron.
Mark II fin (counterbalances removed); 9fc-inch slot; <S« = 20°.
Figure 19. — Normal force per unit length on fin of the Mo-scale model of the
Akron. Mark II fin (counterbalances removed); M-inch slot; 8e=20°.
595
PRESSURE-DISTRIBUTION MEASUREMENTS ON FINS OF U. S.
AIRSHIP “AKRON”
Figure 20.— Normal force per unit length on fin of the Ro-scale model of the
Akron. Fin 3; 5„=20°.
Figure 22. — Comparison of normal force per unit length contributed by upper
surfaces of fin 3 and fin 3-A of the Ro-scale model of the Akron; 5«=20°.
Note.— Pressures on lower surface not measured. Reference pressure is static
pressure in test chamber.
Figure 24. — Moment of forces on fin about fin root of the Ro-scale model of the
Akron. Mark II fin (counterbalances removed); 36-inch slot; b = 20°.
Figure 21. — Normal force per unit length on fin of the Ro-scale model of the
Akron. Fin 4; 5,=20°.
Figure 23. -Moment of forces on fin about fin root of the Bo-scale model of the
Akron. Mark II fin (with counterbalances); S«=20°.
Figure 25.— Moment of forces on fin about fin root of the Bo-scale model of the Akron.
Mark II fin (counterbalances removed); 34-inch slot; 8,=20°.
Normal- force coefffcienf,
596
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 26.— Moment of forces on fin about fin root of the >4o-scale model of the Figure 27.— Moment of forces on fin about fin root of the J4o-scale model of the
Akron. Fin 3; 5„=20°. Akron. Fin 4; «(=20°.
Figure 28. — Normal-force coefficients for horizontal fin surfaces on the
Ro-scale model of the Akron. Mark II fin (with counterbalances).
Figure 29.— Normal-force coefficients for
horizontal fin surfaces on the Uo-scale
model of the Akron. Fin 3.
Figure 30. — Normal-force coefficients for
horizontal fin surfaces on the ‘io-scale
model of the Akron. Fin 4.
597
PRESSURE-DISTRIBUTION MEASUREMENTS ON FINS OF U. S.
AIRSHIP “AKRON”
598
REPORT No. (504— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
DISCUSSION
The results of these tests confirm the conclusions of
reference 1 concerning the presence of very large pres¬
sures near the leading edge of airship fins. Figures 31,
32, and 33 show that the maximum pressure recorded
(p/q= — 13.0) was obtained at the tip section of fin 4,
at the 34° pitch angle. At the same pitch angle the
maximum value of p/q obtained on fin 3 was —9.9, and
the maximum for the Mark II fin was —6.4. Inspection
of figures 31, 32, and 33 also reveals that, although the
maximum values of p/q continued to increase on fin 4
6 , deg.
12 16 20 24 28 32
Figure 37.— Comparison of pitching moments acting on the >4o-scale model of the
Akron when fitted with different horizontal fins; 5,-20°. (Forces on elevators
neglected.)
up to the maximum angle at which tests were run, the
values of p/q obtained on fin 3 reached their maximum
value of —11.1 at 0=29° and on the Mark II fin the
maximum value (—9.2) occurred at 0=28°. It is of
further interest to note that, although at the highest
angles of pitch at which tests were made the greatest
pressure recorded was that obtained on fin 4, the
maximum pressures obtained for all pitch angles below
20° were approximately the same for all fins.
Attention is called to the fact that the pressures cited
were obtained from faired curves and that, since the
peak pressure would not necessarily occur directly at
the points at which the orifices were located and since
the slope of the pressure diagram changes from a very
large positive value to a very large negative value in
the vicinity of the maximum pressure, it is conceivable
that greater pressures occurred than those given.
The effect of slots between the hull and fins on the
location of the span wise center of pressure was deter¬
mined from large-scale pressure diagrams of the type
showm in figures 10, 11, and 12. It was observed that
neither the %-inch slot nor the /4-inch slot had much
effect at pitch angles below 17°. At higher pitch angles
the effect of either slot wTas to increase the negative
pressure at the fin root, thus shifting the center of
pressure inboard. The shift was small, however, and
wras greater for the %-inch slot than for the %-inch slot.
The maximum movement of center of pressure observed
occurred on station D and at 0=30° where the movement
amounted to about 4 percent of the span of the fin at
that station. A comparison of figures 18 and 19 with
figure 17 in conjunction with table VIII reveals that at
the 17° pitch angle, except for an increase in normal
force in the vicinity of the elevator axis, neither slot had
an appreciable effect on the normal force or its chord-
wise distribution on the fin. At higher angles of pitch
large fluctuations in forces occurred and the precision
of the test results is not considered good enough to
draw definite conclusions concerning the effect of the
slots. The effect, however, is considered to be small.
Figures 16 to 22 show' that fins of low' span-chord
ratio have a more nearly uniform load distribution
along their chord than does the Mark II type of fin,
and therefore from structural considerations, provided
the effectiveness as shown later is equal, the low' span-
chord ratio is preferable.
The variation with span-chord ratio of the fin normal-
force coefficients can be determined from an inspection
of figures 28, 29, and 30. The coefficients for the Mark
II fin are, in general, greater than for either of the other
fins. At high angles of pitch the coefficients for the
Mark II fin begin to decrease with further increase in
angle of pitch. The shapes of the curves for the other
two fins are not so clearly defined because of erratic
results at large angles of pitch.
It is interesting to note from inspection of figures 28,
29, and 30 that the slope of the curves of CN against 0
decreases as the span-chord ratio of the fins decreases.
This decrease is in accordance with the principle that
the decrease in span-chord ratio decreases the effective
aspect ratio of the tail.
It has previously been pointed out in this report that
original comparison of these test results did not check
the results of reference 2 and that the discrepancy dis¬
appeared to a large extent when corrections were made
to take account of the air-stream-angle variation in the
wind tunnel. Figure 28, which shows values of Cy
obtained in these tests and corresponding values of Cy
from reference 1 plotted against corrected pitch angle
(fig. 9), compares the twro sets of data. It is to he
noted that agreement is, in general, satisfactory.
The data obtained in these tests indicate that the
plan form of the forward part of the fin is an important
item in fin design. Figure 22 show's a comparison ot
the forces acting on the upper surfaces of the tips of
fins 3 and 3-A. Pressures were not measured on the
lower surface of fin 3-A and it is therefore impossible
599
PRESS U RE-DISTRI B UTION
MEASUREMENTS OX FINS OF U. S. AIRSHIP “AKRON”
to compare the total forces on the two fins. It is be¬
lieved, however, that a comparison of the forces regis¬
tered on the upper surfaces shows the relative merits of
the two different plan forms. Inspection of figure 22
leads to the conclusion that the effect of modifying the
fin tip was to decrease the forces over the forward por¬
tion of the fin, presumably because of the decreased fin
area forward, and to increase the forces in the region
between the elevator axis and the fin tip, thus in effect
shifting the center of pressure toward the elevator axis.
The peaks of the pressure diagrams occur farther in¬
board on fin 3-A (fig. 14) than they do on fin 3 (fig. 13);
also, the magnitude of the pressures near the fin root is
greater on fin 3-A.
A comparison of the chordwise force distribution
curves shown in figure 16 with similar curves in figure
17 leads to the conclusion that for the condition of
i5e=20o the effect of the elevator counterbalances is
to decrease the normal force on the rear part of the fin.
The chief criterion in the selection of tail surfaces for
airships is the ability of the surfaces to give adequate
stability and control. In view of the fact that a large
proportion of the stabilizing force obtained with fins is
due to the influence of the fins on pressural forces on the
hull, it is at once evident that the measurements of forces
acting on the fins alone do not give sufficient infor¬
mation for the selection of the most efficient fin. The
magnitude of the pressural forces from station 14 aft
on the port half of the hull when fitted with the Mark II
fin and with fins 3 and 4 is shown in figures 34, 35, and
36, respectively.
The moment about the center of buoyancy of the
forces represented by the area under the curves shown
in figures 34, 35, and 36 is shown as a function of angle
of pitch in figure 37. It is believed that, since pressure-
distribution measurements were made on all of that
portion of the hull over which the fins appear appreci¬
ably to influence the hull forces, the curves of pitching
moment against angle of pitch (fig. 37) present a valid
comparison of the relative stability characteristics of
the airship when fitted with the various fins tested.
Attention is called to the fact that, since the pressure-
distribution measurements from which this chart is
derived were made at but one elevator deflection
(L=20°), a complete analysis is impossible. It is
believed, however, that the same relative effects as
here shown would obtain for other elevator deflections.
Inspection of figure 37 indicates that at extremely
high pitch angles (0=34°) the pitching moment about
the center of buoyancy due to pressural forces on the
rear half of the hull is approximately equal to the cor¬
responding moment due to the forces on the fins them¬
selves. From the curves in the lower part of figure 37
it is to be seen that, except at angles of pitch greater
than 26°, the stabilizing moment obtained when the
airship is fitted with the Mark II fin is very nearly
equal to the stabilizing moment obtained with fin 3.
39
At angles of pitch greater than 26° the Mark II fin is
somewhat superior. With the exception of a slight
superiority over fin 3 at extremely high pitch angles,
fin 4 is inferior to both of the other fins.
It is desired to point out that, although the narrow
fins appear to compare quite favorably with the Mark
II fins, the results here shown are not conclusive in that
they do not show the effect of the various fins on drag.
It is possible that, if the drag of the different fins could
be compared on the basis of either equal lift or equal
moment coefficients, the fins of low span-chord ratio
would show up to disadvantage.
CONCLUSIONS
1. At angles of pitch below about 20° the maximum
pressure measured was approximately the same for all
fins, regardless of span-chord ratio.
2. At angles of pitch above 20° the maximum fin
pressures increase with decreasing span-chord ratio, the
highest pressure recorded (j)/q~ — 13.0) being that
obtained on fin 4 at a pitch angle of 34°.
3. Slots between the hull and fins, of the type here
tested, had but little effect on either maximum fin
pressures or the position of the center of pressure of
fin forces.
4. The plan form of the forward portion of the fin
is a critical factor influencing the pressure distribution
on the fin.
5. The pitching moment about the center of buoyancy
contributed by the rear half of the hull increases with
pitch until at an angle of 33° it is approximately equal
to the moment contributed by the fins.
6. At any given angle of pitch up to 26° the restoring
moment of the model when fitted with the Mark II
fin was slightly less than that obtained with fin 3 and
appreciably greater than that obtained with fin 4.
7. Neglecting the effect on drag, it appears that fin 3,
owing to its relatively low bending moment about the
fin root, has certain structural advantages over the
Mark II fin.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, \7a., April 4, 1937.
REFERENCES
1. Freeman, Hugh B.: Pressure- Distribution Measurements on
the Hull and Fins of a 1/40-ScaIc Model of the U. S. Airship
Akron. T. R. No. 443, N. A. C. A., 1932.
2. Freeman, Hugh B.: Force Measurements on a 1 /40-Scale
Model of the U. S. Airship Akron. T. R. No. 432, N. A.
C. A., 1932.
3. Weick, Fred E., and Wood, Donald II.: The Twentv-Foot
Propeller Research Tunnel of the National Advisory
Committee for Aeronautics. T. R. No. 300, N. A. C. A..
1928.
38548 — 38
600
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE I
DIMENSIONS OF THE 1/40-SCALE MODEL “AKRON”
[Length, 19.62 ft.; volume, 115.00 cu. ft. ; location of elevator axis, (xjL) = 0.9059; center
of buoyancy, (x/L) = 0.464.]
Distance from bow
Radius (cir¬
cumscribed
circle) (in.)
Distance from bow
Radius (cir¬
cumscribed
circle) (in.)
length
X
T
length
X
~L
0. 00
0. 00
0. 50
19. 80
.02
4. 95
.55
19. 59
.05
9. 96
. 60
19. 12
. 10
14.20
.65
18. 46
. 15
16. 65
. 70
17. 50
. 20
18. 39
.75
16. 15
.25
19. 12
.80
14. 44
. 30
19. 61
. 85
12. 29
.35
19. 85
. 90
9. 61
. 40
19. 90
.95
6. 52
. 45
19. 90
1.00
.00
Fin
Area of
one fin
(with¬
out
eleva¬
tor)
(sq. ft.)
Area of
eleva¬
tor
(sq. ft.)
Area of
eleva¬
tor
counter¬
balance,
(sq. ft.)
Ele¬
vator
chord
(ft.)
Maxi¬
mum
chord
of fill
(ft.)
Maxi¬
mum
span
of fin
(ft.)
Fin span-chord ratio
(maximum span of fin) 2
(area offinj
Mark II...
1. 850
0. 356
0.110
0. 396
2.63
1.028
0. 570
3...
1. 858
. 356
. 402
3. 06
. 943
471
3- A _
1. 775
.356
. 402
3.06
.943
. 590
4 .
1.838
. 356
. 427
3. 55
.880
.421
TABLE II
NORMAL FORCE PER UNIT LENGTH OF FIN AND
MOMENT OF NORMAL FORCE ABOUT FIN ROOT OF
1/40-SCALE MODEL “AKRON”
MARK II FIN (WITH COUNTERBALANCES)
Station
Distance
from
bow (ft.)
5*
(deg.)
Normal force (lb. per ft. length) lq
Moment (ft. -lb. per ft. length) /q
0 (deg.)
9 (deg.)
11.6
17.0
22.5
28. 1
33.9
11. 6
17.0
22.5
28. 1
1
33.9
Elevator axis _ _
17. 78
0. 160
0. 241
0. 295
0. 336
0.286
0. 106
0. 160
0. 179
0. 201
0. 170
A
17. 69
.195
.302
.361
.424
.325
. 120
. 185
.214
. 253
. 185
B
17. 41
. 253
.425
.527
. 666
.412
. 146
. 242
.296
. 380
. 233
C
17.00
.254
.470
. 635
.855
. 545
. 140
. 246
. 325
. 430
. 293
1)
16. 59
.276
. 492
. 710
1.005
.745
. lit)
. 230
.324
. 448
. 358
E
16. 25
0
. 341
. 565
.815
1. 135
1. 105
. 157
.250
.351
.484
. 475
F
15. 97
.415
.715
1.013
1. 391
1. 546
. 176
. 305
. 430
. 565
. 593
G
15. 77
.502
.850
1. 255
1. 673
1.835
. 181
.320
.480
. 623
. 625
11
15. 56
. 610
. 945
1.312
1. 665
1. 755
. 170
. 266
. 375
. 407
. 440
1
15. 36
. 361
.531
.710
.885
. 980
.050
.067
. 095
. 118
. 122
Tip of fin _ _ _
15. 15
. 000
.000
.000
. 000
.000
.000
. 000
. 000
. 000
. 000
Elevator axis - -
17. 78
0. 429
0. 486
0. 522
0. 590
0. 573
0.231
0. 260
0. 280
0.310
0. 286 1
A
17. 09
.420
. 496
. 553
. 655
. 603
. 230
. 268
. 305
.353
.313
B
17. 41
. 383
.515
. 635
.808
. 694
.217
.281
.354
. 447
.375
C
17.00
.345
. 536
. 710
.944
.827
. 181
.274
. 356
. 463
.417
D
16. 59
.322
. 543
. 755
1.033
. 985
. 153
. 255
. 340
. 459
.442
E
16. 25
10
.364
. 574
. 823
1. 155
1. 225
. 161
.255
. 360
.566
.515
F
15. 97
.431
.740
1.046
1. 380
1. 614
. 183
.308
. 445
. 565
. 620
G
15. 77
.515
.844
1. 224
1. 645
1. 975
. 192
. 320
.470
.622
. 670
11
15, 56
. 632
.973
1. 335
1. 655
1. 885
. 178
. 276
. 385
.475
. 465
1
15. 36
. 366
.535
.702
. 866
1.005
. 146
. 070
.092
. 118
. 125
Tip of fin _ _ . ..
15. 15
.000
.000
.000
. 000
. 000
.000
. 000
.000
.000
.000
Elevator axis _
17.78
0. 660
0. 665
0.794
0. 810
0. 800
0.312
0.320
0. 395
0.412
0.388
A
17.69
. 623
. 656
.815
.845
.833
.312
.335
.415
.435
. 420
B
17.41
. 512
. 634
. 867
. 965
.935
. 276
.340
. 460
.477
.480
C
17. 00
.427
.571
.860
1.015
1.028
.220
.290
.418
.491
. 500
1)
16. 59
.362
. 567
.880
1.060
1. 158
. 171
. 261
.391
.474
. 507
E
16. 25
20
.363
.581
.916
1. 165
1.390
. 160
.260
.395
.495
. 565
F
15.97
. 485
.763
1. 133
1. 380
1.725
. 201
.325
.481
.568
. 620
G
15. 77
[ . 585
.930
1.315
1. 665
2. 025
. 210
. 340
.486
.022
. 648
11
15. 56
. 661
1. 019
1. 383
1. 6811
1. 833
. 185
.285
. 400
. 482
.445
I
15. 36
.406
. 557
. 735
. 855
.870
.052
. 073
. 095
. 110
.110
Tip of fin _ , _
15. 15
. 000
.000
.000
.000
.000
.000
.000
.000
.000
.000
601
PRESSURE-DISTRIBUTION MEASUREMENTS ON FINS OF U. S.
AIRSHIP “AKRON”
TABLE III
NORMAL FORCE PER UNIT LENGTH OF FIN ON 1/40-SCALE MODEL “AKRON”
MARK II FIN (COUNTERBALANCES REMOVED)
Station
Distance
from bow
(ft.)
a ,
(deg.)
Elevator axis _ _
17. 78
A
17. (39
B
17. 41
C
17. 00
D
lfi. 59
E
1(5. 25
20
F
35. 97
G
15. 77
11
15. 56
1
15. 36
Tip of fin. __ .. -
15. 15
Normal force (lb. per ft. length)/!/
9 (deg.)
11.6
17.0
22.5
28.1
33.9
0. 740
. 744
.713
.612
. 564
. 615
. 768
.908
1.030
. 620
. 000
1. 122
1. 130
1. 147
1. 156
1.213
1. 306
1.415
1.612
1. 620
.860
.000
- -
TABLE IV
NORMAL FORCE PER UNIT LENGTH OF FIN AND MOMENT OF NORMAL FORCE ABOUT FIN ROOT OF 1/40-SCALE
MODEL “AKRON”
MARK II FIN, 3/8-INCH SLOT (COUNTERBALANCES REMOVED)
Station
Distance
from
bow
(ft.)
S ,
(deg.)
Elevator axis . . _
17. 78
A
17.69
11
17.41
c
17.00
D
16. 59
E
16. 25
20
F
15.97
G
15. 77
11
15. 56
1
15. 36
Tip of fin _ -
15. 15
Normal force (lb. per ft. length)/)/
Moment (lb. -ft. per ft. length)/?
0 (deg.)
6 (deg.)
11.6
17.0
22.5
28.1
33.9
11.6 i 17.0 22.5
28.1
33.9
O S7n
0 <47 1
1. 143
0. 475 0. 508 _
0. 575
774
sss
1. 075
.418 .474 ! _
.560
535
' 743
. 945
.295 .393 i _
. 490
437
664
. 990
.224 . 318 _ ...
.442
410
nos
.193 .276 _
. 435
420
008
1. 090
.184 .263 ! _
.462
520
732
1 360
.216 .314 1 _ ..
. 565
5Q0
S43
' -
1 . 660
.219 | .323 1 _ ..
. 610
712
OSS
1 700
. 202 . 283
. 450
. 413
. 562
.860
.055 .071 _
. 113
_
.000
. 000
—
.000
. 000 . 000
. 000
TABLE V
NORMAL FORCE PER UNIT
LENGTH OF FIN AND MOMENT OF NORMAL
1/40-SCALE MODEL “AKRON”
FORCE ABOUT FIN ROOT OF
MARK II FIN, 3/4-INCH SLOT (COUNTERBALANCES REMOVED)
Station
Elevator axis.
A
B
C
D
E
F
G
II
I
Tip of fin _
Distance
from
bow
5,
(deg.)
Normal force (lb. per ft. length)/?
Moment fib. -ft. per ft. length)/?
0 (deg.)
0 (deg.)
(ft J
11.6
17.0
22.5
28.1
33.9
11.6
17.ll
22.5
28.1
0. 875
0. 986
1. 116
1.055
0. 467
0. 495
0.555
0. 525
17. 69
. 754
. 885
1. 002
.985
. 413
. 450
. 506
.500
17. 41
. 505
.658
.808
.855
.288
. 354
. 421
. 445
17. 00
. 380
. 565
. 782
. 900
. 200
. 285
.370
. 410
16. 59
.339
. 550
.810
.950
. 164
.253
. 358
. 402
16. 25
20
. 345
.545
.810
1. 005
. 160
. 250
. 360
. 430
15. 97
.459
. 706
1. 002
1. 250
. 196
. 304
. 428
.515
. 530
.841
1. 203
1. 560
. 200
. 320
. 460
. 575
15.56
. 661
.944
1.293
1. 575
. 183
. 268
. 370
.425
15. 36
. 404
. 565
. 700
. 870
.053
.070
.088
.110
15. 15
i
.000
.000
.000
.000
.000
. 000
. 000
.000
33.9
602
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE VI
NORMAL
FORCE PER UNIT
LENGTH OF FIN AND MOMENT OF NORMAL FORCE
1/40-SCALE MODEL “AKRON”
ABOUT FIN ROOT OF
FIN 3
Station
Distance \
from
bow
eft 1
5.
(deg.)
Normal force (lb. per ft. length)/?
Moment (lb. -ft. per ft. length)/?
0 (deg.)
0 (deg.)
11.6
17.0
22.5
28.1
33.9
11.6
17.0
22.5
28.1
33.9
Elevator axis _
17. 78
-0. 280
-0. 300
-0. 233
-0. 147
-0. 008
-0. 115
-0. 089
-0. 057
-0. 020
0.011
A
17. 69
-. 140
— . 160
-.077
. 022
. 100
-. 036
-.016
. 002
. 036
. 068
H
17.41
. 108 ;
. 142
.234
. 304
. 365
. 066
. 092
. 128
. 157
. 170
C
17. 00
. 173
. 285
. 396
. 493
.494
.084
. 133
. 180
.218
.208
1)
16. 59
. 221
.345
. 476
. 603
. 565
. 090
. 133
. 187
. 230
. 222
E
16. IS
224 1
.365
. 526
. 685
.690
. 080
. 130
. 179
.228
.240
F
15. 77
15
.260
.425
. 626
.825
. 936
.081
. 135
. 181
. 243
.278
Q
15. 56
. 278
. 478
. 665
. 926
1. 115
.088
. 145
. 196
. 266
.312
11
15. 35
. 335
. 558
. Too
1.066
1. 298
. 100
. 166
. 224
. 304
.363
1
15. 15
. 435
. 675
. 715
1. 265
1. 563
. 110
. 175
.238
. 322
. 370
.1
14. 95
. 450
. 700
.943
1. 195
1. 372
. 075
. 117
. 166
. 204
. 220
Tip of fin. _
14. 72
.000
.000
.000
.000
.000
. 000
. 000
. 000
.000
.000
Elevator axis — _
17. 78
0. 176
0.245
0. 322
0. 270
0. 378
0. 106
0. 158
0. 198
0. 160
0.210
A
17. 69
.290
.275
.383
. 303
.443
. 116
. 160
. 210
. 161
. 225
R
17.41
. 264
. 335
.494
.373
.591
. 130
. 165
. 235
. 180
.262
C
17. 00
. 263
. 370
. 565
. 475
. 719
. 120
. 163
.246
.203
.290
D
16. 59
. 243
. 392
. 610
. 546
.804
. 094
. 150
.233
. 210
. 296
E
16. 18
. 266
.390
. 633
. 593
. 910
.084
. 134
.208
. 200
.292
E
15. 77
u
.288
.443
. 715
. 776
1.065
.089
. 133
. 203
. 221
. 304
(i
15. 56
. 298
.482
.736
.875
1. 160
. 093
. 143
. 216
. 256
. 324
11
15. 35
. 351
. 570
.814
1. 008
1. 305
. 104
. 168
. 242
.300
. 363
1
15. 15
. 455
.743
1. 026
1. 256
1.504
. 113
. 190
. 263
.318
. 360
J
14. 95
.468
, 736
1. 045
1. 247
1.545
.086
. 120
. 175
. 208
.240
Tip of fin. . . .
14.72
.000
. 000
.000
.090
.000
.000
. 000
.000
.000
. 000
Elevator axis .
17.78
0.514
0. 665
0. 690
0.700
0. 738
0.290
0. 353
0.373
0.374
0. 390
A
17.69
.473
.605
. 656
. 677
. 735
.254
.323
.345
. 348
. 365
li
17.41
.375
.506
.585
. 663
. 765
. 182
.244
.280
.304
. 336
C
17. 00
.316
.484
. 582
.708
. 863
. 137
. 206
. 250
.300
. 343
1)
16. 59
.294
.473
.592
.742
. 906
. 114
. 180
.228
.280
.337
E
16. 18
.276
.464
.627
.774
. 983
. 100
. 157
. 210
. 257
.313
E
15. 77
10
.287
.504
.675
. 867
1. 127
.090
. 155
. 200
. 254
. 321
G
15. 56
.288
.540
.706
.930
1. 125
. 090
. 164
. 206
. 265
.336
11
15. 35
.347
.624
.805
1. 063
1. 275
. 106
. 183
.235
.307
.358
1
15. 15
.446
.746
. 975
1.263
1.504
. 113
. 190
. 250
.325
.368
J
14. 95
.480
.755
1. 020
1. 203
1. 500
.074
. 125
. 175
.205
.245
Tip of fin _
' 14.72
.000
.000
.000
.000
. 000
.000
.000
.000
. 090
. 000
Elevator axis . .
17.78
0.916
1.020
1.043
0. 947
0. 867
0. 542
0. 550
0. 568
0. 494
0. 445
A
17. 69
.822
.910
. 955
.905
.no
. 428
.467
.486
. 452
.375
R
17. 41
.54.3
.656
. 756
. 792
. 615
. 255
.304
.347
.356
. 260
C
17. 00
.404
.538
.688
.732
. 626
. 170
. 226
. 288
. 302
.205
1)
16. 59
.352
. 504
. 655
.730
. 655
. 135
. 190
.246
.280
.220
E
16. 18
.318
. 473
. 667
. 765
. 735
. 110
. 160
.220
.253
.245
E
15. 77
20
. 323
. 522
.753
.874
.918
. 100
. 108
. 220
. 250
. 268
G
15. 56
. 326
. 525
. 756
.880
1. 030
. 100
. 108
.218
.257
. 296
11
15. 35
. 362
. 592
.850
. 994
1. 192
. 110
. 126
. 250
.295
.338
1
15. 15
. 445
.715
.995
1. 235
1. 443
. Ill
. 134
. 255
.320
.355
J
14. 95
.525
. 737
. 955
1. 185
1.313
.088
. 126
. 161
. 204
.215
Tip of fin -
14. 72
.000
.000
.000
.000
.000
.000
.000
. 000
1
. 000
.000
PRESSURE-DISTRIBUTION MEASUREMENTS ON FINS OF U. S. AIRSHIP “AKRON”
603
TABLE VII
NORMAL FORCE PER UNIT LENGTH OF FIN AND MOMENT OF NORMAL
1/40-SCALE MODEL “AKRON”
FORCE
ABOUT FIN ROOT OF
FIN 4
Distance
Normal force (lb. per ft. length)/?
Moment (lb. -ft. per ft. length)/?
Station
from
bow
<5,5
(deg.)
6 (deg.)
6 (deg.)
(ft 1
11.6
17.0
22.5
28.1
33.9
11.6
17.0
22.5
28.1
33.9
Elevator axis _
17. 78
-0. 195
-0. 167
-0. 062
-0. 100
0. 000
-0. 073
-0. 047
0.000
-0. 010
0.025
A
17.69
-.119
-.056
.030
.014
. 161
-.038
.000
.040
.025
. 093
B
17.41
.057
. 190
.280
.240
.534
.039
.095
. 130
. 108
. 225 ;
C
17. 00
. 148
.295
. 405
.290
.745
.065
. 122
. 156
. 120
. 265
D
16. 59
.213
. 330
.430
.422
.785
.073
.110
. 148
. 142
. 244
E
16. 18
.214
.335
.444
.495
.705
.007
.098
. 134
. 150
. 195
F
15. 56
-15
.214
. 336
.468
. 559
. 675
.051
.080
.110
. 135
. 157
G
15. 15
.210
.340
.516
.655
.720
.047
.070
. 104
. 130
. 140
H
14. 95
.227
. 357
.565
.740
.748
.044
.074
. 108
. 140
. 140
I
14. 74
. 262
.415
.654
.870
.875
.048
.083
. 125
. 164
. 164
.1
14. 54
.305
.512
. 755
.992
1.035
.049
.084
. 120
. 160
. 174
K
14.35
. 135
.203
.275
.333
.385
.020
.031
.041
.075
. 100
Tip of fin _
14.23
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000 ;
1
Elevator axis -
17.78
0. 210
0. 305
0. 388
0. 357
0. 370
0. 123
0. 160
0.203
0. 190
0. 181
A
17. 69
. 196
.295
.390
.410
.394
. 104
. 150
. 192
.202
. 185
B
17.41
. 180
. 306
.413
.516
.495
.084
. 141
. 180
.212
.208
C
17. 00
214
.356
.475
. 565
.695
.088
. 140
. 180
.204
.233
1)
16. 59
.218
. 367
.495
. 592
. 635
.077
. 123
. 165
. 192
.207
E
16. 18
.213
.360
.480
. 602
.618
.063
. 104
. 140
. 175
. 178
F
15. 56
0
.220
.355
.481
.608
.612
.051
.0S1
.110
. 142
. 142
G
15. 15
.212
.355
.504
. 660
.735
.043
.072
. 102
. 130
. 140
1L
14.95
.226
. 375
.535
.712
.790
.043
.076
. 105
. 135
. 146
I
14. 74
.263
.434
.650
.820
.915
. 051
.083
. 122
. 152
. 168
.1
14. 54
.324
.509
.747
. 965
1.084
.050
. 085
. 125
. 161
. 184
K
14.35
. 160
.205
.248
.370
. 50S
.017
. 036
. 053
.092
.114
Tip of fin _
14. 23
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000 j
Elevator axis -
17. 78
0. 550
0. 650
0. 738
0.602
0. 620
0. 255
0. 305
0.350
0. 268
0. 300 1
A
17.69
.453
.560
.655
. 545
.637
.227
.270
.313
.260
.295
B
17.41
.322
.400
.540
.453
. 695
. 147
. 175
. 232
.232
.287 !
C
17.00
.275
.361
.525
.572
.793
. 110
. 143
. 200
.216
.275
D
16. 59
.277
. 373
. 522
. 523
.775
. 100
. 130
.172
. 170
. 234 ;
E
16. 18
.287
.338
. 483
.521
.735
.088
. 100
. 143
. 152
.208
F
15. 56
10
.265
.325
.494
.572
.714
.058
.072
. 114
.135
. 165
G
15. 15
.240
.344
.533
.670
. 742
. 050
.072
. 108
. 130
. 145
n
14. 95
.245
.374
.558
.736
.735
.050
.075
. 108
. 133
. 145
i
14.74
.274
.418
.667
.870
.924
. 052
. 079
. 125
. 162
. 170
j
14. 54
.326
.492
. 744
1.008
1. 106
.053
.080
. 120
. 169
. 185
K
14.35
. 160
.230
.470
.620
.815
.021
. 035
. 052
.070
. 086 |
Tip of fin _
14.23
.000
.000
.000
.000
.000
.000
.000
.01X1
. 000
.000 1
Elevator axis.. - -
17. 78
0.878
0. 990
1.050
0. 950
1.082
0.412
0.470
0.485
0. 440
0. 467
A
17.69
.746
.874
.922
.845
.903
. 355
.410
.430
.392
. 425
B
17.41
.453
.588
.662
.625
.800
. 197
.253
.276
.256
.310
C
17.00
.338
.487
.575
.575
.705
. 130
. 185
. 206
.205
. 245
D
16. 59
.296
.450
.514
.590
.635
. 103
. 150
. 170
. 190
. 200
E
16. 18
.272
.415
.484
.584
. 660
.085
. 122
. 145
. 176
. 190
F
15. 56
20
.249
.389
.485
. 613
.700
.060
. 090
. 112
. 145
. 158
G
15. 15
.240
.390
.505
. 684
.825
. O'. 2
.084
. 102
. 133
. 162
II
14.95
.244
.407
.546
.750
. 925
.048
.081
. 108
. 140
. 168 J
1
14.74
.278
.464
.652
.867
1. 100
.053
.090
. 125
. 162
.202
J
14. 54 1
.332
.555
.743
1.033
1. 275
.054
. 090
. 125
. 172
.205
K
14. 35 !
. 125
. 170
.213
. 260
.305
.018
.037
.055
.071
. 118
Tip of fin _
14.23
.000
1
.000
.000
.000
.000
.000
.000
.000
.000
. 000
604
REPORT No. 604— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TABLE VIII
VALUES 01
, NORMAL FORCE
AND DISTANCES OF CENTER OF PRESSURE OF FIN FORCES FROM ELEVATOR
AXIS FOR VARIOUS FINS TESTED ON 1/40-SCALE MODEL “AKRON”
rvalues of norir^ilJoree are for one fln onjy J
s .
(deg.)
e
(deg.)
Normal force (lb.)/g
Distance of center of pressure from elevator axis (ft.)
Mark II
fln (with
counter¬
balances)
Mark II
fln
(counter¬
balances
removed)
Mark II
fin (34-in.
slot)
Mark II
fln (34- in.
slot)
Fin 3
Fin 4
Mark II
fin (with
counter¬
balances)
Mark 11
fln
(counter¬
balances
removed)
Mark 11
fin (34-in.
slot)
Mark II
fin (44-in.
slot)
Fin 3
Fin 4
116
0. 65
0. 61
1. 96
2. 15
17 0
1.05
1 . 06
1. 94
2. 01
22 5
1.50
1.52
1. 87
2 01
28. 1
2. 00
1.70
1. 87
2. 17
33. 9
2. 27
2. 39
1.91
1. 88
n.fi
0. 84
. 87
1. 47
1. 64
1. 82
17. 0
1 42
1.31
1.25
1. 44
1. 70
1. 81
0
22. 5
1 96
1. 96
1. 71
1. 47
l. 68
1. 83
2$. I
2 60
2.01
2. 14
1. 47
1. 83
1. 88
33. 9
2. 37
2. 80
2. 32
1. 60
1. 76
1 91
f ll.fi
1.02
1.01
1.00
1.33
1. 49
1. 63
17. 0
1. 56
1.60
1.31
1.38
1 69
10
22. 5
2. 09
2. 03
1.89
1.41
1. 60
1. 76
28. 1
2. 71
2. 50
2. 12
1.41
1. 92
33. 9
2. 85
3.05
2. 68
1. 48
1 67
1 82
ll.fi
1.20
1.29
1. 16
1.25
1. 11
1.25
1.23
1.23
1.34
1.45
17. 0
1. 70
L 77
1.80
1.68
1. 74
1.63
1.34
1.30
1.25
1. 28
1.44
1. 56
20
22. 5
2. 24
2. 27
2. 25
1.96
1. 34
1. 31
1 51
1 64
28. 1
2. 88
3. 15
2. 89
2. 67
2. 53
2.28
1. 36
1.30
1.34
1.36
1. 57
1. 79
33. 9
3. 18
2.52
2.73
1.40
1.70
1.81
TABLE IX
NORMAL FORCE ON FINS AND HULL AND PITCHING MOMENT ABOUT CENTER OF
AND AFTER PART OF HULL OF 1/40-SCALE MODEL “AKRON”
BUOYANCY OF FINS
[Values are for one fln and starboard half of hull aft of station 14; <5«=20°.]
Fin
g
(deg.)
'1 ransverse force
<i~
on hull
(?)
<1
of forces
on hull
m
Normal force
Q
on fin
(!)
AIc.b.
Q
of force
on fin
m
Transverse force
9 ~
on hull plus
Normal force
(7
on fin
(!)
1
of forces on
hull and
fin
Uf)
11.6
0. 17
_ 2 7
1.20
-8.9
1.37
-11.6
17.0
. 78
-6.3
1. 70
-12.5
2.48
-18.8
Mark 11 (with counterbalances)
22. 5
1.44
-9.0
2. 24
-16.4
3. 68
-25. 4
28. 1
2. 33
-12. 5
2. 88
-21. 1
5.21
-33. 6
33. 9
4. 25
-21.0
3. 18
-23. 1
7. 43
-44. 1
11. 6
.30
-3.6
1.25
-9. 2
1.55
-12.8
17.0
.89
-6.8
1.74
-12.6
2. 63
-19.4
22. 5
1. 65
-9.8
2. 25
—16. 1
3. 90
-25.9
28. 1
2. 65
-15.3
2. 53
-18. 0
5. 18
-33. 3
33.9
4. 21
-22. 1
2.51
-17.5
6. 72
-39. 6
11.6
. 23
-2. 7
i. 11
-8.0
1.34
-10.7
17.0
1. 14
-7.3
1. 63
-11.6
2.77
-18. 9
4
22 5
1 63
9 6
1 96
13 8
28. 1
2. 73
-U. 4
2. 28
— 15. 7
5. 01
-30. 1
33.9
4.35
-22. 0
2. 73
-18.8
7.08
-40. 8
TABLE X
LOCATION OF STRUCTURAL FRAMES ON U. S. AIR¬
SHIP “AKRON” AND THEIR CORRESPONDING
LOCATION ON A 1/40-SCALE MODEL
Ring location
from 0 sta¬
tion (full-
scale)
(meters)
Ring location
from bow
(1/40-seale
model)
(feet)
Ring location
from 0 sta¬
tion (full-
scale)
(meters)
Ring location
from bow
(1/40-scale
model)
(feet)
0
17. 51
125. 0
7.26
17.5
16.08
147.5
5.41
35.0
14.64
170.0
3. 57
57.5
12. 80
187.5
2. 13
80.0
10. 95
198. 75
1. 21
102.5
9. 10
210. 75
.23
REPORT No. 605
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
By Fred E. Weick and Robert T. Jones
SUMMARY
An analysis of the principal results of recent N. A. C. A.
lateral control research is made by utilizing the experience
and progress gained during the course of the investigation.
Two things are considered of primary importance in
judging the effectiveness of different control devices: The
(. calculated ) banking and yawing motion of a typical small
airplane caused by a deflection of the control , and the stick
force required to produce this deflection. The report in¬
cludes a table in which a number of different lateral control
devices are compared on these bases.
Experience gained while testing various devices in
flight with a Fairchild 22 airplane indicated that, follow¬
ing a sudden deflection of the control at low speed, an
angle of bank of 15° in 1 second represented a satisfactory
minimum degree of effectiveness for this size of airplane.
Some devices capable of giving this degree of control were,
however, considered to be not entirely satisfactory on ac¬
count of sluggishness in starting the motion. Devices
located near the trailing edge of the wings had no detectable
sluggishness . Lateral control forces considered desirable
by the test pilots varied from 2 to 8 pounds; 15 pounds was
considered excessive.
Test flights demonstrated that satisfactory lateral control
at high angles of attack depends as much on the retention of
stability as on aileron effectiveness.
The aerodynamic characteristics of plain sealed ailerons
could be accurately predicted by a modification of the
aerodynamic theory utilizing the results of experiments
with seeded flaps. Straight narrow-chord sealed ailerons
covering GO to 80 percent of the semispan represented about
the most efficient arrangement of plain unbalanced ailerons
from considerations of operating force. The stick force of
plain ailerons can be effectively reduced by the use of a
differential linkage in conjunction with a small fixed tab
arranged to press the ailerons upward.
INTRODUCTION
In 1931 the Committee started a systematic wind-
tunnel investigation of lateral control with special
reference to the improvement of control at low air
speeds and at high angles of attack. Many different
ailerons and other lateral control devices have been
subjected to the same systematic investigation in the
7- by 10-foot wind tunnel. (See reference 1.) The
devices that seemed most promising were tested in
flight (references 2 and 3). In many cases, however,
devices that produced what seemed to be satisfactory
rolling moments and favorable yawing moments did
not give satisfactory control.
An analytical study of control effectiveness was
therefore made (reference 4) taking into account a
number of secondary factors, including the yawing
moments produced by the controls, the effect of the
controls on the damping in rolling, the lateral -stability
derivatives of the airplane, the moments of inertia, and
the time required for the control moments to become
established after the deflection of the surfaces. The
computations consisted of step-by-step solutions of the
equations of rolling and yawing motion for the condi¬
tions following a deflection of the controls. The results
of these computations based on aerodynamic data ob¬
tained from wind-tunnel tests of wings incorporating
various devices agreed satisfactorily with the results
measured in flight for widely different forms of control,
such as ailerons and spoilers.
The study of conditions above the stall indicated
that satisfactory control could not be expected without
some provision to maintain the damping in rolling and
that a dangerous type of instability would arise if the
damping were insufficient. Since damping in rolling
depends on an increase in the lift of the airfoil with
increasing angle of attack, it follows that, in order to
obtain satisfactory lateral control, the outer or tip por¬
tions of the wing, which govern the rolling moments,
must remain unstalled. If damping in rolling is re¬
tained, it is practically insured that control moments
will be retained as well.
The progress of the investigation has thus led to a
more accurate interpretation of the results of the wind-
tunnel tests. In the present paper the experience
gained during the course of the investigation is made
the basis of a revised method of comparison of lateral
control devices. Wind-tunnel measurements of control
and stability factors (reference 1) are utilized in com¬
putations to show the banking and yawing motions
that would be produced by the controls acting on a
small typical airplane. These computations follow the
method of analysis given in reference 4. In section I of
the report the new basis of comparison is explained and
605
606
REPORT NO. 605—NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
a number of the devices that were tested in reference 1
are analyzed and compared. The principal items of
comparison are collected into a table. Section II
presents an analysis of the rolling, yawing, and binge
moments of plain flap-type ailerons and deals with the
application of these data in the design of control
systems.
I. COMPARISON OF LATERAL CONTROL
DEVICES
REVISED BASIS OF COMPARISON
AIRPLANE USED IN COMPARISON
The procedure adopted in the lateral control investi¬
gation has comprised a wind-tunnel test program fol¬
lowed by flight tests of the different devices on the
Fairchild 22 airplane. Not all of the devices tested
in reference 1 have been tried in flight, however, and
the present report may be considered an analytical
extension of the flight-test procedure that was applied
to some of the devices. The procedure employed to
test lateral controls in flight is simulated by means of
computation. Thus, the comparative criterions used
herein are based on application of the devices to a hypo¬
thetical Fairchild 22 type of airplane, which is the type
used in the flight tests.
The Fairchild 22 airplane was necessarily somewhat
modified for each different flight test and wings of differ¬
ent moment of inertia, plan form, and section were
used in some cases. The wing of the hypothetical air¬
plane assumed in the computations represents an aver¬
age of the tested wings. Furthermore, since the char¬
acteristic ratios of dimensions (tail length, tail area,
radii of gyration about various axes, etc.) used agree
very closely with statistical averages of these quanti¬
ties, the assumed airplane may be considered to embody
average stability characteristics. The principal charac¬
teristics of the assumed airplane are as follows:
Weight, W _ 1,600 lb.
Wing span, b _ 32 ft.
Wing area, S _ 171 sq. ft.
Wing loading, W/S _ 9.4 lb. per sq. ft.
Area of fin and rudder _ 10.8 sq. ft.
Tail length _ 14.6 ft.
Ix - 1,216 slug-ft.2
Iz - 1,700 slug-ft.2
ROLLING ACTION
It is recognized that different types of airplanes re¬
quire different amounts of control. At the start of
the wind-tunnel investigation of lateral control devices
(reference 1) a rolling criterion ( RC=CijCL ) represent¬
ing a conservative lower limit of rolling control for all
types was assumed. The assumed satisfactory value
of the rolling criterion was 0.075, which corresponds to
a lateral movement of the center of pressure of 7.5
percent of the wing span. Recent experience indicates
that this value is likely to be ample for any condition
of flight that might be encountered and is therefore a
desirable value to attain. Where a compromise must
be made between the rolling moment and some other
characteristic of the control system, particularly the
control force, a decidedly lower value of the rollino'
o
criterion may be used. It appears that a value pos¬
sibly as low as half the original one may be found
reasonably satisfactory for practically all conditions of
flight with nonacrobatic airplanes.
The criterion of rolling control used in the present
analysis is the angle of bank attained in 1 second fol¬
lowing a sudden deflection of the control. This criterion
shows the actual amount of motion produced and
depends on both the acceleration at the start and the
final rate of roll. It includes the effect of yawing
moment given by the control as well as the stability
characteristics and moments of inertia of the airplane.
The values of the criterion are found by computation
and as such are applicable only to the particular type
of airplane (F-22) that has been assumed.
Experience gained in flight tests of the Fairchild 22
airplane with various lateral control devices indicated
a minimum satisfactory amount of rolling control cor¬
responding to about 15° of bank in 1 second. (See
fig. 1.) Ailerons capable of giving this amount of bank
0 .2 .4 .£ .8 1.0 1.2
Time, sec.
Figure 1. — Banking of Fairchild 22 airplane after sudden deflection of lateral con¬
trol devices at low speed. (The narrow plain ailerons and the retractable ailerons
were considered to give a satisfactory amount of control; the floating-tip ailerons
were reported as weak.)
at low speed have been found reasonably satisfactory
in practice with this type of airplane. Owing to the
present general use of high-lift flaps on airplane wings,
the size and deflection of ailerons are usually deter¬
mined by the low-speed condition of flight with the
flaps deflected. For comparative computations, in the
present report, a lift coefficient of CL= 1.8 is assumed as
representative of the low-speed condition of flight with
RESUME and analysis of n. a. c. a. lateral control research
607
flaps. The sizes or deflections of the lateral controls
are selected in each case to give an angle of bank of 15°
in 1 second at 67 =1.8.
In addition to providing a sufficient amount of bank¬
ing motion, two further desirable characteristics of the
rolling action are: (1) The response of the airplane in
roll to any movement of the lateral control surface
should be immediate, any noticeable delay or hesita¬
tion in the action being objectionable; and (2) the
action should be so graduated that the acceleration and
maximum rate of roll increase smoothly and regularly
as the stick deflection is increased. Conventional
ailerons or similar lateral control devices located near
the trailing edge of the wing easily meet these require¬
ments and show, in analyses of motions recorded in
flight, practically instantaneous response of rolling
acceleration to control-surface movement. From 0.1
to 0.2 second is ordinarily required to deflect the
surfaces and, during this interval, the rolling accelera¬
tion apparently keeps pace, although only a slight
amount of rolling motion is accumulated by the time
of full deflection. Comparison shows that good
synchronization of the calculated motion with the flight
records was obtained when the assumed full deflection
was taken at the instant the actual deflection reached
half its ultimate value. This assumption was used
in the computations for plain ailerons and other
devices that gave no indication of sluggish response
characteristics.
CONTROL FORCE
During the course of the lateral control investigation
it became apparent that the force required to move the
controls is of extreme importance in obtaining satisfac¬
tory lateral control. As shown by the flight tests of
references 2 and 3, an airplane that requires a light
control force is likely to seem more controllable to a
pilot than one that requires a heavy control force, even
though with full deflection the heavier control may be
considerably more powerful than the lighter one. It
seems desirable to have the control force as light as pos¬
sible and yet to maintain the feeling of a definite neu¬
tral position. This characteristic is especially impor¬
tant in the aileron control since the effort expended in
moving the stick sidewise is relatively greater than for
other control movements. (See reference 5.) Correla¬
tion of test-flight reports and control-force records indi¬
cates that the forces required to operate the ailerons
should not exceed about 8 pounds in order to be con¬
sidered desirable. A lower limit of stick force of about
2 pounds at full deflection is apparently considered
essential so that there may be a noticeably regulated
increase of force with deflection. Friction of the con¬
trol mechanism plays an increasingly important part
as the operating force is reduced and should in no case
be great enough to mask the “feel” of the control. It
is probable that with sufficiently little friction a force
not greatly in excess of 2 pounds would be considered
38548—38 - 40
most desirable. A force of 15 pounds is to be consid¬
ered excessive.
As previously stated, the size or maximum deflection
of the control devices compared in this paper have
been selected to give an angle of bank of 15° in 1 sec¬
ond following full deflection and considering the aver¬
age airplane fitted with a high -lift flap and flying at a
lift coefficient of 1.8. The ailerons are compared (see
table I) on the basis of the stick force required to
attain this angle of bank of 15° in 1 second at lift
coefficients of 0.35, 1.0, and 1.8, which compose the
usual flight range. The lift coefficient of 0.35 repre¬
sents the conditions of high-speed and cruising flight.
The lift coefficient of 1.0 is considered to represent two
conditions, the first being that of low-speed flight with¬
out a flap, such as is used in an approach to a landing
with an unflapped airplane, and the second being one
with a flap fully deflected, which represents as high a
speed as is usually attained in that condition. The
value 67=1.8 can be obtained only with the flap de¬
flected and represents the low-speed flight condition
with the liigh-lift device in use. When representative
values of this nature are used, it is necessary to exam¬
ine the complete original data to show that the critical
values are representative of conditions throughout the
flight range. Such an examination has been made for
the comparisons of the present report.
The stick force for a 15° bank in 1 second is used iis
the basis of comparison at all flight speeds and lift co¬
efficients even though the conventional ailerons will
produce a decidedly greater bank in 1 second at higher
speeds. The 15° value is taken throughout because it
is considered to represent the maximum control likely
to be used in ordinary flight at any speed and is there¬
fore of greater interest as a basis for stick forces re¬
quired than the maximum possible deflection, as long
as the force at maximum deflection does not approach
the strength of the pilot.
The data for some of the ailerons were obtained with
plain unflapped wings with which a lift coefficient of 1.8
could not be attained and, in order to have all the
lateral control devices on a comparable basis whether
mounted on flapped or unflapped wings, their sizes and
maximum deflections were selected to give essentially
the same rolling effect as the others at a lift coefficient
of 1.0. The analysis showed that conventional ailerons
which give an angle of bank of 15° in 1 second on a
flapped wing at a lift coefficient of 1.8 could, when
fully deflected, give an angle of bank of 22.5° with the
flap retracted at a lift coefficient of 1.0. The ailerons
on the unflapped wings were therefore selected to be
capable of giving 22.5° bank in 1 second at a lift co¬
efficient of 1.0, but the values of the stick forces required
were computed for partial deflections giving a 15° bank
in 1 second at lift coefficients of both 1.0 and 0.35. The
first aileron of table I is of the conventional unbalanced
flap type on a rectangular wing of aspect ratio 6. It
has a chord 0.25 cw and a span 0.40 6/2 and has equal
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
608
up-and-down linkage. It will be noted that, for an air¬
plane equipped with these ailerons, the stick force com¬
puted for a 15° bank in 1 second at the cruising-flight
condition is 4.7 pounds with aileron deflections of only
±3.4°. At a lift coefficient of 1.0, representing the low-
speed flight condition for the unflapped wing, the same
amount of control was obtained with a stick force of
3.G pounds and aileron deflections of ±7.4°. All the
stick forces are given for an assumed aileron linkage
such that at the maximum deflection the control stick,
which has a length of 20 inches on the Fairchild 22
airplane and is so assumed for the average airplane, is
deflected 25° from neutral. The maximum aileron
deflection is If. 2° and is the deflection required to
produce a bank of 22.5° in 1 second at CL= 1.0. Here
the ailerons are not being taxed to their fullest extent.
The maximum amount of control specified in a design
has a predominating effect on the operating force.
Figure 2 shows a calculated example of the variation of
Figure 2.— Relation between stick force and maximum amount of control obtained.
Fairchild 22 type airplane; 0.80 b- sealed ailerons deflected ±20°; aileron chord
varied.
operating force with specified control in which it was
assumed that ailerons with equal up-and-down motion
and the most efficient length and deflection (±20°)
were used in each case. The rate of increase of operating
force with amount of control depends on the manner
in which the increase of control is obtained, as will be
more fully developed in a later section.
YAWING MOTION AND SIDESLIP
The effect of the yawing moment produced by the
ailerons is considered in two ways. First, the secondary
effect of yaw on the rolling motions is inherently in¬
cluded in the computed banking effectiveness. Thus,
the bank in 1 second is that produced by the ailerons
without aid from the rudder. If it is assumed that a
sufficiently powerful rudder were used in such a way
as to prevent sideslip, a given aileron device would,
in general, produce a somewhat greater banking effect.
This assumption is not used here, however, and the
deflections of the control surfaces given in table I are
those required to produce the specified angle of bank in
1 second with the particular combination of rolling and
yawing moments produced by the aileron in question.
The second effect considered is the sideslip produced
by the sudden use of the aileron control for banking.
In flight the rudder is used to avoid sideslipping and
the amount of rudder action necessary for this purpose
is in direct proportion to the sideslip incurred by the
ailerons alone.
The angle of sideslip accompanying a 15° bank in 1
second following the sudden displacement of the lateral
controls is also given in table I. The first aileron
listed, it will be noted, produces a sideslip of 7° at CL—
1.0 and of 3° at C7,=0.35 when the rudder is not used
to correct for this condition.
LATERAL STABILITY
In the ordinary unstalled-flight range the effects of
the lateral-stability factors on the lateral control ob¬
tained are included in the computations of the angle of
bank reached in unit time. The angle of bank <t> i is the
angle that would be produced by the control operating
on the average airplane. The effect of a given control
on an airplane of greatly different lateral-stability
characteristics might, of course, be considerably different
than indicated in this case.
One of the most important factors in the interaction
of lateral stability and control below the stall is the
effect of the secondary yawing moment induced by the
control and an allowance for this effect should be made in
the proportioning of the airplane for lateral stability.
Modifications that tend to increase spiral stability in
free flight (namely, reduced vertical-fin area and in¬
creased dihedral) tend to render the airplane uncon¬
trollable under the action of ailerons giving adverse
yawing moment. The degree of “weathercock” stability
should be sufficient to restore the airplane from a yawed
attitude when the wings are held level by use of the
ailerons. For safety in this respect the ratio of adverse
yawing to rolling moment given by the ailerons should
not be allowed to approach the ratio of yawing to roll¬
ing moments that naturally act on the airplane either
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
in pure sideslipping or pure yawing motion. (See
reference 6.)
One of the lateral-stability factors, the damping in
rolling, has been shown by the analysis in reference 4 to
have a critical effect on the controllability obtained,
satisfactory lateral control requiring that positive damp¬
ing exist. Since the damping in rolling depends on a
positive slope of the lift curve, the damping exists only
at angles of attack of the outer portions of the wing that
are below the maximum lift coefficient. While some
semblance to control may be obtained at angles of
attack above the stall if controls giving favorable yaw¬
ing moments as well as sufficiently powerful rolling
moments are used, the instability associated with
uneven stalling and autorotation is so violent that it is
necessary for the pilot to use the controls continually to
keep the airplane near the desired attitude. If suffi¬
ciently rapid rolling is once started, either by the controls
themselves or as the result of gusty air, it cannot be
stopped. The angle of attack at which the damping in
rolling becomes zero and above which autorotation takes
place («lp= o) is used herein as an indication of the
limit of the flight attitude above which satisfactory
lateral control cannot be obtained. This value was
given in the reports of reference 1 for both the angle of
attack at which autorotation was selfstarting and the
angle of attack at which the damping became zero when
the wing was rotating at the rate pb/2V=0.05, a value
representative of the rolling likely to be caused by gusty
air. The latter value of a has ordinarily been found to be
about 1° lower than the former value and, being there¬
fore more decisive, is used in the present report. The
difference between the angle of attack for zero damping
and the angle of attack for the maximum lift coefficient
of the entire wing («lp=o has been tabulated
under Lateral Stability to show whether the maximum
lift coefficient can be expected to be reached in flight
before satisfactory lateral control is lost. It will be
noted that for ailerons 3 and 4 the wing loses its damp¬
ing in roll at an angle of attack 1° higher than that at
which the maximum lift coefficient is reached. Thus, as
far as the stability is concerned, lateral control should
be possible throughout the entire unstalled-flight range,
including the angle of attack for maximum lift coeffi-
cient.
WING PERFORMANCE CHARACTERISTICS
The same criterions used throughout the reports of
reference 1 to show the relative performance character-
istics of the wings are used in the present report and
are tabulated in the last three columns of table I.
The maximum lift coefficient CV is given as an
indication of the wing area required for a desired mini¬
mum speed. The ratio CLmjCDmin is an indication of
the speed range and, for a given minimum speed, shows
the relative effects of the wings on the maximum speed
attainable. The ratio LID taken at a value of the lift
coefficient (A = 0.70 is an indication of relative merit in
climbing flight. In a series of performance computations
made for airplanes of different wing loadings and power
loadings and with both plain and slotted wings, this
criterion was found to be satisfactory throughout the
entire range. It should be noted that the comparative
values used in the present report are based on tests made
in the 7- by 10-foot atmospheric wind tunnel and hence
do not coincide in absolute value with results of tests
made at different Reynolds Numbers.
APPLICATION TO AIRPLANES OF DIFFERENT SIZES AND LOADINGS
Because the flight experience that led to the specifi¬
cation of a satisfactory degree of control was restricted
to the Fairchild 22 type of airplane, there is some doubt
about the application of this experience to other types
and especially to large or very small airplanes. The
Fairchild 22 type of airplane, of course, serves as well
as any other when different aileron devices are simply
compared among themselves. The principles govern¬
ing the extension of the computations of motion to
geometrically similar airplanes of different sizes and
loadings are well known and can be applied here, but
this extension of the computations does not definitely
answer the question as to what constitutes a satisfactory
degree of control for large (or very small) airplanes.
According to the principles of dynamical similarity,
large or small similar airplanes of the same wing loading
would show the same linear rise and fall of the wing
tips during a 1-second banking motion. Large
and small airplanes do actually show a tendency toward
similarity in important dimensions and size of control
surfaces, and it seems logical to assume that a given
value of the vertical distance described by the wing
tips within 1 second following a sudden control deflec¬
tion that represents a satisfactory amount of control
for the Fairchild 22 airplane should be satisfactory for
any size of airplane.
For similar airplanes the linear distance described
by the wing tips in banking (^r *s independent of
the size. Figure 3 shows this distance plotted against
wing loading and gives the separate effects of rolling
and yawing moments of coefficient 0.01 at different
lift coefficients. The banking effect of any combination
of rolling and yawing moment may be found by
superposition, i. e.,
- Ct(
/(p\b\
L /
'4nb\
2
0.01'
\ 2 /cj= o.oi
1 0.01'
\ 2 /cn= o.oi
(1)
The ordinates of the figure give directly the circum¬
ferential displacement of the wing tip in feet for a
unit of 0.01 rolling- or yawing-moment coefficient.
It is important to note that the banking effects of
rolling and yawing moments can be separately con¬
sidered and later added in any desired proportion to
obtain the total combined effect.
610
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The computations show that, in general, smaller
values of the control-moment coefficients are required
to produce a given wing-tip displacement in a unit of
time for the more heavily loaded airplanes. Another
point of interest in connection with the secondary
adverse yawing moments produced by conventional -
VJing loading, lb. per sq. ft.
Figure 3. — Wing-tip displacement produced in 1 second by suddenly applied rolling
and yawing moments for different wing loadings and flight speeds.
•tb ^ Ci / 4>\b\ . Cn / <tn b\
2 =0.01 \ 2 / c-rooi 0.01 \2 ) c„- ooi
type controls is that these moments are more effective
in hindering the control with lightly loaded airplanes
than with heavily loaded ones. Note that in the usual
case the banking effect of the yawing moment is to be
deducted in equation (1) since this moment is usually
adverse and therefore negative.
The variation of control force with size and loading
of the airplane may be determined from general rules
as in the case of the variation of the amount of rolling
o
motion. As shown by figure 3, heavily loaded air¬
planes require smaller control-moment coefficients for
a comparable amount of control than do lightly loaded
airplanes. In general, a heavily loaded airplane that
is otherwise similar to a lightly loaded one will have
smaller control surfaces. On the other hand, the heav¬
ily loaded airplane will fly at a higher speed so that the
dynamic pressure will be greater. Figure 4 shows a
calculated example of the variation of stick force with
wing loading at a given lift coefficient and for a given
maximum amount of control. Here, as in figure 2,
the most efficient combination of size and deflection
is assumed for each point. Figure 4 shows that the
stick force required to obtain a given angle of bank in 1
second is practically the same for all wing loadings up
to 10 pounds per square foot but that it increases
somewhat as the wing loading increases further.
With moderately large airplanes, somewhat higher
stick forces are apparently tolerated by pilots without
serious objection. With extremely large airplanes,
however, the operating force becomes too great to be
satisfactorily overcome by the pilot and either servo
controls or auxiliary power is required. With auxil¬
iary power, the pilot might presumably operate a valve
or easily deflected controller governing a special power
—
!
/
F~22 fypt
? airplane.
>
/
0 10 20 30
Wing loading, /b.per sq. ft.
Figure 4.— Relation between the wing loading and the stick force required for a
given amount of control (<t> imoi=22.5°; Cl— 1.0).
source that deflected the control surfaces. Under such
conditions the magnitude and variation of the hinge
moments would be relatively less important and the
maximum deflection of the control surfaces would
very likely be determined by the maximum rolling and
yawing moments they could produce rather than by
the hinge moments and the resultant deflecting force
required. Although some indication of the relative
performance of the various lateral control devices
compared in this report can be obtained from the data
as given, it would be desirable to reanalyze the original
data given in references 1, 7, 8, 9, and 10 if a compari¬
son on the basis of ailerons operated by auxiliary power
were desired.
COMPARISONS OF VARIOUS DEVICES
PLAIN AILERONS
Effect of aileron and wing plan form. — The tests of
reference 1, part I, were made with rectangular wings
having ailerons of three different proportions: 0.25 cw
by 0.40 b\ 2 (which were taken as the standard for
comparison throughout the series), 0.15 cw by 0.60 6/ 2,
and 0.40 cw by 0.30 6/2. These sizes were selected to
give approximately equal rolling moments with the
same angular deflection. These ailerons are numbered
2, 3, and 4, respectively, in table I. With equal
up-and-down deflection, the stick force is much larger
for the short, wide ailerons than for the long, narrow
ones and is, in each case, slightly less for the low-speed
condition than for high speed. If a suitable differential
linkage is employed, the stick forces at the low-speed
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
611
condition, where the wide ailerons have the advantage
of a large floating angle, are quite low for all three
sizes of aileron. At the high-speed condition, however,
the 0.40 cw by 0.30 6/2 aileron requires a rather high
stick force, even with the best differential.
The sideslip incurred by an angle of bank of 15° in
1 second is not greatly different for the different aileron
plan forms either with or without differential linkages.
The values are slightly lower at CL~ 1.0 with the differ¬
ential linkages than with the equal up-and-down, and
with the 0.25 cw by 0.40 6/2 plan form than with either
of the others.
It is possible by methods to be described in section II
to compute an optimum size of the aileron, i. e., the size
giving the desired amount of control with the least stick
force. The effect of varying the aileron span and chord
is shown in figure 5, the chord for each span value being
Figure 5.— Variation of stick force with aileron span. Aileron chord proportioned
to give <t> i m „j-= 22.5° with maximum deflection of ±25° and ±20°; rectangular wing,
average airplane; Ct = 1.0; sealed ailerons.
the smallest that will give an angle of bank of 15° in 1
second with the assumed average airplane. From this
figure it is apparent that with equal up-and-down deflec¬
tion an aileron span of 80 percent of the wing semispan
will give the lowest stick force, but the variation is small
for ailerons between 60 percent and 100 percent of the
wing semispan. Other computations not shown lead
to the same conclusion for ailerons having differential
linkages.
The relations of aileron chord and span, considering
especially that the hinge moment increases with the
square of the chord while the rolling moment increases
only as the square root of the chord, are such that lower
stick forces are obtained with narrower chords. The
narrower ailerons require greater deflections and the
reduction in chord size is limited by the fact that
deflections greater than about ±20° are inefficient.
Marked separation of the air flow takes place at about
this angle of deflection on all the conventional flap-type
ailerons tested and, as shown by the typical curves of
figure 6, the rolling-moment coefficients increase at a
lower rate beyond 20° deflection. If it is attempted to
Aileron defleclion, <5 , deg.
Figure 6.— Typical rolling- and hinge-moment coefficient curves for plain ailerons.
reduce further the chord of the aileron by extending the
deflection beyond this break, the stick force will be
higher because of the loss in mechanical advantage.
Figure 5 illustrates this point, for when an aileron
deflection of ±25° is assumed, narrower ailerons are
required but the stick force is larger for all aileron spans
than with a deflection of ±20°.
Aileron 5 (table I) represents the narrowest sealed
aileron covering 80 percent of the wing semispan that
gives the required control with a deflection of ±20°.
The aileron chord in this case is only 5.3 percent of the
wing chord, and the stick forces are lower than for any
of the previous ailerons. If a differential motion is
used, a somewhat wider aileron is required. With
narrow ailerons the floating angle is very small, and a
tab is required to make the ailerons float at a suffi¬
ciently high angle that the differential linkage will be
effective in reducing the stick force. (See reference 11.)
Aileron 6 of table I is the smallest one covering 80
percent of the semispan that will give the required
012
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
amount of control with a differential motion and with
suitable aileron tabs. The assumed tab covers the
entire trailing edge of the ailerons, has a chord 1.5
percent of the wing chord, and is permanently bent
downward 14°. For this case the entire aileron chord
including the tab is 7.8 percent of the wing chord and
the stick force is only 0.5 pound for the high-speed
condition and 0.1 for low speed.
These values of stick force are lower than are con¬
sidered desirable for the Fairchild 22 airplane but are
interesting in showing the possibility of obtaining a
satisfactorily low stick force in larger and heavier
airplanes. For small airplanes, one satisfactory method
of increasing the stick force to the value desired would
be to use greater up travel than 20° with differential
ailerons, thus getting into the range of inefficient stick
force although obtaining the advantage of slightly
smaller adverse yawing moments.
In many practical cases the chord of the aileron varies
along the span. Inasmuch as the hinge moment varies
as the square of the chord and the control effectiveness
only about as the square root of the chord of an aileron
element, the stick force required to give a certain
amount of control is inherently greater if the chord of
the aileron varies appreciably along the span. This
relation is true in spite of the fact that the portion of
the aileron nearer the tip of the wing has a greater
lever arm, which suggests that it might be advantageous
to increase the chord of the aileron as the wing tip is
approached. Thus, it is possible to state as a general
rule that tc obtain the lowest stick force, ailerons should
have an essentially constant chord over their entire
span.1
On wings having rounded tips it is sometimes the
practice to use ailerons having skewed hinge axes like
aileron 7 in table I. This aileron corresponds in span,
area, and gap to the 0.25 cw by 0.40 6/2 aileron 2, but
the stick force is decidedly higher for the skewed ailerons
on account of the variation of the aileron chord along
the span.
Ailerons 8 and 9 of table I are of tapered plan form
and are mounted on tapered wings. In the computa¬
tions of the rolling effect with the tapered wdngs the
reduction in the moments of inertia due to the taper
are taken into account. For example, for the wing
with 5: 1 taper, the value of Ix was changed from 1,216
slug-feet 2 for the original average airplane to 860,
and the value of Iz from 1,700 to 1,400 slug-feet2. The
lateral-stability derivatives were also changed to take
account of the taper. (See reference 4.)
A comparison of ailerons 8 and 9 with aileron 1,
which has the same relative chord size but is attached
to a rectangular wing, shows that the stick force be¬
comes lower as the taper of the wing is increased. The
sideslip or adverse yawing effect is also smaller with
the tapered wings than with the rectangular. The
1 The greatest taper mathematically compatible with a minimum stick force is
ess than about 3 percent of the aileron chord.
lateral-stability factor, damping in roll, is reduced to
zero at an angle of attack 3° below the stall with the
5 : 1 tapered wing, indicating that the airplane could
not be safely maintained at the maximum lift condition
in flight.
The ailerons on tapered wings dealt with up to this
point have had chords that were the same percentage
of the wing chord at each position along the span, the
ailerons tapering with the wings. It has been stated
that the lowest stick force would be obtained with
constant-chord ailerons. Computations have been
made comparing the straight or constant-chord ailerons
on a tapered wing with the ailerons that taper with the
wing, and the results are shown in figure 7. The straight
5
=5
-4
<b
£
-sc
•2 3
V)
pr
nstc
(given
terms o
tip chore
Cons tan
percent
chord
7
f
\
—
*> ~
/ _
\
1
\
1
\
\
AHet
-on c
horc
/
\
\
\
\ ,/
'ing-
-tip c
- horc
/
• \
\
'
Ait
eron
cho
rd "
\
\
Wing
\ J
Y
o
d
\
\
S tick
- force
__ --r1
r '
N
\
\
'ST
— ____
y
/
/
y
for
<fi, =/5‘
\
\ \
✓
O .2 .4 .6 .8
Aileron span/ wing semispan
U
o
•8
A
|
Q
/$
' \
O
/.o
Figure 7. — Variation of stick force with aileron span and chord for straight and
tapered ailerons on 5:1 tapered wing. Aileron chord proportioned to give
22.5° with maximum deflections of ±20°; Cz, = 1.0; sealed ailerons.
or constant-chord ailerons require lower stick forces
for any given aileron span. It is interesting to note
that with tapered ailerons the aileron span giving the
lowest stick force is about half the wing semispan;
whereas with constant-chord ailerons the best aileron
span is 80 percent of the wing semispan, as it is in the
case of rectangular wings. Ailerons 10 and 11 are
the optimum sizes for the tapered and straight
ailerons, respectively, on a 5:1 tapered wing. With
equal up-and-down deflections, the stick forces for the
straight ailerons are about half those for the tapered.
In either case the stick forces could be nearly counter¬
balanced by means of a suitable differential linkage and
tab, as will be developed more fully in section II.
Effect of hinge gap. — Wind-tunnel tests have shown
that even a slight gap between ordinary unbalanced
ailerons and the wing upon which they are mounted
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
613
causes a relatively large loss in rolling moment. This
loss for unbalanced flaps having a gap of one thirty-
second inch on a wing of 10-inch chord was found to be
approximately 30 percent. The hinge moment is also
reduced by the gap but to a much lesser extent and the
resultant stick force for a given amount of lateral con¬
trol is greater because a larger aileron deflection is
required, which necessitates a linkage having a poorer
mechanical advantage. The effect on the stick force
is shown in table 1 by a comparison of the values for
aileron 2, which has a gap, with those for aileron 1,
which is sealed.
BALANCED AILERONS
unbalanced but sealed ailerons shows that the stick
forces at the low-speed condition are about the same
for both types of aileron, both with equal up-and-down
and with differential motion. At the high-speed con¬
dition the Frise ailerons have somewhat lower stick
forces than they have for the same control at low speed.
It is worthy of note that, although the deflections are
small in both cases, the Frise ailerons are apparently
not greatly oversized for, in their case, substantially
greater deflections would be inefficient. The plain
ailerons, on the other hand, have maximum deflections
well under the limiting 20° value and are decidedly
oversized, considering the amount of control specified.
Balanced ailerons of the Frise and Handley Page
types are widely used at the present time, the particular
forms of aerodynamic balance incorporated in these
ailerons giving improved yawing moments as well as
reduced hinge moments. Good results are obtained
with proper designs but the exact shape of these ailerons
has a critical effect on the rolling and hinge moments,
and each different installation is likely to require con¬
siderable individual development. Figure 8 shows
typical curves of rolling and hinge-moment coefficients
for Frise type ailerons. The rolling-moment coefficient
for the example shown increases less rapidly with de¬
flection after an upward angle of 7° to 10° has been
reached, which is considerably lower than the 20°
critical deflection for plain unbalanced ailerons (fig. 6).
Thus, it is uneconomical with respect to stick force to
use large up deflections and, owing to the smaller maxi¬
mum deflections, larger ailerons are required for effi¬
ciency than when ailerons of the plain unbalanced
sealed type are used. The break in the curve of rolling-
moment coefficient against deflection is associated in
the case of the Frise and Handley Page types of aileron
with the downward projection of the nose of the aileron
and the resultant breaking away of the flow from the
under side of the aileron. This effect can be reduced
or possibly eliminated by using a raised-nose portion.
The Frise and Handley Page types of aileron have
gaps between the aileron and the wing, and the effective¬
ness of the ailerons cannot be assumed equal to that of
smoothly sealed flaps.
The hinge-moment curves as shown in figure 8 have
very low' and even negative slopes at places, and ex¬
treme differential linkage cannot be used because over¬
balance would occur with medium or small deflections
of the up aileron. Because the hinge-moment curves
are far from straight, it is more difficult to select suit¬
able differential linkages for ailerons of this type than
for plain unbalanced ailerons. Satisfactory linkages
have often been obtained in practice, however, and there
are many excellent examples in which a nice balance
of conditions has been obtained with satisfactory con¬
trol and light stick forces.
Ailerons 12 and 13 are examples of the Frise type.
A comparison of aileron 12 with the same size of plain
Figure 8. — Typical rolling- and hinge-moment coefficient curves for Frise ailerons.
If a fixed tab is used to trim the ailerons upward,
lower values of stick force can be obtained with the
plain unbalanced ailerons (reference 11). The tab will
not give the same improvement with the Frise ailerons
because of the varying slopes of the hinge-moment
curves.
The 0.40 cw by 0.30 6/2 Frise aileron 13 has a different
sectional form than aileron 12 in that the nose portion
is raised, and this aileron gives smoother curves of roll¬
ing and hinge-moment coefficients. The Frise aileron
with the raised nose show's no improvement in yawing
effect over the plain unbalanced ailerons of the same
size, but the 0.25 cw by 0.40 6/2 Frise aileron, which has
the more typical Frise sharp nose, gives a slight im¬
provement in this respect.
The drag of all commonly used forms of Frise and
Handley Page ailerons is sufficiently great to be •'Con¬
sidered a serious disadvantage .in connection w'ith
614
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
modern high-performance airplanes. For this reason,
the development of a type of aerodynamic balance that
does not add to the drag is desirable.
FLOATING-TIP AILERONS
•Conventional ailerons operating on a lifting portion
of the wing suffer several fundamental disadvantages.
First, the production of rolling moment by a lifting
wing gives rise to the adverse yawing moment; and,
second, the loss of lift at the stall is accompanied by a
loss of effectiveness of the ailerons. It has become ap¬
parent during the investigation, however, that the stall
of the wing or, at any rate, of the outer portions of the
wing, is accompanied by such a loss of stability that it is
hardly an advantage to retain aileron rolling moments
in this condition.
In the case of floating-tip ailerons, control is secured
by surfaces that contribute no lift. This arrangement
avoids both the adverse yawing moment of ordinary
ailerons and the loss of rolling moment associated with
stalling of the main wing; but it increases the drag of
the airplane and adds to the over-all dimensions. If
the airplane is designed to fulfill certain performance
specifications, such as landing speed, climb, ceiling, etc.,
the floating-tip ailerons cannot be considered an integral
part of the main wing as they do not contribute effec¬
tively to the area or span so far as induced drag and
lift are concerned.
A number of floating-tip aileron devices were tested
in the course of the investigation of reference 1. Ap¬
parently the most usable of these are the tip ailerons on
the 5:1 tapered wing. Two methods of comparison
have been followed. In one case (aileron 14) the ail¬
erons were included within the over-all dimensions of
the 5:1 tapered-wing average airplane. The values
given in the table for this case (short wing) were based
directly on the results of tests made in the 7- by 10-foot
wind tunnel (reference 1, part XI). The criterions
show the effect of reduced area and span of the lifting
portion of the wing as a reduction of the climb and
maximum lift.
In order to take account of the effect of simply
adding a tip aileron to a normal-size wing, further cal¬
culations were made. In this case (aileron 15) it was
assumed that the over-all span of the average airplane
was increased by the additional span of the tip ailerons;
hence, the aspect ratio of the lifting portion of the wing
remained the same. The added span of the wing, al¬
though it contributed practically no lift and hardly
modified other stability characteristics of the airplane,
considerably increased the damping in rolling. This
fact was accounted for in the computations, data on
damping of the tested 5:1 tapered wing with floating-
tip ailerons included in the original plan form being
extrapolated for this purpose. It would be natural to
assume that the floating-tip ailerons would be just as
effective as the main portion of the wing in contributing
damping. The tests showed, however, that the damp¬
ing of the 5:1 tapered wing with floating tips was only
85 percent of that with the tips rigid.
The rolling moments produced by floating-tip
ailerons can be predicted with good accuracy by the
conventional aileron theory. The induced yawing
moments correspond to those given by plain ailerons
with an extreme uprigging or negative droop corre¬
sponding to the neutral floating positions of the tip
ailerons. Ordinarily, the tip ailerons, on account of
the local upwash at the end of the rigid wing, float at a
negative angle, of attack relative to the mean direction
of flight and hence give slight favorable induced yawing
moments with respect to the wind axes. The yawing
and hinge moments used in table I for the long-wing
airplane (aileron 15) were predicted from the results
of the wind-tunnel tests on the short 5:1 tapered wing.
The tabulated results of the computations show that
the stick forces recpiired for satisfactory control are
reasonably low in the case of the short 5:1 tapered wing.
It will be noted that only relatively small deflections of
these ailerons are required for control, a fact that can
be attributed partly to the reduced damping in rolling
shown by this wing. On the other hand with the long
wing, when the tip ailerons were added to the regular
wing span, the damping in rolling and moment of
inertia were increased and, hence, larger stick forces
were required to produce the given bank. The same
hinge-axis location, and hence the same degree of
balance of the ailerons, were assumed in both cases.
It will be noted that about the same force was required
to produce 15° bank at high and low lift coefficients.
Although the floating-tip ailerons give small favor¬
able yawing moments, it will be noted that their use
results in some inward sideslip during the 15° bank.
The rolling motion of the wing induces a small adverse
yawing effect as is indicated by the adverse sign of the
yawing moment due to rolling. This cause combined
with the inward acceleration due to gravity is sufficient
to bring about the inward sideslip in spite of the favor¬
able yawing moment of the floating ailerons.
It has often been suggested that tip ailerons be
trimmed by tabs so as to float downward and give
some lift. Such an arrangement should improve the
performance characteristics but would void the advan¬
tage of these ailerons in giving favorable yawing
moments. If the tip ailerons were trimmed so as to
produce as much lift as the adjacent rigid portion of
the wing, it is to be expected that they would show the
same proportion of adverse yawing moment to rolling
moment as do conventional ailerons.
At stalling angles of attack for the main wing the
floating tips remain unstalled. Hence, they should be
expected to aid in preventing the loss of damping in
rolling at or near the stall. The only floating aileron
device that effectively prevented the loss of damping in
rolling in the wind-tunnel experiments was the long nar-
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
615
row aileron attached to a rectangular wing. (See refer¬
ence 1 , part XI.) In this particular case the performance
characteristics were so poor that the device as tested
could not be considered practical for application.
As noted in table I, the lateral-stability character¬
istics of the 5:1 tapered wing with the floating-tip
ailerons are almost as bad as those on the conventional
rigid 5: 1 wing and are somewhat worse than those of
the rigid rectangular wing. Inasmuch as the damping
in rolling is lost at an angle of attack 2° below the
angle for maximum lift, the airplane could not be safely
maintained in flight above this angle even though the
ailerons continue to give undiminished rolling moments.
Flight tests of floating-tip ailerons on a tapered wing
fitted to a Fairchild 22 airplane support this conclusion.
Wind-tunnel results with floating-tip ailerons showed
a smaller adverse effect on the performance character¬
istics of the 5: 1 tapered wing than on any of those
tested. The effect of reducing the span and area of
the rigid portion of a given wing is shown by the
comparison of the performance criterions of the short
5:1 tapered wing, having an over-all aspect ratio of 6,
with those tabulated for the conventional rigid 5:1
tapered wing, having the same over-all span and area.
Here the maximum speed of the airplane will be hardly
affected while the climb and maximum lift will be
reduced, as indicated. Simply adding the tip portions
to the normal-size wing will increase the parasite drag
at high speed but, as shown by the tabulated criterions
for this case, will probably slightly improve the climb.
SPOILERS
Spoilers in the form of small flaps or projections
raised from the upper surface of the wing have pre¬
sented attractive possibilities as lateral control devices
because they give positive or favorable yawing moments
and large rolling moments at the high angles of attack
through the stall. (See fig. 9.) As spoilers giving
apparently satisfactory rolling and yawing moments
had been developed in the 7- by 10-foot wind-tunnel
investigation (reference 1, part V), they were tested
in flight on a Fairchild 22 airplane (reference 2). When
the spoilers were first tried in flight, the pilots noticed
that the airplane apparently did not react until the
control stick had been given a medium amount of
deflection, after which the rolling velocity suddenly
built up to a much higher value than had been experi¬
enced with any previously tested control system.
This characteristic made it impossible to perform
smooth maneuvers requiring the coordination of the
spoilers with the elevator or rudder and led to over¬
controlling when an attempt was made to keep the
wings level in gust}7 air. Closer inspection of the
spoiler action, however, disclosed that for any spoiler
movement there was actually an appreciable delay
between the movement of the spoiler itself and the start
of the desired rotation in roll of the airplane. In
order to substantiate the pilot’s findings, records were
made of the rotation of the airplane in roll immediately
following a movement of the stick and a specimen
Figure 9. — Comparison of rolling- and yawing-moment coefficients obtained with
ailerons and spoilers.
time history of the motion is shown in figure 10, to¬
gether with similar information for other lateral con-
Figure 10. — Bank curves derived from flight records illustrating response charac¬
teristics of various lateral control devices.
trol devices including conventional ailerons. The
records showed that the delay before rotation started
616
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
in the desired direction was of the order of half a second.
This lag seems surprisingly short to have much effect
on the control obtained with spoilers, but apparently
it is sufficient to prohibit the use of the spoilers close
to the ground because of the danger of overcontrolling.
The lag of spoilers was then studied by means of a
special hinged wing model of 4-foot chord mounted
in the 7- by 10-foot wind tunnel (reference 12). This
installation reproduced the conditions encountered in
the flight tests. The tests with spoilers located in
different positions along the chord of the wing showed
that the lag was relatively large with the spoilers near
the leading edge and became less after the spoiler was
moved to the rear until it was zero for normal trailing-
edge flap-type ailerons.
The spoiler located near the rear of the wing was
found to act with a negligible amount of lag (less than
one-tenth second could not be detected by the pilots)
and seemed to give some promise of making a satis¬
factory lateral control device. Flight tests were there¬
fore made of a retractable spoiler located 83 percent
of the wing chord back of the leading edge which,
because of its rearward position, was referred to as a
“retractable” aileron. The aileron was made in the
form of a plate curved in a circular arc to form a seg¬
ment of a cylinder and was moved in and out through
a slit in the upper surface of the wing and about an
axis at the center of the cylinder. This arrangement
produced no aerodynamic hinge moment and was
found to operate satisfactorily in flight on a Fairchild
22 airplane (reference 3). The retractable aileron
mounted on the assumed average airplane is number
16 in table I. The stick-force characteristic (zero
force) is not the most desirable but could be brought
up to a desired value either by the addition of a spring
in the aileron linkage or by an off-center location of
the hinge axis of the aileron. A large amount of con¬
trol is available from ailerons of this type and the
yawing characteristics are more satisfactory than those
of conventional ailerons.
Combinations of conventional ailerons with spoilers
located ahead of them and deflected simultaneously
showed some promise in the wind-tunnel investigation
(reference 1, part V) and were found to give satis¬
factory control free from lag when tested in flight on
the Fairchild 22 airplane (reference 2). With the
spoiler deflected in front of the aileron, the floating
angle of the aileron is raised and, if properly developed,
certain combinations seem very promising in regard to
both yawing effect and stick force. Estimated char¬
acteristics of one such combination are given in table I,
aileron 17.
Another possible combination that has been tested
and may deserve further development is one in which
two spoilers are located in tandem and deflected simul¬
taneously. The tests with this arrangement (reference
12) showed that the lag of the combination was no
greater than that for the rear spoiler alone, whereas the
final rolling moment was the same as for the front one
when used without a flap. Later tests indicate that
spoilers located on the forward portion of the wing
may be rendered ineffective by the action of a split
flap. One other point has not yet been completely
determined, namely, whether the rolling motion would
get under way with sufficient acceleration immediately
after the start. This point will be dealt with further in
the next section on slot-lip ailerons.
SLOT-UP AILERONS
Means for the elimination of the lag of spoilers were
investigated in the 7- by 10-foot tunnel and it was found
that the lag could be eliminated by providing a slot or
passage through the wing back of the spoiler. This
investigation has resulted in the development of what
have been termed the “slot-lip” ailerons (references 8
and 12). The slot-lip aileron is a combination of a
spoiler- type flap located on the upper surface of the
wing and a continuously opened slot, the flap forming
the upper portion or lip of the slot. The computed
control performances for two arrangements of slot-lip
ailerons in different positions along the chord of the
wing are listed 18 and 19 in table I.
The slot-lip ailerons satisfactorily eliminate or reduce
to a negligible value the actual lag intervening before
the wing starts moving in the desired direction, and
they give a very high maximum rate of rolling; but the
rolling nevertheless increased less rapidly immediately
after the start of the motion than with conventional
trailing-edge flap-type ailerons. This condition is
illustrated in figure 10, which includes curves from
flight records of slot-lip ailerons on the Fairchild 22
airplane and slot-lip ailerons on the Wl-A airplane.
It will be noticed that with the Wl-A the rate of roll
increases nearly as rapidly as with conventional ailerons
but with the Fairchild 22 the action was considerably
more sluggish. The differences in the behavior of these
two airplanes have been studied (reference 8) and it
has been concluded that the superior response character¬
istics shown by the Wl-A are due in large measure to
the relatively great dihedral (5°) and to the smaller
moments of inertia of this airplane. The secondary
yawing action of the slot-lip ailerons is favorable, hence
the dihedral effect increases the rolling action. Other
differences favorable to improved response of the
Wl-A are: (1) The more rearward location of the
aileron (0.30 cw compared with 0.20 cw tested on the
Fairchild 22) and (2) the slightly greater size of the
slot.
The lateral control with the slot-lip ailerons on the
Wl-A seemed satisfactory to the pilots, but on the
Fairchild 22 it was found to be too sluggish and to give
somewhat the same feeling as a slight amount of lag.
This comparison, aided by several others of a pertinent
nature, indicates that an additional point must be
RESUME AND ANALYSIS OF N. A C. A. LATERAL CONTROL RESEARCH
covered in a specification for a completely satisfactory
lateral control dealing with the acceleration or rate at
which the rolling increases during the first half second
or so following the actual start. It may be stated in
simple quantitative terms, applying to the conditions
for the assumed average airplane, that the angle of
bank one-half second after a sudden deflection of the
controls should be at least one-third the angle of bank
reached at 1 second. Thus, if a bank of 15° is reached
in 1 second, at least 5° of this should be attained in the
first half second.2
The sluggishness of the slot-lip ailerons is a great
handicap in the method of comparison of control effec¬
tiveness used in the present report, in which a certain
angle of bank must be obtained in a time of 1 second.
Even though these ailerons give a high final rate of roll,
excessively great deflections are required to attain an
angle of bank of 15° in 1 second at a lift coefficient of
1.8, and the stick forces are excessively high. This
particular disadvantage might be overcome by the use
of a suitable aerodynamic balance but, even so, the
sluggishness of the slot-lip ailerons might prevent them
from being considered satisfactory if it were of the
magnitude found on the Fairchild 22 instead of that
found on the Wl-A.
The sideslip accompanying a 15° bank in 1 second is
negligible with the 0.55 cw slot-lip ailerons in the usual
flight range with unflapped wings. With more forward
locations the yawing moment becomes decidedly posi¬
tive, resulting in outward sideslip. Because of the
action of the slots at high angles of attack, the damping
in rolling is retained to an angle of attack beyond that
for maximum lift coefficient and, for this reason, it
should not be difficult to design an airplane incorporat¬
ing these ailerons in such a manner that lateral control
and stability would be reasonably satisfactory at all
angles of attack that could be maintained in flight.
The continuously open slot, however, results in a high
drag, which reduces the high-speed and climbing per¬
formance to a noticeable extent. The drag is less for
the rear positions of the slot-lip ailerons and a special
investigation has been made in the 7- by 10-foot tunnel
to develop slots with reduced drags. Some success has
been attained but, considering the best results to date,
these ailerons do not seem suitable for modern high-
performance airplanes.
LATERAL CONTROL WITH HIGH-LIFT FLAPS
Since the inception of the research program of refer¬
ence 1 , wing flaps have come into very general use and
have further complicated the problem of lateral control.
In steady flight ordinary ailerons give rolling moments
that vary almost inversely with the lift coefficient;
hence, wings equipped with higli-lift devices require
2 As mentioned previously, in order to simplify the computations and to make
possible a comparison with flight records, the starting time has been arbitrarily taken
s the instant at which the control surfaces reached half their final deflection.
017
relatively large control surfaces. The installation of
an effective flap then becomes more difficult.
Another problem introduced by the use of liigh-lift
devices concerns the adverse yawing moment of the
ailerons. The ratio of induced yawing to rolling
moment increases (adversely) in direct proportion to
the lift coefficient. Furthermore, the effect of a given
yawing moment on the rolling control is usually greater
with flaps in use on account of the increased dihedral
effect due to the flap. Thus it appears almost neces¬
sary to use some device that causes large changes of
profile drag resulting in a favorable component of yaw¬
ing moment or to use wings with washout at the tip
portions (partial-span flaps) so that the induced yawing
moment is reduced. Many of the devices developed
in reference 1 for use with full-span flaps show satis¬
factory yawing moments on account of the profile-drag
increments caused. Comparisons of a number of the
most promising devices have been made and are listed
in section B of table I.
Plain ailerons on wings with partial-span flaps. — On
account of the general use of partial-span split flaps
with ordinary ailerons, some tests of this arrangement
were made in the 7- by 10-foot wind tunnel (reference
7). The tests were made with tapered wings because
they represent the most efficient application of the ar¬
rangement and are most used in practice. The most
interesting result of these tests was the small loss of
maximum lift coefficient entailed by the substitution of
ailerons for the tip portions of the flap, particularly in
the case of ailerons 21 and 23 as listed in table I, where
only 30 percent of the semispan was used for the aileron
portion. The indicated reduction amounted to less
than 10 percent of the maximum lift shown by the same
tapered wings with full-span split flaps. The reduction
was about the same for the two taper ratios tried. It
will be noted that the 5:1 tapered wing gave more
efficient control as regards stick forces under all condi¬
tions. In each case the stick force is slightly less for
the longer ailerons, although of course the wings with
shorter ailerons showed better performance character¬
istics. Both sizes of ailerons on the 5:1 tapered wings
showed a marked diminution of effectiveness above
about 10° angle of attack, presumably due to flow
separation at the tip portions.
The deflection of the partial-span flap introduces a
large relative washout of the aileron portions so that at
a given over-all lift coefficient the ratio of yawing to
rolling moments is less with flap down than with flap
neutral. It will be noted that the tabulated values of
sideslip remain about the same at CL=1.8 as at CL= 1.0.
The sideslip at CL=l.O would have been appreciably
less than indicated if a flap-down condition had been
assumed here.
Although the lateral-stability characteristics of the
highly tapered wing are unfavorable, there are indica-
618
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
tions that the use of a partial-span Hap may not ag¬
gravate the instability in every case. The results of
the aileron tests, as well as visual observations of the
flow by means of tufts, show that the effect of the up-
wash at the tips introduced by lowering the flap may
be compensated by a strong spanwise flow, which
inhibits the stalling of these portions. The indications
are that the angle of attack for autorotational instability
would be about the same with the flaps as without for
the wings tested, although rolling experiments were not
tried.
Plain ailerons with retractable flap. — A plain aileron
with a split flap retracting ahead of it was developed as
a means of control with a full-span flap. This device
has been tested in flight with a modified Fairchild 22
airplane and is one of the few lateral control systems
incorporating full-span flaps that has proved entirely
satisfactory in flight (reference 3). This device is so
designed that the retracted flap does not interfere with
the ailerons in any way and hence the control char¬
acteristics with flap neutral are those of plain ailerons.
With the flap deflected, however, the characteristics are
similar to those of the upper-surface ailerons tested in
the 7- by 10-foot wind tunnel (reference 1, part XII).
Although the deflected flap is in such a position as to
shield the under surface of the ailerons entirely, it was
observed in the tests that the ailerons in this condition
were nearly as effective as conventional ailerons with
unsealed gaps. The effectiveness of downward deflec¬
tion, however, falls off rapidly at an angle of about 8°.
The rolling-moment characteristics of the plain
ailerons with retractable flaps are such as to favor a
differential motion, since the upgoing aileron is more
effective than the downgoing one at high lift coefficients.
The hinge-moment characteristics are, however, dis¬
tinctly unfavorable for this mode of operation inas¬
much as the ailerons show a downward floating tend¬
ency with the flap down. Relatively large deflections
of the ailerons are required to meet the control require¬
ments at low speed on account of the shielding effect of
the flap, and consequently a relatively high gearing
ratio of ailerons to control stick is needed. The result
is that the stick forces required for the specified banking
control are somewhat higher than those for conventional
ailerons throughout the flight range. These forces (see
aileron 24, table I) are well within the desirable range
for the Fairchild 22 airplane, although they indicate
undesirably high values for larger airplanes.
The yawing action of these ailerons is about the same
as that of the conventional ailerons with partial-span
flaps. Although the induced yawing moment of the
ailerons with the full-span flap is greater than that with
the partial-span flap, the ailerons cause larger com¬
pensating changes of profile drag.
Several possible means of improving the control-force
characteristics of these devices suggested themselves.
The device listed next in table I (aileron 25) shows the
calculated effects of such improvements. First, the
span of the aileron was increased to what has previously
been found the most efficient value and the chord of the
aileron was reduced as much as seemed practical.
Second, it was assumed that a trailing-edge tab (0.02
cw bent down 15°) was attached to the aileron so as
to avoid the downward-floating tendency. It was
assumed that lowering the flap caused the same change
in floating angle with the tab as without. Since the
deflection of the flap caused a large change in the
floating position of the aileron, it was desirable to
change the balancing characteristics of the differential
with flap deflection. Consequently, it was assumed
that the differential cranks were rotated into new
positions as the flap was deflected. The resulting stick
forces tabulated give an indication of the improvement
that might be effected by such development of the
device.
Retractable ailerons (spoilers). — Tests of spoilers
(reference 12) showed that for locations behind about
80 percent of the wing chord the lag in rolling action
would probably be negligible. Flight tests were subse¬
quently made of a Fairchild 22 airplane equipped with a
curved-plate spoiler that moved edgewise into and out
of the wing through a narrow slit in the upper surface
at 83 percent of the airfoil chord. This plate was
arranged to rotate about a hinge at the center of curva¬
ture, so that the air pressure (being normal to the plate)
caused no resultant hinge moment. The test airplane
incorporated a full-span split flap and, inasmuch as the
downward motion of the spoiler took place entirely
within the wing, the flap and spoiler did not interfere.
The flight tests showed very promising results, al¬
though the feature of zero hinge moment was not
found especially desirable. Angular-velocity and con¬
trol-position records taken simultaneously in flight
showed no definite lag or sluggishness in the response
to control movements. (See reference 3.) The devices
as tested (0.15 cw by 0.50 5/2) were somewhat larger
than necessary to give the assumed satisfactory degree
of control. As is indicated in the table, a maximum
deflection causing a 7.4 percent cw projection of the
spoiler should be sufficient for control in the flap-down
condition.
An important advantage of the retractable ailerons
(aside from their advantage in permitting the use of a
full-span flap) is that they give small favorable yawing
moments throughout the greater portion of the flight
range. At high lift coefficients with the flap in use,
however, small adverse yawing moments result. (See
reference 13.)
Although the deflected spoiler causes quite an increase
of profile drag, it is not expected that the incidental
deflections required for control in normal flight would
appreciably affect the performance. The performance
criterions listed are, of course, for undeflected controls.
External-airfoil flap-type ailerons. — The external-
airfoil (Junkers or Wragg) type flap has been studied
as a possible means for improving the take-off and
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
619
ceiling characteristics of airplanes in addition to pro¬
viding the high-lift features of ordinary and split
flaps. As this device showed promise of improved
performance, several methods of securing lateral control
with such a flap have been studied.
A simple method of providing lateral control with
full-span external-airfoil flaps is to move the flaps
themselves independently as ailerons. (See reference
10.) Thus the ailerons are used simultaneously as a
high-lift device and to provide rolling moments without
sacrificing a special part of the wing span. In order to
employ these flaps to their best advantage, it is neces¬
sary to deflect them downward over the entire wing
span, thereby avoiding excessive induced drag. The
action of the flaps deflected downward as ailerons is
similar to the action of ordinary ailerons with droop.
The external-airfoil flaps show a superiority over ordi¬
nary flaps for this purpose, however, in that they
retain their lift-changing effectiveness at greater
downward deflections (in excess of 20°).
Aileron 27 in the table is an arrangement of these
flaps whereby the entire span is deflected downward
20° and the semispan portions are moved differentially
from this downward position to provide rolling control.
This arrangement was tested in flight with the
Fairchild 22 airplane and was found to give unsatis¬
factory yawing characteristics, although the rolling
moments seemed to be ample. The computations
made for the average airplane indicated an adverse
sideslip of 10° accompanying a 15° bank at low speed
with the flaps down.
A possible way of improving the adverse-yaw char¬
acteristics of these devices is to make use of the effect
of washout. This method was used in the case of
aileron 28, where the flap was considered to extend
unbroken over the middle portion of the wing with the
parts of the flap used as ailerons covering the outer 50
percent of the semispan portions. Wind-tunnel tests
(reference 10) showed that, with the inner portion
down 30° and the outer, or aileron, portions down only
10°, the performance criterions were about the same
as with the whole flap down 20°. This change re¬
duced the yawing effect considerably, as shown by the
table, although the sideslip is still somewhat worse than
is the case with most of the other devices.
When the stick forces and deflections for these two
arrangements are compared, it will be noted that the
deflection required with the full semispan aileron is
almost as great as that required when only half the
flap is used for control. This fact is partly accounted
for by the difference in yawing effects.
In the low-speed conditions (Cz, = 1.8) the ailerons
are lowered 20° in one case and 10° in the other and
the effective floating angles are thereby increased by
these amounts. This fact introduces a difficulty into
the design of a suitable differential linkage. A linkage
designed to accommodate the floating tendency with
flaps neutral will overbalance when the flaps are
deflected. In the computations it was assumed that the
additional floating tendency was neutralized by a long
spring that came into action as the flaps were lowered.
The external-airfoil flaps permit high lift coefficients
to be attained without excessive profile drag. The
advantage over a split flap begins to be apparent at
lift coefficients in excess of 0.7, aiding the take-off and
the low-speed climb but hardly affecting the maximum
rate of climb. Hence, in this particular case, the per¬
formance criterions listed in table 1 do not fully indicate
the differences to be expected with these devices.
Ailerons with external-airfoil flaps. — A logical exten¬
sion of the development of the slot-lip aileron has led
to a device in which the aileron forms the lip of the
slot between an ordinary external-airfoil-type flap and
the main wing. (See aileron 29, table I.) This
arrangement avoids the excessive drag entailed by
other forms of slot and, on account of the rearward
position of the aileron, should give good response
characteristics (except, possibly, under certain condi¬
tions noted later).
The device as tested (see reference 9) comprised an
aileron 0.12 cw wide and 6/2 long. The tests showed
that, in general, the effectiveness of the aileron was
reduced by the presence of the flap, in accordance with
the theoretical consideration that any change in slope
of the wing section ahead of the trailing edge is less
effective than a corresponding change at the trailing
edge itself. When the flap is lowered, however, an
upward deflection of the aileron apparently causes
separation of flow over the flap, thus greatly reducing the
lift and developing a large rolling moment. With
the flap down 30° this change occui’s at the beginning
of the aileron deflection, while at intermediate flap
deflections the change occurs at greater up aileron
angles. This more or less sudden change of conditions,
in addition to giving a large increase of rolling moment,
also caused a reduction or a reversal of hinge moment;
hence, the device may be impracticable for use at
intermediate flap settings. (See reference 9.)
In the device as shown in table I the downward deflec¬
tion of the aileron is limited by the presence of the flap
nose to a maximum of about 7°, and it is consequently
necessary to use a differential movement. Change of
setting of the flap lias a pronounced effect on the
floating angle of the aileron. With the flap set at 30°
a differential giving no more than 7° downward deflec¬
tion of the aileron will be overbalanced by this floating
tendency. In the computation it was assumed that a
spring tending to turn each aileron downward (with a
torque of 8.7 foot-pounds acting at the aileron hinge)
was brought into action by lowering the flap. With
the flap neutral the floating angle of the aileron is too
small for satisfactory balance, although wind-tunnel
tests showed that it could be effectively increased by a
tab. Consequently, the device was assumed to incor-
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
620
porate such a tab (0.018 cw, down 5°) and the spring
tension was adjusted to accommodate the effect of the
tab with flap down.
The resulting stick forces, together with the deflec¬
tions required for control, appear in the table. It will
be noted that the greatest deflection required is that at
CL= 1 .0. In this condition the aileron does not produce
the previously discussed change in flow over the flap.
At (7/,= 1.8 the deflection required is small because a
small upward movement of the aileron in the flap-down
condition produces a large rolling moment. The yawing
effect is adverse but is not excessive.
The performance characteristics of this wing (with
the N. A. C. A. 23012 airfoil flap) are somewhat better
than those of the two wings previously considered,
which had flaps of Clark Y section.
II. ANALYSIS OF CONVENTIONAL FLAP-TYPE
AILERONS
The practical advantages of plain ailerons are well
known and, since they are universally used in more or
less modified form, the following section is devoted to
an analysis of factors involved in their design.
One of the conclusions of the lateral control investi¬
gation has been that no decisive benefit was to be
gained from a device that continued to give rolling
moments when the major outer portions of the wings
were stalled. If stalling of the aileron portions of the
wing is prohibited, plain ailerons or other devices
located near the trailing edge of the wing will retain
their effectiveness.
If the loss of rolling effect on a stalled wing is dis¬
counted, it appears that the primary disadvantage to
be associated with plain ailerons is their adverse yawing
effect. For this reason the yawing action of plain
ailerons will be rather fully analyzed.
ROLLING MOMENT
For the purpose of calculating the coefficients of
rolling and yawing moment, the effect of a deflected
aileron may be ascribed to a change of angle of attack
of the wing sections comprising the aileron portions.
Thus, the localized effect of the deflected aileron is
measured by the change in the angle of zero lift. This
change is proportional to the angle of deflection of the
aileron for deflections below about ±20° and the factor
of proportionality (denoted by Aa/A8) depends on the
chord of the aileron. Thus, the plain flap-type aileron
is considered merely as a device for changing the angle
of attack. The section lift increment is not used to
characterize the effect of the flap because this increment
cannot, in general, be specified, being dependent on the
plan form of the wing. The effective change in angle
of attack per unit change of flap deflection is, however,
theoretically independent of the aspect ratio and the
plan form.
Figure 11 summarizes the results of a number of
wind-tunnel experiments with plain flaps (references
14, 15, and 16) and shows the measure of flap effec¬
tiveness (Aa/A8) as a function of the relative flap
chord. A curve predicted by wing-section theory
(reference 17) is also shown for comparison. The sur¬
prisingly powerful effect of a narrow flap should be
noted. Thus, deflecting a 0.20 cw flap is about half as
effective as deflecting the entire wing section.
Since the effective angle of attack of a wing section
is a linear function of the camber (reference 17), the
curve of figure 11 may be used to predict the effect of a
multiply hinged flap, such as an aileron equipped with
a balancing tab. The combined effect of a succession
of bends along the wing section may be found by
calculating the separate effects of each bend and
adding them. Thus the effect of a 0.20 cw aileron equipped
with a 0.05 c,w tab is (using values from fig. 11)
Ao; = 0.515a + 0.215r (2)
where 8a is the deflection of the aileron with respect to
the wing and 8t is the deflection of the tab with respect
to the aileron. This simple relation should not be
expected to apply beyond ±20° deflection and, in the
case of very narrow tabs, beyond about ±15°
Deflected ailerons thus cause, in effect, a discon¬
tinuous change of angle of attack across the wing span.
The lift change caused by the ailerons cannot be dis¬
continuous, however, because of the natural equaliza¬
tion of pressure along the span. Ailerons covering
only a portion of the span influence the lift at every
span wise point and this effect appears to be satisfac¬
torily predicted by the airfoil theory. Calculations of
the effects of ailerons based on this theory have been
made, the most extensive series being reported in
reference 18. Figure 12 shows the rolling-moment
coefficient Cx caused by a 1° difference in angle of
attack of various right and left portions of a rectangu¬
lar wing of aspect ratio 6. The abscissa of this dia¬
gram represents a semispan of the wing with the
midspan point at the origin and the tip at the point
1.0. The ordinate gives directly the rolling- (or
yawing-) moment coefficient due to a unit change of
angle of attack extending from the point indicated on
the abscissa out to the tip. The rolling effect of two
ailerons is twice as great as that of a single one and
hence the difference of the increments of equivalent
angle of attack, as indicated, should be used. The
rolling moment is not appreciably changed by differ¬
ential deflection.
The curves give the values predicted by the theory
and the points indicate values obtained in various
experiments as noted on the figure. The wing-section
characteristic Aa\A8 of the devices tested was deter¬
mined from figure 11.
t>\ t>
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
621
.90
o N.A.C.A- 7- by 10- foot funnel; R = 609,000
_ ( reference 16) | | I | | i
" o British A.R.C. Compressed- oir funnel; R = 4,000,000
C referencelA ) ) I I I I I
v N.A.C.A. Variable- density tunnel R= 4,000,000
( reference 15)
0 .04 .08 J2 .16 .20 .24 .28
Aileron chord /wing chord
Figure 11.— Change of effective angle of attack of a wing section per unit change of
flap angle. Plain flaps of various chords at small deflections; c5<±2 0°.
Figure 12. — Variation of rolling- and yawing-moment coefficients with aileron span
and a comparison of theoretical and experimental values. Rectangular wings;
62/S=6; A5<±20°.
The rolling-moment characteristics of the plain 0.25 cw
by 0.40 6/ 2 sealed ailerons (aileron 1 of table I)
were calculated with the aid of figures 11 and 12.
Reference to figure 11 shows that the equivalent
change in angle of attack produced by a 0.25 cw sealed
flap is 57.5 percent of the angle of deflection of the
flap. Thus, a deflection of ±7.4° (see table I) is
equivalent to a change in angle of attack of
0.575X7.4°=4.26° (3)
or a difference of angle of the right and left aileron
portions of 8.52°. According to figure 12 the rolling-
moment coefficient per degree of this difference for a
0.40 6/2 aileron portion extending to the wing tip is
0.0039; hence, the coefficient predicted is
<7i=8.52X0.0039 = 0.0332 (4)
Working charts for predicting the rolling moment of
plain ailerons of any size on monoplane wings of
various aspect ratios and different degrees of taper are
given in figure 13. In order to use these charts it is
necessary to ascertain from figure 11 the section
characteristic Aa/A8, which is a function of the relative
chord of the aileron. The charts may be used for
differential ailerons merely by taking the difference of
angle of attack of the right and left aileron portions.
The theoretical rolling moment is independent of any
initial washout of the wing sections along the span;
hence, the rolling-moment curves are applicable to
wings with partial-span flaps. The charts cannot be
used with devices that change the slope of the lift
curve nor for excessive deflections that introduce dis¬
turbed air flow. In this connection it appears that a
deflection of plain ailerons involving disruption of the
air flow is inefficient from considerations of stick force.
It will be noted that two sets of curves are given for
tapered wings. The solid lines apply to ailerons that
are not tapered with the wing, i. e., ailerons of constant
actual chord. For this type the change of equivalent
angle of attack should be calculated on the basis of the
wing-tip chord (whether or not the aileron extends to
the wing tip). The long-dash curves are for the par¬
ticular case in which the aileron chord is a constant
proportion of the wing chord along the span, in which
case the change of equivalent angle of attack does not
vary along the aileron portion. The additive effect of
an element of aileron covering any spanwise portion of
the wing may be determined from the increment of the
Ci/ A-a curve over that portion. Although the curves of
figure 13 show increasing rolling-moment coefficients
with increased aspect ratios of the wings, the control
requirement (rolling-moment coefficient for a given
banking effect) also increases with aspect ratio and, on
account of the damping, in nearly the same way as
does the coefficient. (See reference 4.) In general, it
may be said that the relative proportions of the ailerons
622
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
should not be reduced on account of increased aspect
ratio.
YAWING MOMENT
Yawing moment with equal up-and-down deflec¬
tion. — The results of experiments indicate that the
primary source of adverse yawing moment given by
plain ailerons at small deflections is the theoretical, or
induced, yawing moment. The production of rolling
moment results in an induced twisting flow analogous
to the downwash in direct lift. The yawing moment
arises from the resultant inclination of the supporting-
lift vectors along the span. If the wing is supporting-
no lift, the production of rolling moment by equal and
opposite lift increments on the two wing halves will not
result in a yawing moment because the lift increment
vectors are all inclined backward by the induction,
resulting in a drag. Hence, only the interaction of an
initial lift and a rolling moment give rise to an induced
yawing moment.
A more specific treatment of this theory is given in
reference 18. The formula for yawing moment that
results for equal up-and-down deflections is
Cn=KCLXCi (5)
where K is a factor dependent on the aspect ratio and
the plan form of the wing, and to some extent, on the
span wise position of the aileron. It is interesting to
note that with a given equal up-and-down aileron
deflection the induced yawing moment is the same
throughout the speed range, while the rolling moments
and the stabilizing factors are greatly reduced at the
lower speeds.
Figure 12 gives a comparison of theoretical and
P CjAa
q for a rectangular wing of
experimental values of
Figure 13.— Charts for calculation of rolling and yawing moments of plain ailerons, showing the effects of span and spanwise location of ailerons with straight and
tapered wings.
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
623
aspect ratio 6. Deviation from the theory is to be
expected at excessive deflections of ordinary ailerons
and with special types of devices, since important
changes of profile drag may be introduced. If com¬
plete wing section data are available, however, the
profile-drag part of the yawing moment may be readily
estimated.
As in the case of rolling moment, the yawing moment
of an aileron at any spanwise position may be calculated
by taking the difference of ordinates at abscissas cor¬
responding to the ends of the aileron. Unlike the roll¬
ing moment, however, the yawing moment of differ¬
ential ailerons is not the same as that of ailerons with
equal deflections. In the general charts given in figure
13 the ratio of yawing to rolling moments at CL = 1 .0 is
given rather than CnlAa. In this case the differences
between two points cannot be used directly to give the
yawing moment of an aileron extending between these
two points. The yawing moment caused by an aileron
ending inboard of the tip may be found, howrever, by
taking the difference of the yawing moments given by
two ailerons, one extending from the inboard end of
the actual aileron to the wing tip and the other extend¬
ing from the outboard end to the tip. The straight
and tapered ailerons should give yawing moments in
practically the same ratio to the rolling moment;
hence, only a single set of values of K =
Cn/Cl
CL
is given.
Referring again to the 0.25 cw by 0.40 6/2 plain
aileron (aileron 1) of table I, it is found that the ratio of
yawing- to rolling-moment coefficients for this case is
77 = — 0.216 (6)
t <
at CL = 1.0. (See fig. 13.) At the deflection given the
rolling-moment coefficient previously found is
D, =0.0332 (7)
Hence, the yawing-moment coefficient at Cx = 1.0 is
Cn=- 0.216X0.0332 = — 0.0072 (8)
The values of both yawing- and rolling-moment
coefficients for these ailerons having been obtained, it
is now possible to calculate their rolling effectiveness by
means of figure 3. The wing loading of the average
airplane assumed in table I is 9.4 pounds per square
foot; hence, at Cl =1.0 the banking effect of a rolling
moment of coefficient 0.01 acting for 1 second is
4>\b
= 1.42 feet
2 /Ci=0.0l
and for a rolling-moment coefficient of 0.0332
<t>ib
(9)
2
= 1.42X3.32=4.7 feet
(10)
The effect of the yawing moment of coefficient —0.0072
is calculated in the same way, i. e.,
~ = — 0. 72X0. 65 = -0.47 foot (11)
The effect of these rolling and yawing moments applied
simultaneously is
7^=4. 7-0.47=4.23 feet (12)
Thus, deflecting the ailerons suddenly to ±7.4° causes
a 4.23-foot displacement of the wing tips in 1 second.
The angle of bank for the average airplane (6/2 = 16
feet) is
<61=-r-X57.3 = 15° (13)
AT
as appears in the table.
Yawing moment with differential deflection or
droop. — The effect of an unequal movement of the
ailerons may be taken into account by considering an
equivalent equal up-and-down deflection from a mean
upward position of the ailerons. Thus, deflections of
15° up and 5° down may be considered as equivalent
to 10° equal up-and-down from a mean position 5° up.
Inasmuch as a differential deflection of the ailerons
changes the mean lift of the wing, figure 13 cannot be
used without correction to calculate the yawing moment
due to unequal deflection. As was brought out in the
preceding discussion, the yawing moment is caused by
the interaction of the wing lift and the induced flow
caused by the rolling moment. Hence, the yawing
moment incident to a given rolling moment depends
on the distribution of the basic or symmetrical part of
the lift. The basic lift distribution upon which the
yawing moment depends is, then, the distribution for
a wing with both ailerons raised. The adverse yawing-
moment will, in this case, be reduced because of the
lessened lift over the tip portions. For the conditions
following sudden aileron deflections the average upward
movement of both ailerons will entail an actual reduc¬
tion for a short time of the lift of the wing without
correspondingly increasing either the flight speed or
the angle of attack. The conditions will, of course, be
different for steady flight with ailerons held over. For
practical purposes it is sufficient to calculate an incre¬
ment of CJCi due to the increment of lift produced by
the symmetrical droop or uprigging of both ailerons.
This increment would be the yawing moment incident
to a unit rolling moment when the entire lift of the air¬
foil was due to the droop of the ailerons. The ratio of
yawing to rolling moment thus found will be a constant
additive contribution to equation (5) at all lift coeffi¬
cients.
Figure 14 shows the reduction of the ratio of adverse
yawing to rolling moment in terms of the reduction of
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
624
over-all lift coefficient for a rectangular wing of aspect
ratio 6. The experimental points indicated were de¬
rived by taking the differences of yawing moment
measured with equal up-and-down deflections and up-
only deflections and dividing these differences by tbe
measured reduction in total lilt coefficient caused by
the up-only deflection.
If CL is the lift of the wing with ailerons undeflected
and A arn is the equivalent angle of washout of the
Figure 14.— Increment of induced yawing moment due to differential deflection of
ailerons; AQ is the reduction of lift coefficient due to differential deflection.
Rectangular wing; b!/S= 6.
aileron jportions introduced by the unequal aileron de¬
flections, then
(14)
since the reduction of lift is proportional to A am. The
factor k, like the factor K, depends on the wing plan
form and the relative length of the aileron portion.
Figure 15 shows theoretical values of k for wings of
aspect ratio 6 and ATarious plan forms. It should be
remembered that CL as used in equation (14) is the
lift coefficient with ailerons undeflected. Correction of
the values given in figure 15 for wings of different aspect
ratio may be made by considering that k is very nearly
inversely proportional to the aspect ratio.
It is evident that the foregoing remarks apply equally
as well to wings having washout at the tips or to wings
with partial-span flaps. For wings with partial-span
flaps Aam is simply the reduction of the effective angle
of attack at the tips due to removal of the tip portions
of the flap. It should be remembered that droop of
the outer portions (negative AaTO) increases the adverse
(negative) yawing moment while washout (positive
A am) decreases it.
The increment of yawing moment due to the sum of
two distributions of droop or washout is equal to the
sum of the increments associated with each separate
distribution. This property may be used to compute
quite accurately, though not exactly, the yawing
Figure 15. — Ratios for calculating additional induced yawing moments of differen
tial ailerons or ailerons on wings with washout; b2/S=G; A am is in degrees
(1 + A) — /if Cl+kAo m
Ci
moment of differential ailerons that end inboard of the
wing tip.
CONTROL FORCES
Hinge moment. — The available experimental data
indicate that the hinge-moment coefficient Ch of an
ordinary aileron can be treated with sufficient accuracy
as a characteristic of the wing section, that is, as a
characteristic independent of the plan form of the
aileron or the wing. An average experimental value
for the slope of the hinge-moment curve against deflec¬
tion is
-^--=—0.0085 per degree (15)
for sealed ailerons of chord ca and span ba, where
n hinge moment of aileron element
Thus, the actual hinge moment at a given deflection
varies as the aileron span and as the square of the aileron
chord.
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
625
Strictly speaking, the hinge moment of a deflected
flap should be calculated in two parts. The primary
part arises from that component of the distributed
pressure change which does not contribute to the lift of
the airfoil section. Since no lift is involved, this com¬
ponent is independent of the aspect ratio. The second
component of the hinge moment, proportional to the
lift change, is subject to the ordinary aspect-ratio cor¬
rection. The correction is, however, small except for
wide flaps.
Some additional considerations arise in the applica¬
tion of aileron hinge moments to the calculation of
control force. The angular travel and the length of the
control stick (or radius of the control wheel) are limited
in practice. Thus, ailerons requiring large deflections
must be geared to the control stick or wheel in a high
ratio. In the case of the average airplane the total cir¬
cumferential movement of the end of the control stick
was assumed to be 0.73 foot in the case of each of the
control devices. This value corresponds to a ±25°
deflection of a 20-inch stick corresponding to that avail¬
able in the Fairchild 22 airplane.
If reference is made to the tabulated results for
aileron 1, it is seen that the total deflection necessary to
insure the assumed satisfactory degree of control (<f>i =
22.5° at Cjc,= 1.0, in this case) is ±11.2°. The work
of deflecting ailerons of chord ca and span ba is
M*6JLacib _ 11.2X11.2
db 57.3 QCa ,UUb X 57.3
X9.4X (0.25X5. 3)2X 0.4X16
= 1.97 foot-pounds (16)
The control force is equal to twice the total work di¬
vided by the linear travel of the end of the stick, or
Stick force
3.94
0.73
= 5.4 pounds
(17)
The stick force at the partial deflection required for
$1 — 15° is
2-31x Jr^=2-31xn^=3-° p°unds cs)
These simple relations apply, of course, only to linear
variation of the hinge moment and to nondifferential
gearing.
Differential linkages.— It appears that a differential
linkage can, when properly designed, be a very effective
means of reducing the operating force of flap-type
ailerons (reference 11). The reduction of operating
force is accomplished by taking advantage of the up-
floating tendency of the ailerons. With differential
linkage the ailerons on opposite tips of the wing begin to
move at different rates immediately after they are
deflected from neutral, the downgoing aileron moving
more slowly than the upgoing one. The upgoing aileron
thus has the greater mechanical advantage at the con¬
trol-stick connection. It is evident that the reduced
upward pressure of the upgoing aileron is partly com¬
pensated by its increased mechanical advantage and
that the increased upward pressure on the downgoing
aileron is also partly compensated by its reduced
mechanical advantage. At a certain deflection the
downgoing aileron reaches dead center and, regardless
of its aerodynamic pressure, cannot contribute to the
stick force; if the upgoing aileron is then at the floating
angle (i. e., angle of zero hinge moment), the stick force
will be zero.
Ordinary ailerons show nearly straight-line hinge-
moment curves
0.0085
and in this case the
balancing effect of a given differential linkage depends
only on the upfloating angle. A formula for a differ¬
ential motion that gives zero operating force over a
range of deflections may be obtained by writing the
expression for the work of deflection of the ailerons and
equating it to zero at every point.
da=^(duf+8uy-2bu2-buf (19)
where bu and bd are the upward and downward deflec¬
tions of the ailerons and 8uf is the floating angle meas¬
ured upward from the neutral position. A practical
limitation of this formula is reached when dbdfdbu
approaches — 1 , for then both ailerons begin to move
in the same direction and at the same rate.
It should be appreciated that a differential designed
in accordance with equation (19) will give complete
balance at the specified floating angle. It is, however,
considered desirable not to eliminate completely the
control force at any flight condition, as the pilots’ feel
of the control would be taken away. This condition
can be avoided by designing the linkage for a fictitious
floating angle somewhat higher than the maximum
actually reached in flight. If A buf is the difference
between the floating angle at which the differential
gives complete balance and the actual floating angle
of the aileron in the given flight condition, the resultant
stick coefficient Cho will be
Stick moment ~ . s dCJ dbu . dbd\ . .
- - =<7*'=A8“' '35\W+^f (2<))
where 6 is the angular deflection of the control stick.
In any given case the stick force can be balanced out
at only one angle of attack and, in general, the balancing
effect diminishes as the angle of attack is reduced.
Hence, if the stick force is made to become zero at an
angle of attack above maximum lift, overbalance of
the control in normal flight will be avoided.
A more or less complicated mechanical linkage that
would give aileron movements approximating equation
(19) could be devised. The ordinary simple linkage
consisting of two properly set cranks connected by a rod
can, however, be arranged to give the desired motion
with close approximation, and such an arrangement will
be given primary consideration.
626
REPORT NO.
605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Such a simple linkage can be made to satisfy two con¬
ditions for a minimum stick force. Figure 16 shows a
type of stick-force curve that satisfies two very simple
criterions. First, the slope of the curve is zero at the
beginning of the deflection and, second, the resultant
stick force is zero at a stick deflection corresponding to
the floating angle of the up aileron. As was stated
earlier, the latter condition is satisfied by arranging for
the downgoing aileron to reach dead center when the
upgoing aileron reaches the floating angle. Figure 17
shows geometrical arrangements of linkages that satisfy
these two criterions for a minimum stick force. If the
spacing of the crank centers is known in terms of the
crank radius, the figure gives directly the neutral set¬
tings of the two cranks. The differential thus chosen
will give what amounts to complete balance at the
specified floating angle. The maximum downward
Stick deflection, A0
Figure 16.— Type of curve that satisfies simple criterions for minimum stick force.
travel of the aileron is shown in each case and it is to
lie noted that, if the maximum deflection of the upgoing
aileron exceeds the assumed floating angle, the down¬
going aileron will pass dead center and return toward
neutral.
Since the floating tendency of a given aileron has a
primary influence on the design of the differential
linkage, it will be necessary to devote some study to
this aileron characteristic. It appears that the floating
angle of a plain flap-type aileron can be attributed to
two effects: (1) a hinge moment proportional to the
angle of attack of the wing, this moment being greater
for large flap chords but independent of the shape of
the wing section; and (2) a hinge moment attributed to
the camber of the wing section, which remains constant
as the angle of attack is changed. This second moment
is primarily influenced by the camber of the aileron por¬
tion itself and is greatly affected by small changes at
the extreme trailing edge. Thus, a small fixed tab can
be used to introduce a large constant floating moment.
Figure 18 shows the variation of floating angle with
Hap chord and lift coefficient for the Clark Y wing sec¬
tion. The floating angles shown were indirectly com¬
puted from floating moments that were found by inte¬
gration of pressure-distribution diagrams for a smooth
wing (reference 20) and hence correspond to smoothly
sealed flaps.
For the comparisons given in table I, infinite linkages
(/?=0 in fig. 17) were assumed to simplify the computa¬
tions of control force. In most cases of differential
ailerons listed, several trial computations of stick force
were made to ascertain the optimum differential ar¬
rangement. These trial computations included the
Figure 17. — Specifications of simple differential linkages that satisfy criterions for
minimum stick force.
fdCh A
\~w)
determination of the curve of stick force against deflec-
tion to insure that no reversals of slope of the stick-
force curve occurred at any point.
Aileron 1 may be used to illustrate the use of figure
17 in the selection of a differential. Assuming that the
greatest possible reduction in stick force is desired, a
floating angle only slightly higher than the maximum
shown by figure 18 will be assumed. On the assump¬
tion that it is permissible to allow the control force to
become zero at CL= 1.25 (5M/=11°), the differential
chosen by means of the chart will have neutral settings
of 0^=15° and 5„ = 30°, approximately. As indicated
by figure 17, the maximum downward deflection obtain-
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
able with this arrangement will be about 4}(° and this
angle will be reached when the upgoing aileron reaches
11° deflection. For greater deflections the downgoing
aileron will return, reaching neutral when the up aileron
is at 22°.
Effect of a fixed tab used in conjunction with a
differential linkage. — Figure 18 shows that the floating
angles of plain ailerons are reduced as the lift coefficient
is reduced. It is on this account that the balancing
effect of the differential diminishes. The stick forces
tabulated for the differentially linked aileron 1 show
this effect as an increase of stick force at high speed.
It is possible to introduce a large constant floating mo¬
ment by means of a properly formed fixed tab. The
effect of such a tab is to increase the floating angle at all
flight speeds by a constant amount so that the per-
Figure 18. — Floating angles of sealed flaps of various chords on a Clark Y wing as
computed from pressure-distribution data (reference 20).
centage variation with flight speed is reduced. This
effect is especially pronounced in the case of very narrow
ailerons, which do not show a very great variation of
floating angle with angle of attack.
Furthermore, the maximum floating angle shown by
very narrow' ailerons is not great enough to permit the
use of a differential to the best advantage. Thus, if
the floating angle is considerably smaller than the
maximum upward deflection required to produce suffi¬
cient control, the stick force may rise considerably after
this point is reached on account of the return of the
downgoing aileron and the consequent extra deflection
required of the upgoing aileron. Advantageous use of
a differential in such cases can be accomplished by in¬
corporating a fixed tab (or a small amount of camber)
arranged to trim both ailerons upward. In order to
secure satisfactory results with a tab, a reasonably
smooth inset t}q3C with a sealed juncture should be used.
Attached tabs or tabs set at large angles (<h)>±150)
have been found to cause an adverse increase in the
slope of the hinge-moment curve.
Figure 19 shows the summarized results of experi¬
ments with tabs made in the 7- by 10-foot wind tunnel
627
As was stated before, the tab produces an essentially
constant change in floating angle. The variation of
floating angle with angle of attack can be found from
figure 18. Figure 19 gives the change of aileron floating
angle with tab deflection. (See references 9 and 21.)
The experiments indicated that this ratio depended
primarily on the ratio of tab chord to aileron chord in¬
dependently of the chord of the aileron, although this
relation can not be expected to apply as the aileron
chord is indefinitely increased. At the Reynolds Num¬
ber of the tests the tabs began to lose effectiveness when
Figure 19.— Effect of inset tabs on aileron floating angles (references 9 and 21);
St^dz 15°.
deflected past 15°; hence, the ratios given should be
considered applicable to tab deflections not exceeding
this angle. Figure 19 may also be used to estimate the
balancing effect of a movable tab.
It appears from figure 19 that a very large floating
angle can be obtained by the use of a relatively small
inset tab and deflection. Thus, the floating angle can
very easily be altered to suit a given set of conditions.
It has been pointed out that it is desirable to have the
floating angle at least as large as the maximum upward
deflection required for control so that the stick-force
curve will lie reasonably near the minimum throughout
the range. The smaller the percentage variation of
floating angle with angle of attack, the smaller will be
the variation of the actual stick force with flight speed.
It would therefore appear desirable to trim the ailerons
up as far as possible by means of a tab. On the other
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
hand, inasmuch as the deflected tab is made an in¬
herent part of the airfoil camber, the size and deflection
of the tab cannot be indefinitely increased without ad¬
versely affecting the pitching-moment and drag char¬
acteristics of the airfoil.
Reference to figure 19 shows that a 0.10 ca (2% percent
cw) tab deflected downward 10° will change the floating
angles of aileron 1 by approximately 9°, raising the
maximum floating angle to about 20°. This tab on the
average airplane would be only 1.6 inches wide and the
deflection of 10° would displace the trailing edge of the
wing section by only one-third inch and would conse¬
quently not be expected to make a noticeable change in
the drag or the pitching moment of the wing as a whole.
The differential linkage giving complete balance at a=
15° with this floating angle can be found from figure 17.
The neutral settings of the cranks are
0„=28°, <5b=59° (21)
The maximum downward deflection found on the chart
is about 8°, but in this case the aileron is not required
to reach this deflection (20° up and 8° down) to produce
a sufficient bank. Reference to figure 18 shows that
the reduction in floating angle between CL= 1.25
(maximum) and 6^= 1.0 is 2.5° so that, with the tab
assumed, the floating angle at a=10° (Oz,= 1.0) will be
20° — 2.5°— -17.5° (22)
Similarly, the new floating angle at « = 0° (Cl=0.35)
will be
20°— 4.8° = 15.2° (23)
These values indicate that the balancing effect of the
differential will not be greatly reduced at the higher
speeds. Table I gives the actual stick forces as com¬
puted at these lift coefficients and indicates the reduc¬
tion possible with a tab. An even better degree and
range of balance could be attained with narrower
ailerons on account of the smaller variation of floating
angle with angle of attack.
CONCLUDING REMARKS
The provision of control rolling moments at high
angles of attack or beyond the stall is not sufficient to
secure control in flight at these angles unless the damp¬
ing in rolling is retained. This requirement necessitates
that at least the tip portions of the wing remain un¬
stalled; hence, it cannot be considered a decided ad¬
vantage to retain control rolling moments far above the
stall with conventional wings.
The flight-testing experience gained throughout the
course of the lateral control investigation has led to
more or less definitely quantitative ideas regarding the
desired effectiveness of the lateral control and the
desirable variation of the control forces in normal flight.
From considerations of operating force required for a
given amount of control, plain narrow sealed ailerons
with deflections limited to 20° seem about the most
efficient. Very great taper, or change of aileron chord
along the span, leads to inefficiency whether used with a
straight or a tapered wing. A differential linkage can
be so designed as to reduce considerably the operating
force of ordinary unbalanced ailerons, especially if a
small fixed tab is used to increase the floating angle.
Several devices, notably the plain ailerons with flap
retracting ahead, and the retractable aileron or spoiler
located at 0.80 cw have been developed and proved in
flight to be suitable for use with full-span flaps. It was
found, however, that the maximum lift of a tapered
wing with split flaps was reduced less than 10 percent
by the removal of the outer 0.30 6/2 portions of the flap,
so that a conventional aileron could be used over that
portion of the wing without great loss.
Aerodynamic theory can be successfully applied to
the calculation of rolling and yawing moments of plain
ailerons provided that experimental section character¬
istics are used in the computation of the local changes in
angle of attack along the wing span caused by the
ailerons. Further calculations involving the airplane
stability characteristics can be applied to the pre¬
diction of the actual resultant motions caused by a given
deflection of the control, thus giving a measure of ef¬
fectiveness in controlling the movements of the air¬
plane.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., April 20, 1937.
REFERENCES
1. Wind-Tunnel Research Comparing Lateral Control Devices,
Particularly at High Angles of Attack.
I. Ordinary Ailerons on Rectangular Wings, by Fred E.
Weick and Carl J. Wenzinger. T. R. No. 419,
N. A. C. A., 1932.
II. Slotted Ailerons and Frise Ailerons, by Fred E.
Weick and Richard W. Noyes. T. R. No. 422,
N. A. C. A., 1932.
III. Ordinary Ailerons Rigged up 10° When Neutral, by
Fred E. Weick and Carl J. Wenzinger. T. R. No.
423, N. A. C. A., 1932.
IV. Floating Tip Ailerons on Rectangular Wings, by
Fred E. Weick and Thomas A. Harris. T. R. No.
424, N. A. C. A., 1932.
V. Spoilers and Ailerons on Rectangular Wings, by
Fred E. Weick and Joseph A. Shortal. T. R.
No. 439, N. A. C. A., 1932.
VI. Skewed Ailerons on Rectangular Wings, by Fred E.
Weick and Thomas A. Harris. T. R. No. 444,
N. A. C. A., 1932.
VII. Handley Page Tip and Full-Span Slots with Ailerons
and Spoilers, by Fred E. Weick and Carl J. Wen¬
zinger. T. N. No. 443, N. A. C. A., 1933.
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
VIII. Straight and Skewed Ailerons on Wings with
Rounded Tips, by Fred E. Weick and Joseph A.
Sliortal. T. N. No. 445, N. A. C. A., 1933.
IX. Tapered Wings with Ordinary Ailerons, by Fred E.
Weick and Carl J. Wenzinger. T. N. No. 449,
N. A. C. A., 1933.
X. Various Control Devices on a Wing with a Fixed
Auxiliary Airfoil, by Fred E. Weick and Richard
W. Noyes. T. N. No. 451, N. A. C. A., 1933.
XI. Various Floating Tip Ailerons on Both Rectangular
and Tapered Wings, by Fred E. Weick and Thomas
A. Harris. T. N. No. 458, N. A. C. A., 1933.
XII. Upper-Surface Ailerons on Wings with Split Flaps, by
Fred E. Weick and Carl J. Wenzinger. T. R. No.
499, N. A. C. A., 1934.
XIII. Auxiliary Airfoils Used as External Ailerons, by
Fred E. Weick and Richard W. Noyes. T. R.
No. 510, N. A. C. A., 1935.
2 Weick, Fred E., Soule, Hartley A., and Gough, Melvin N.:
A Flight Investigation of the Lateral Control Character¬
istics of Short Wide Ailerons and Various Spoilers with
Different Amounts of Wing Dihedral. T. R. No. 494,
N. A. C. A., 1934.
3. Soule, H. A., and McAvoy, W. H.: Flight Investigation of
Lateral Control Devices for Use with Full-Span Flaps.
T. R. No. 517, N. A. C. A., 1935.
4. Weick, Fred E., and Jones, Robert T.: The Effect of Lateral
Controls in Producing Motion of an Airplane, as Computed
from Wind-Tunnel Data. T. R. No. 570, N. A. C. A.,
1936.
5. Gough, M. N., and Beard, A. P.: Limitations of the Pilot
in Applying Forces to Airplane Controls. T. N. No. 550,
N. A. C. A., 1936.
6. Jones, Robert T.: A Study of the Two-Control Operation
of an Airplane. T. R. No. 579, N. A. C. A., 1936.
7. Wenzinger, Carl J.: Wind-Tunnel Investigation of Tapered
Wings with Ordinary Ailerons and Partial-Span Split
Flaps. T. R. No. 611, N. A. C. A., 1937.
8. Shortal, J. A.: Wind-Tunnel and Flight Investigation of
Slot-Lip Ailerons. T. R. No. 602, N. A. C. A., 1937.
629
9. Platt, Robert C., and Shortal, J. A.: Wind-Tunnel Investi¬
gation of Wings with Ordinary Ailerons and Full-Span
External-Airfoil Flaps. T. R. No. 603, N. A. C. A., 1937.
10. Platt, Robert C.: Aerodynamic Characteristics of Wings
with Cambered External- Airfoil Flaps, Including Lateral
Control with a Full-Span Flap. T. R. No. 541, N. A. C.
A., 1935.
11. Jones, Robert T., and Nerken, Albert L: The Reduction of
Aileron Operating Forces by Differential Linkage. T. N.
No. 586, N. A. C. A., 1936.
12. Weick, Fred E., and Shortal, Joseph A.: Development of
the N. A. C. A., Slot-Lip Aileron. T. N. No. 547, N. A.
C. A., 1935.
13. Shortal, J. A.: Effect of Retractable-Spoiler Location on
Rolling- and Yawing-Moment Coefficients. T. N. No.
499, N. A. C. A., 1934.
14. Williams, D. H., and Brown, A. F.: Experiments on a Small-
Chord Flap on a Clark YH Aerofoil in the Compressed
Air Tunnel. R. & M. No. 1681, British A. R. C., 1936.
15. Higgins, George J., and Jacobs, Eastman N.: The Effect of a
Flap and Ailerons on the N. A. C. A. — M6 Airfoil Section.
T. R. No. 260, N. A. C. A., 1927.
16. Wenzinger, Carl J.: Wind-Tunnel Investigation of Ordinary
and Split Flaps on Airfoils of Different Profile. T. R.
No. 554, N. A. C. A., 1936.
17. Munk, Max M.: Elements of the Wing Section Theory and
of the Wing Theory. T. R. No. 191, N. A. C. A., 1924.
18. Pearson, H. A.: Theoretical Span Loading and Moments of
Tapered Wings Produced by Aileron Deflection. T. N.
No. 589, N. A. C. A., 1937.
19. Heald, R. H., and Strother, D. H.: Effect of Variation of
Chord and Span of Ailerons on Rolling and Yawing
Moments in Level Flight. T. R. No. 298, N. A. C- A.,
1928.
20. Wenzinger, Carl J., and Harris, Thomas A.: Pressure Dis¬
tribution over a Rectangular Airfoil with a Partial-Span
Split Flap. T. R. No. 571, N. A. C. A., 1936.
21. Harris, Thomas A.: Reduction of Hinge Moments of Air¬
plane Control Surfaces by Tabs. T. R. No 528, N. A.
C. A., 1935.
630
REPORT NO. 605— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Table I (A).— COMPARISON OF VARIOUS LATERAL CONTROL DEVICES
RESUME AND ANALYSIS OF N. A. C. A. LATERAL CONTROL RESEARCH
631
TABLE I (B).— COMPARISON OF VARIOUS LATERAL CONTROL DEVICES
Up vice
23012
Criterion
Link¬
age
Control force and aileron deflection to
produce specified bank in 1 second
Sideslip
with 15° bank
in 1 second
(degrees)
Performance
01 _ j 50
Cl =0.35
Cl= 1.0
Cl = 1.8
Stick
force
(lb.)
Aileron
angles
(degrees)
Stick
force
fib.)
Aileron
angles
(degrees)
Stick
force
(lb.)
Aileron
angles
(degrees)
Cl =
0.35
Cl —
l 0
Cl =
1.8
Maxi¬
mum
lift
Speed
range
CL
max
C ^ min
Climb
L „
D at
Cl=0.7
20. Tapered ailerons,
sealed. 5:3 tapered
wing. Partial-span
split flap:
Ailerons
0.25c u,X0.41g.
Flap 0.15c„X0.59fj.
Equal..
'Dill....
4.0
2.4
±3.0 _
3. 4X2. 6...
3.7
1.5
±7.5 .
8. 4X4. 8—
3.5
.8
±12.0....
15.0X5.6-
3
3
7
7
8
7
1.88
1.88
125
125
19.5
19.5
21. Tapered ailerons,
sealed. 5:3 tapered
wing. Partial-span
split flap:
Ailerons
0.25„X0,30c|.
Flap 0.15c»X0.7o|.
Equal..
'Dilf _
4.0
2. 1
±4.3 .
5.0X3.6—
3.6
1. 1
±9.6 .
13.0X5.1-.
4.5
1.3
±16.0 _
25.0X1.5...
3
3
7
6
8
6
1.97
1.97
130
130
19.5
19.5
22. Tapered ailerons,
sealed. 5:1 tapered
wing. Partial-span
split flap: «
Ailerons
0.25c u>X0.5o|
Flap 0.15^X0.502.
Equal..
Diff _
2.4
1.4
±2.8. . —
3.1X25...
2.2
1.2
±7.4 _
8. 2X6.0..
1.9
. 1
±11.7 _
13.0X7.8-
3
3
6
6
6
6
1.81
1.81
129
129
18.2
18.2
23. Tapered ailerons,
sealed. 5:1 tapered
wing. Partial-span
split flap:
Ailerons
0.25c u,X0.30^‘
Flap 0.15c„X0.7o|.
Equal. .
Dill....
2.4
1.5
±4.2 .
4.5X3.6—
2.5
1.4
±12.0 _
14.0X18.0
2.8
1.5
±20.0....
26.0X10.0
2
2
6
5
0
5
1.97
1. 97
141
141
IS. 2
18.2
24. Plain ailerons. Re¬
tractable flap:
Ailerons
0.15c„X0.6o|.
Flap 0.15c»X1.0o|.
Equal—
Diff....
6.2
5.7
±3.8 . ..
4.7
3.7
±7.8. ..
6. 7
6.4
±25 0....
28.0X11.0
4
4
8
8
8
7
2. 05
2. 05
143
143
18.5
18.5
4.0X3.5—
8.7X7. 1...
25. Plain sealed aile¬
rons. Retractable
flap: B
Ailerons
0.116Cu>X0.80g-
Flap 0.15c„X1.0o|.
Die.
with
tab.
1.4
3. 4X4.2 _
0.9
8.4X6. 6. .
2.7
35 0X0. 6..
3
8
6
2. 05
143
18.5
26. Retractable aile¬
rons. Split flap:
Ailerons
0.15c u,X0.502-
Flap 0 .2Oc.rXl.OO5.
Up only.
0
0.025c u>f-.
0
0.062c J..
0
0.074c J..
1
4
6
2.19
149
18. 1
27. External-airfoil
flaps 6 0.20cwX1.002"
Diff....
5.5
3. 2X3.0...
3. 1
6. 0X5. 5...
0.2
13.0XU.0
3
7
10
1.83
172
18.7
28. External-airfoil flap
ailerons »
0.20c*X0.502.
Diff.—
0.9
3.7X3. 7...
0.8
7. 6X7.3...
0.3
16.0X9.2-
3
7
8
1.80
172
18.7
29. Slot-lip ailerons.
External-airfoil
flap: e. d
Ailerons
0.12c «,X1.00|.
Flap 0.20c„X1.0q|.
Diff.
with
tab.
2.4
10.0X6.0_.
2.3
25.0X6.5..
1.4
14.0X6.8..
3
6
7
1.92
202
19.0 |
a Computed or estimated results. 0 Spring mechanism assumed to avoid overbalance with flap down,
o C’l slightly below 1.8. f Deflection given in percentage of wing chord.
<i Device may not give satisfactory response characteristics.
38o48— 38-
41
REPORT No. 606
ELECTRICAL THERMOMETERS FOR AIRCRAFT
By John B. Peterson and S. H. J. Womack
SUMMARY
Electrical thermometers commonly used on aircraft are
the thermoelectric type jor measuring engine-cylinder
temperatures, the resistance type for measuring air tem¬
peratures, and the superheat meters of the thermoelectric
and resistance types for use on airships. These instru¬
ments are described and their advantages and disad¬
vantages enumerated. Methods of testing these instru¬
ments and the performance to he expected from each are
discussed. The field testing of engine-cylinder thermom¬
eters is treated in detail.
INTRODUCTION
On aircraft a knowledge of the temperature of the
engine is valuable (1) as an indication of trouble and
(2) as an aid in normal operation. An indication of
abnormal temperature of the engine cylinder, lubri¬
cating oil, or cooling liquid may forewarn of impending
failure. Where temperature controls are provided, the
temperature of the engine may be maintained at values
for which the operation of the engine is most efficient.
A knowledge of the air temperature is essential in
flight testing and as a warning of the possibility of ice
formation. One of the most important quantities
measured in airplane and balloon flights made to obtain
meteorological data is the air temperature.
On airships both the air temperature and the differ¬
ence between the air and lifting-gas temperatures are
commonly measured. These data arc vital factors in
airship navigation.
When measuring temperatures on aircraft, it is
obvious that the indicator must in most cases be at a
distance from the point of measurement. Electrical
thermometers, being inherently suitable for distant
indication, are widely used. As an exception, vapor-
pressure thermometers are commonly used to measure
the temperature of the cooling water or lubricating oil
of aircraft engines (reference 1).
Both thermoelectric and resistance types of electrical
thermometers are used on aircraft. The choice be¬
tween the two types of instruments lies principally in
the accuracy required. An accuracy of 10° C. is suf¬
ficient in the measurement of engine temperatures
whereas an accuracy of 1° C. is desired in the measure¬
ment of air temperatures. The thermoelectric type is
used, to the exclusion of other types, for the indication
of the temperature of air-cooled engine cylinders.
This type is particularly suitable for this use because
(1) the required accuracy can be obtained by using a
single thermocouple with a relatively rugged moving-
coil instrument, and (2) the thermocouple element is
more easily connected thermally to the engine cylinder
than any other type. The resistance thermometer is
used when a more accurate determination of tempera¬
ture over a shorter range is desired, as in the measure¬
ment of air temperatures.
Superheat meters for airships may be either of the
thermoelectric or resistance type. A number of
factors must be considered in choosing between the
two t}7pes. These are discussed in the section on these
instruments.
The instruments described in this report include (1)
the thermoelectric-type engine-cylinder thermometer,
(2) a resistance-type thermometer for measurement of
air temperatures, (3) the thermoelectric and the resist¬
ance types of superheat meters, and (4) a tester for
testing engine-cylinder thermometers. All of these
instruments with the exception of the first have been
developed at the National Bureau of Standards for use
of the Bureau of Aeronautics, Navy Department.
The National Advisory Committee for Aeronautics
furnished the financial assistance necessary for the
preparation of this report.
Where testing methods are described in detail in this
report, the methods are those followed at the National
Bureau of Standards in testing instruments purchased
by the Bureau of Aeronautics, Navy Department.
ENGINE-CYLINDER THERMOMETERS
The thermoelectric circuit. — A diagram of the elec¬
trical circuit of an engine-cylinder thermometer with a
copper-constantan thermocouple is shown in figure 1.
Figure 2 is a diagram of the electrical circuit of a ther¬
mometer using several iron-const antan thermocouples
with a selector switch. The comparative advantages
633
REPORT NO. G06 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
r>:u
and disadvantages of different thermoelectric materials
will be discussed later.
Reference junction - „ Moving coil
Adjusting
resistance . _
Measuring (constonton)
junction Constontan
Constonton terminal
-o-
-o
Carbon
resistor
Indicator
Copper Copper terminal ■'
Fioukk I. -Diagram of the electrical circuit of an engine-cylinder thermometer with
a copper-constantan thermocouple.
Moving coil
Fioukk 2. Diagram of the electrical circuitof an engine-clyinder thermometer with
a four-position selector switch and iron-constantan thermocouples.
The final design of the circuit is a compromise be¬
tween many conflicting requirements. The energy
available to operate the indicator is limited to the out¬
put of the single thermocouple. It follows that a
sensitive indicator should he used; yet for operation
on an airplane the indicator should have a high torque.
The use of a stronger permanent magnet offers ad¬
vantages in this respect hut the difficulties of shielding
the instrument so that it will not affect the magnetic
compass are increased. The increased weight of a
larger magnet is also objectionable.
Thermocouples and leads. — The choice of the most
suitable combination of thermoelectric materials de¬
pends on several factors:
1. The thermoelectric power (dE/dT) should he
high.
2. The mechanical strength after repeated heating
and cooling should be good.
3. There should be high resistance to corrosion.
4. The thermal conductivity of the material should
be low, so as not to conduct heat away from the part,
the temperature of which is being measured.
5. The electrical resistance should be low.
6. The temperature coefficient of electrical resistance
should be low.
7. A uniform supply of the material should be
obtainable.
A comparison of these seven characteristics for
several combinations of thermoelectric materials is
given in table I. The first three combinations are at
present used in measuring aircraft engine cylinder
temperatures, and for the fourth, chromel P-constantan
is proposed.
It should be pointed out that the change in resistance
per °C., given in table I applies only to the resistance of
the leads, which is usually about 0.1 of the total resis¬
tance of the circuit.
TABLE I.— PROPERTIES OF THERMOELECTRIC
MATERIALS
din
dT
Elec¬
trical
resist¬
ance 2
Change
in re¬
sistance
per
degree
centi¬
grade 3
Rela¬
tive
thermal
conduc¬
tivity 4
Mechan¬
ical
strength
Resist¬
ance to
corro¬
sion
Uniformity
of supply
Copper. ...
Constantan..
\ 49. 5
.074
.012
/ 100
l 6
Poor . . .
Good...
Fair.-.
Good.—
Excellent.
Fair.
Chromel P.
Alumel. ..
| 40. 7
. 147
. 09(3
f 5
l 7
...do _
. .do —
l 1
o o
T2
do.
Good.
Iron .
J 55. 2
.087
.094
f 18
...do....
Poor. . .
Fair.
1 Constantan..
l 6
...do....
Good...
do.
Chromel P. .
Constantan..
}70.I
. 176
.024
/ 5
l 6
1 l
o o
T3 T3
-..do _
-_.do _
Good.
Fair.
1 Average microvolts per degree centigrade in the range 0 to 300° C.
2 Ohms per foot of no. 14 duplex lead, at 20° C„ based on the following resistances
of the materials in ohms per foot of no. 14 wire: Copper, 0.002525; constantan, 0.0719;
chromel P, 0.104; alumel, 0.0433; iron. 0.0149.
s Average change in resistance per degree centigrade for the range 20 to —30 C.
expressed as a percentage of the resistance at 20° C.
1 Thermal conductivity of copper=100.
TABLE II.— AVERAGE TEMPERATURE-E. M. F. CHAR¬
ACTERISTICS OF THERMOCOUPLES
[Reference 2 is the source of data for ehromel-alumel and copper constantan in the
range —20 to 50° C. The data for higher temperatures for ehromel-alumel were ob¬
tained from reference 3, and for copper constantan from reference 4. The tron-
constantan and chromel P-constantan curves are from unpublished data on file in
the Pyrometry Section of the National Bureau of Standards. J
Temperature
Electromotive force, millivolts
° C.
OF.
Copper-
constantan
Chromel
P-alumel
Iron-con¬
stantan
Chromel
P-con-
stantan
-20
-4
-0.
75
-0. 77
-X.
03
-1. 14
-15
5
— .
57
-.58
- .
77
-.86
-10
14
— .
38
-. 39
52
-. 58
23
19
-.20
26
-. 29
0
32
0
0
0
0
5
41
19
. 20
26
. 29
10
50
39
.40
52
.59
15
59
59
.60
78
.89
20
68
79
.80
1.
05
1. 19
20
77
99
1.00
1.
31
1.49
30
86
1.
19
1. 20
1
58
1. 79
35
95
1
40
1. 40
1
85
2. 10
40
104
1
61
1.01
2
12
2.41
45
113
1
82
1.81
2
38
2. 72
50
122
2
03
2. 02
2.
66
3.04
100
212
4
28
4. 10
5.
40
6. 32
150
302
6
70
6. 13
8
19
9. 79
200
392
9
28
8. 13
10
99
13. 42
250
482
12
01
10. 15
13
79
17. 18
300
572
14
86
12. 21
16
56
21.03
350
662
17
82
14. 29
19
32
24. 96
400
752
16. 39
22
07
28. 94
450
842
18. 50
24
82
32. 96
.500
932
20.64
27
58
37. 00
550
1,022
22. 77
30
39
41.05
ELECTRICAL THERMOMETERS FOR AIRCRAFT
035
Average temperature-e. m. f. relations for thermo¬
couples of four combinations of materials are given in
table 11. The data for the lower temperatures are
given at short intervals for convenience in applying
corrections for the reference junction temperature or in
calculations dealing with the range of compensators.
Figure 3.— Thermocouples of the gasket and rivet types and a pair of leads.
A photograph of two types of thermocouple is shown
in figure 3. This particular equipment was constructed
according to specifications of the Bureau of Aeronautics,
Navy Department. The gasket-type thermocouple is
mounted in place of the regular spark-plug gasket. The
rivet-type thermocouple is inserted in a drilled hole,
/s inch in diameter and in depth, and a steel pin concen¬
tric with the rivet is driven down to expand the copper
to hold the rivet securely in place. The thermocouple
wires are welded to the gasket or rivet head.
The United States Army has standardized on 2-ohm
iron-constantan thermocouples and the Navy, on 2-ohm
copper-constantan thermocouples; engine manufactur¬
ers install 3-ohm iron-constantan thermocouples in
commercial airplanes. These resistance values include
both the resistances of the leads and thermocouples.
Thermocouple leads are made in lengths to fit any
installation requirement. In order to make leads of
different lengths interchangeable, the cross-sectional
area of the stranded wire is varied directly as the
length so that all leads will have the same resistance.
The leads are composed of two insulated conductors,
of the same materials as the thermocouple, laid parallel,
covered over-all with braid and saturated with flame-
and moisture-resistant lacquer.
Selector switches. — When the temperatures of two or
more points are to be measured with the same indi¬
cator, a selector switch of the required number of posi¬
tions, a switch lead, and additional thermocouples arc
required. The switch lead and switch contact rosist-
Figure 4.— Rotary selector switches for connecting an indicator to any one of a
number of thermocouples.
ancos are made low so as not appreciably to affect the
indicated temperature. (See fig. 2 for a diagram of a
4-position and fig. 4 for a photograph of a 4-position
and an 18-position rotary selector switch.) It is neces¬
sary that these switches he of the 2-pole type to avoid
REPORT NO. 600— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
636
stray voltages that might cause erroneous indications
if one side of all the thermocouples remained per¬
manently connected to the indicator.
The electrical indicator. — A face view of two electrical
indicators is shown in figure 5. Both instruments are
inclosed in Army-Navy standard cases of 2% inch dial
Figure 5.— Two engine-cylinder thermometer indicators.
diameter. Attached to the rear of the cases are ter¬
minals for connecting the thermocouple leads.
Because of the excessive vibration sometimes en¬
countered on airplane instrument panels, the pivots
which carry the moving coil of these indicators have
been made blunter than those ordinarily used in elec¬
trical instruments. On airplanes there is always enough
vibration to overcome the slight friction caused by the
blunt pivots. These blunt pivots are known as “air¬
plane pivots.”
The electrical indicator must be magnetically shielded
to reduce the effect of the permenant magnet on a
magnetic compass. A soft-iron cup covers the sides
and rear of the instrument and the front is shielded by
a soft-iron dial. The shielding adds undesirable weight
to an instrument already cpiite heavy because of the
permanent magnet. The weights of indicators range
from 1 to 1 % pounds.
Reference -junction compensation. — Compensation
for the temperature of the reference junction is accom¬
plished by a small bimetallic spiral, which controls the
position of the outside end of one of the hairsprings.
This construction is shown in figure 6. The proper
Figure 6.— Electrical indicator showing the Bristol reference junction compensator.
B is the bimetallic spiral one end of which is fastened to the pole piece at A and the
other to the hairspring at C.
action of the compensator is to cause the indicator,
when there is no current in the moving coil, to indicate
the ambient temperature. The bimetallic compensator
and the reference junction should be placed closely
together so that their temperatures will be the same.
This requirement necessitates that the indicator termi¬
nal posts be constructed of the thermoelectric materials,
so that there will be no intermediate junctions outside
the instrument case. Furthermore, the rates of heating
and cooling of the bimetallic compensator and reference
junction should correspond, so that their temperatures
will be the same for rapidly changing ambient tem¬
peratures.
It has become the general practice to connect a carbon
resistor of negative temperature coefficient in series
with the moving coil of the indicator, to compensate
for the positive temperature coefficient of resistance of
the copper in the moving coil.
Tests and performance of indicators. — The errors in
indication of thermoelectric thermometers may be
directly determined by immersing the measuring junc¬
tion in a liquid bath and comparing the readings at a
number of points with those of a calibrated thermome¬
ter. In practice, however, a more convenient method
of determining the errors of engine cylinder thermome-
ELECTRICAL THERMOMETERS FOR AIRCRAFT
ters in use by the Bureau of Aeronautics is to test the
indicator, leads, and thermocouple separately.
The Bureau of Aeronautics does not specify the
resistance of the indicator, except that it shall be not
less than 12 ohms at a temperature of 20° C. Since it
is specified that the indication shall be correct when
connected to a 2-ohm copper-constantan thermocouple,
an exact specification of the resistance would be super¬
fluous and would unnecessarily increase the cost of the
instrument.
The scale errors of a millivoltmeter type indicator at
room temperature are conveniently determined in the
laboratory by connecting the indicator to a standard
thermocouple (standard as regards tempera ture-e. m.f.
relation and resistance) and then introducing into the
circuit a voltage corresponding to that developed by
the measuring junction at a given temperature. This
junction is kept at a constant known temperature by
placing it in an ice bath. The reading of the instrument
Figure 7. — Engine-cylinder thermometer errors for different indicator temperatures.
The curves show the average of the errors of five indicators.
minus the temperature corresponding to the applied
voltage gives the scale error.
Tests similar to the test described are made with the
indicator at temperatures of —25 and 45° C. to test
the operation of the reference junction compensator
and to determine the over-all effect of temperature on
the scale error.
The average scale errors of five instruments at three
temperatures have been plotted in figure 7. These
instruments were equipped with bimetallic compensa¬
tors and series carbon resistors of negative temperature
coefficient. Besides affecting the reference junction
and its compensator, a change in indicator temperature
also affects the stiffness of the hair springs, the strength
of the permanent magnet, and the resistance of the
moving coil. The data in figure 7 show that for these
instruments the bimetallic spiral overcompensates for
the temperature of the reference junction, while the
carbon resistor undercompensates for the change in
resistance of the copper coil. The combination is
adjusted so that the temperature error for the most
important part of the scale, 200 to 350° C., is very small.
Figure 8 shows the results of a test to determine the
change in reading of an indicator produced by a rapidly
changing ambient temperature. The indicator is
mounted in a chamber, the temperature of which is
uniform and controllable, and connected to a thermo¬
couple immersed in a liquid bath at room temperature.
The pointer of the indicator is set to indicate the
temperature of the bath. The temperature of the
chamber in which the indicator is mounted is reduced
from room temperature to approximately —25° C. at a
rate of approximately 5° C. per minute. The indicator
should continue to indicate the constant temperature
of the measuring junction in the liquid bath. Assuming
that the bimetallic compensator has been properly
adjusted and that the resistance of the carbon resistor
has been properly selected so that the indication finally
reaches the bath temperature, the deviation of the
20.
o
o
qT
b
Q)
I
£
-20
- c
—
,-lndi
-j L
cotor
readir
>9
''Ten
iperatu
re oft
neasun
ng jum
ztion
v
A
"1
Terr
L
■p erati
jre of
air sur
~ round
ing in a
icator
V
l" +^"
_
•
0
20 40
Time, minutes
60
90
Figure 8. — The results of a temperature lag test on an indicator equipped with a
bimetallic reference junction compensator.
indication from the bath temperature, as the tempera¬
ture of the instrument is changed, is due to one or more
of the following causes: (1) Improper placing of the
reference junction with reference to the compensator;
(2) uneven rates of heating and cooling of reference
junction and compensator; (3) uneven rates of heating
and cooling of the carbon resistor and copper coil; and
(4) differences in temperature between the two ends
of the carbon resistor.
The effect of vibration on the performance of the
indicator is determined by subjecting the indicator to a
vibration such that each point on the instrument case
describes, in a plane inclined 45° to the horizontal, a
circle of /32-inch diameter. During this test the
indicator is in the normal, face-vertical position. A
description of the vibration machine on which this test
is performed is given in reference 1. A voltage of
specified value, which is normally sufficient to keep the
pointer at approximately half of full-scale deflection,
is introduced into the indicator circuit. The total
REPORT NO. 606— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
resistance in the indicator circuit is made equal to that
existing in service, so as to obtain the same damping.
The frequency of vibration is changed from 1,000 to
2,500 cycles per minute by steps, at each of which the
average position of the pointer and the amplitude of
oscillation is observed. The results of such a test are
plotted in figure 9.
The cumulative effect of continuous vibration on the
indicator is determined by subjecting it for periods up
to 50 hours to vibrations at 1,800 vibrations per minute,
maintaining the supply voltage as previously explained.
Scale-error tests are made before and after vibrating,
to determine the effect of vibration.
The effect of the indicator on the reading of a stand¬
ard-type aircraft compass is determined by placing the
indicator in various positions about the compass. The
horizontal intensity of the magnetic field about the
compass should be equal to 0.18 gauss for this test.
'Phe indicator shielding is considered satisfactory when,
at a distance of 8 inches between the center of the
indicator and the center of the compass, the change in
compass reading is not more than 4°.
Figure 9.— Error in average position and amplitude of oscillation of pointer of typical
engine cylinder thermometer when subjected to vibration.
Testing thermocouple material. — Thermocouple ma¬
terials are tested at certain fixed points on the tempera¬
ture scale. The melting point of ice (0° C.), the normal
boiling point of water (100° C.), the freezing point of
tin (231.9° C.), and the freezing point of lead (327.3°
C.) are convenient points in the range of engine-cylinder
thermometers. The methods used are described in
detail by Roeser and Wensel in reference 2.
Some difficulties are experienced in testing short
thermocouples, such as those illustrated in figure 3.
If the longer wires necessary to connect the thermo¬
couple to the potentiometer have not exactly the same
thermoelectric properties as the wire of which the ther¬
mocouple is constructed, intermediate junctions are
formed, the temperatures of which may be much higher
than room temperature, owing to heat conduction along
the short length of the thermocouple. Approximate
corrections may be made for the temperatures of the
intermediate junctions if these temperatures are meas¬
ured by auxiliary thermocouples soldered onto the in¬
termediate junctions. An easier and more accurate
method, however, is to test sample thermocouples made
of longer lengths of wire, from each batch of wire
purchased.
The thermoelectric characteristics of the leads is
found by joining the pair at one end to form a measur¬
ing junction. The e. m. f.’s developed for measurin'*
junction temperature elevations of 50 and 100° C are
measured directly on a potentiometer.
The Navy Department, Bureau of Aeronautics
specifications allow a deviation of approximately ±1
percent from the e. m. f. of the standard temperature-
e. m. f. relation for copper-constantan thermocouples
and ±2 percent for the leads. For interchangeability
the resistances of thermocouples and leads should be
uniform.
Engine-cylinder thermometer tester. — An instrument
used in the field for testing copper-constantan thermo¬
electric type engine cylinder thermometers is shown in
figure 10. Figure 11 is a diagram of the electrical con-
fcNGUNfc CYLINDER THERMOMETER TESTER
MARK i
JSU8EAU Of At* I NAUTICS U. A NA VT
INSTRUCTIONS FOR USE
tuoic* ro«
Tit twreH'K
■"**<*««* »»»(.> -
■ -i \bovt, l> !». ,
• > f <3
•' • ) fcfcj
< ».
■" * rfJsS-x'i'lfJ
• :r 9hsxai* be
• >i f<-A tw <■■■ ■:&&
• ■<• astr>* >'.4< «v
i»l'! iw<s<4* **&&&.
HWINO.mSTftUMEWT CO.
PHILADELPHIA,. U.S.A.
ylESTO*
DEGREES CENTIGRADE
SSt'Ct,:":
SSsT
iV ..Wn,
Figure 10. — Tester for copper-constantan thermoelectric thermometers.
nections of the tester. This tester was built according
to the design and specifications of the Bureau of Aero¬
nautics. The tester is designed for testing the cali¬
bration of the indicator and for checking roughly the
resistance of the leads and the thermocouples.
ELECTRICAL THERMOMETERS FOR AIRCRAFT
639
When testing an indicator, it is connected by means
of the 1-ohm copper-constantan clip leads furnished
with the tester to the binding posts marked “Indicator
test” (fig. 10). Since the resistance between the termi¬
nals marked “Indicator test” plus the resistance of the
1-ohm leads is exactly equal to the resistance of a Navy
standard 2-ohm thermocouple and leads, indicators of
any resistance are properly tested.
If there is a change in indication of the indicator
when the circuit is completed and with the tester cur¬
rent off, it is due to a difference in temperature between
the reference junction in the indicator and the measuring
junction in the tester. If this change in reading ex¬
ceeds 10° C., time should be allowed for the tester and
indicator to come to the same temperature. When the
limit of 10° C., is not exceeded, the error obtained in the
comparison test ordinarily will not be more than 2° C.
When proceeding with the test, the pointers of both
the indicator and the milliammeter of the tester are
set to the measuring junction temperature as indicated
by the mercury thermometer on the tester.
The tester is designed for testing only one indicator
at a time. The connection of two or more indicators
in parallel will lead to erroneous results.
Figcre 11.— Diagram of electrical connections of tester for copper-constantan thermo¬
electric thermometers.
RESISTANCE THERMOMETER
For the measurement of air temperatures on aircraft,
thermometers of the resistance type are especially
suitable on account of their features of remote indication
and short-time lag. The temperature-sensitive ele¬
ment may be located in places or at distances impos¬
sible or impracticable for liquid-in-glass or bimetal
thermometers. Although a resistance thermometer
may be made to indicate over the range from —70
to 100° C., no thermometer of the liquid or vapor-
pressure type that will operate satisfactorily over this
range is known. The winding of the resistance element
may be so made that the time lag in air is very much
shorter than that of temperature elements of other
types. One indicator may be used to indicate suc¬
cessively the temperature of a number of resistance
elements by using a selector switch.
38548 — 38 - 12
The resistance thermometer described in this report
was originally designed and constructed for use in the
flight testing of airplanes. Instruments of this type
have also been used for the indication of air tempera¬
ture on lighter-than-air ships of the United States
Navy, on the National Geographic Society-Army Air
Corps stratosphere balloons, and for the determination
of temperature of the mixture in gasoline engine intake
manifolds.
Indicator. — The instrument is essentially an unbal¬
anced Wheatstone bridge arrangement, as shown sche¬
matically in figure 12. Figures 13 and 14 are, respec-
Figure 12. — Schematic diagram of resistance thermometer.
tively, a front view and an inside rear view of the
indicator unit. The electrical instrument is a Weston
Model 269 milliammeter, giving a full-scale deflection
on 3 milliamperes and having a resistance of approxi¬
mately 35 ohms. The moving coil of the milliammeter
is mounted on airplane pivots. If the double amplitude
of vibration of the airplane member to which the instru¬
ment is fastened exceeds 0.005 inch, shock-absorbing
means should be provided to reduce the instrument
vibration to or below this value. The zero, or open-
circuit, position of the pointer is approximately one-
fourth of the length of the scale, from the left, as shown
in figure 13. The calibration of the scale is approxi¬
mately linear.
The bakelite case built around the electrical instru¬
ment (fig. 13) houses the 30-ohm rheostat, the switch,
and the separable terminals carrying leads to the
electrical supply and to the temperature element.
The fixed manganin resistances of the bridge are
mounted inside the electrical instrument case. The
weight of the indicator unit is approximately 2% pounds.
For accurate indications it is necessary that the switch
be turned occasionally to the test position and the rlieo-
640
REPORT NO. 606— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
st.at adjusted to cause the indicator pointer to stand at
the test point (20° C. on fig. 13). When in the test
position the switch substitutes a fixed resistance for
the temperature element. The value of this fixed
resistance is equal to that of the temperature element
when it is at the temperature of the test point. Ad-
Figure 13.- Resistance-thermometer indicator.
Figure 14. — Rear inside view of resistance-thermometer indicator.
justing the rheostat varies the voltage impressed on the
bridge. Proper adjustment compensates, exactly at
the test point, for variations in the supply voltage and
for temperature variations in the resistance of the copper
in the moving coil of the electrical instrument. It is
obvious that the indications at the balance point
(—20° C. in fig. 13) are also free of errors due to these
causes. Assuming that the proper voltage adjustment
has been made, the errors due to these causes at points
on the scale other than at the test and balance points
will be negligible.
Temperature element.— Details of a temperature sen¬
sitive element designed for strut mounting on an air¬
plane are shown in figure 15. The temperature sensitive
part is a single layer of no. 34 gage single silk-covered
nickel wire wound on a bakelite tube of approximately
%4-inch wall thickness. The wire is held onto the
tube and protected from moisture by several coats of
bakelite varnish. The construction of the bakelite
base is clearly shown. The connections between the
nickel wires from the element and the copper lead
Figure 15. — A resistance-thermometer temperature element.
wires are inside the base. The outside nickel-plated
tube, which has a diameter of 1 inch and a length of
2% inches, serves to protect the element from the direct
rays of the sun.
The element should be mounted where its tempera¬
ture will not be affected by the heat from the engine
exhaust. When possible, the leads from the tempera¬
ture element to the indicator are installed inside the
airplane wing covering at the factory. When neces¬
sary to make an installation on a finished airplane, a
fiat duplex lead K6 inch thick and % inch wide is some¬
times used. This flat lead is held under a strip of
fabric attached by dope to the airplane strut or wing.
ELECTRICAL THERMOMETERS FOR AIRCRAFT
641
Driver-Harris Grade A nickel wire lvas been used in
the construction of the temperature elements. It has
been found that all the wire from any one spool has
approximately the same resistivity and temperature
coefficient of resistivity. The resistance It of elements
made in the last three years at the National Bureau of
Standards (all from one spool) may be expressed by the
following equation:
77 = 55.22 (1 +4.857’ X l(r3 + 67’2X 10"6) (1)
in which 7’ is the temperature of the element in degrees
centigrade. The data used for determining the con¬
stants of this equation were obtained by a null bridge
method, a temperature element of the usual construc¬
tion being one arm of the bridge. The temperature
element was installed in a temperature chamber in front
of a fan giving an air current of approximately 17 miles
per hour. The electric current in the temperature ele¬
ment was approximately the same as that in the tem¬
perature element of circuit shown in figure 12. The
temperature of the air in the chamber was held constant
by hand regulation, holding the null indicator on zero.
The values of the several constant temperatures were
determined from an accurately calibrated copper-con-
stantan thermocouple element installed just ahead of
the resistance element. The temperature range of —70
to 40° C. was covered in this calibration. The best
curve of the form of equation (1) was then fitted to the
observed points. Aire from several spools of Driver-
Karris Grade A nickel wire has been tested and found
to have appreciably different temperature coefficients.
All resistance elements with the exception of those
used on the stratosphere flights have been adjusted to a
resistance of 60.7 ohms at a temperature of 20° C. The
resistance at —20° C. is 50 ohms. These specified
resistances include the resistance of copper lead wires to
the element. These leads may be made of no. 16 gage
wire, 10 or 20 feet long, the resistance of the two wires
being of the order of 0.1 ohm. In use, the difference in
temperature between the element and the lead wire is
small; since the temperature coefficient of copper is
approximately the same as that of the nickel wire used,
the error introduced by using the copper lead is con¬
sidered negligible. If the element and the leads with
which it was adjusted are considered as a unit, the
units are interchangeable.
Stratosphere instrument. — Resistance thermometers
with several special features were constructed for use on
the National Geographic Society-United States Army
stratosphere balloon flights (reference 5). Figures 16
and 17 are photographs of the indicator and the tem¬
perature element. The indicator has a range of —70
to 40° C. The indicator face was photographed during
the flights at 90-second intervals. A black scale with
white graduations and pointer was used because it has
been found that clearer photographic records are thus
obtained. Since the knob used to switch from the “on”
position to the “test” position in the course of adjusting
the voltage did not appear in the photograph it was
necessary to install an auxiliary indicator, which may be
seen at the upper left-hand corner.
Without special precautions the lag in the tempera¬
ture element of this instrument would have been pro-
DEGREES
CENTIGRADE
/ NATIONAL
BUREAU 0E STANDARDS
O resistance thermometer
N* I7-3S
3 -VOLTS
Figure 10. -Resistance-thermometer indicator constructed tor stratosphere balloon
flights.
Figure 17.— Temperature element of resistance thermometer used on stratosphere
flight. This element is ventilated by an electric fan.
liibitive because at the highest altitude reached the air
density was only 5 percent of standard sea-level density
and there was practically no movement of the balloon
relative to the air. As may be seen in figure 17, the wire
of the temperature element was wound on an open frame
so that practically the entire surface of the wire was
642
REPORT NO. 606— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
exposed to the air. The element was shielded from the
direct rays of the sun by two coaxial fiber tubes, the
outer of which was 6 inches in diameter. Ventilation
was secured by a fan operated by a small electric motor
that drew air through the tube.
Time lag. — A detailed discussion of the time lag of
thermometers is given by Harper (reference 6). Hen-
rickson (reference 7) describes experimental methods
and apparatus for the determination of time-lag
constants and gives values of the time-lag constants
for various aircraft thermometers.
A convenient method for determining the time-lag
constant of air thermometers is to raise the temperature
of the element to approximately GO0 C. and then
suddenly to place it in an air stream at room tempera¬
ture, measuring with a stop watch the time required
for a change in indication between two convenient
points on the scale. The time-lag constant X, in seconds,
is defined by the equation,
x t
^ (2)
logif— J
j- 2 2 o
where T0 is the temperature of the air stream, Tx the
indication when timing is started, T2 the indication
when timing is stopped, and t the time in seconds for
the indication to change from rL\ to T>.
Tests at air speeds of 30 to 60 miles per hour indicate
that approximately, the time lag varies inversely as the
air speed V.
(3)
where X0 is the value of the time-lag constant at the air
density p0 and L is a constant, characteristic of the
temperature element. Koning discusses this relation
in reference 8. It is evident that at very low air speeds,
under a mile or two per hour, convection currents in
the air become predominant so that formula (3) does
not apply. The value of X remains finite when V=0.
However, for airplane speeds the convection constant
may be neglected.
Smolar (reference 9) gives the variation of X with
air density as
x=x°V^ <4)
Combining equations (3) and (4)
Since the true air speed V may be expressed as a
function of the pitot-static indicated air speed T rf,
V=VJ* (6)
\ P
it follows that,
x=F (7)
y i
This equation gives X as a function of the indicated air
speed, independent of air density.
If Vi is expressed in miles per hour and X in seconds
L for the resistance element illustrated in figure 15 is
equal to approximately 160. At an indicated air speed
of 100 miles per hour, X is 1.6 seconds.
It is of interest to review two physical conceptions
of the time-lag constant X. First, assume that the
temperature is changing at a rate which has remained
constant for some time (fig. 18). The indication T
Figure 18.— Graphical illustration of time lag of a thermometer in a medium, the
temperature To of which is varying at a constant rate. The thermometer indica¬
tion is T, the time-lag constant is X, and the temperature lag is To — T.
of the thermometer will lag behind the actual tempera¬
ture 7’q, indicating the temperature that existed X
seconds earlier. The lag in temperature indication,
T0-T (in degrees) is the product of the time-lag con¬
stant (in seconds) by the rate of change in temperature
(in degrees per second). Second, assume that the
temperature element is suddenly taken from air at one
temperature and placed into air at a different tempera¬
ture. After X seconds the indication will still have
l/e( = 0.37) times the total temperature difference to
go before the new temperature is accurately indicated.
The value of e, the base of the natural logarithm system,
is approximately 2.72. The variation in indication
with time is given by equation (2) when Tx is the indica¬
tion at time t= 0 and the indication T2 at time t.
Temperature rise due to PR loss. — Equation (2) was
derived on the assumption that Newton’s law of cooling
holds for the resistance element; that is, that the rate
of heat transfer to or from the element is directly pro¬
portional to the difference in temperature between the
element and the surrounding air. This law may be
expressed by
M^rt=k(T-T0) (8)
where M is the heat capacity of the element and k
is a factor of proportionality. In equation (2), M/k
was set equal to the single constant X, the time-lag
constant for the element.
If there is an I2R loss in the element maintaining the
element at a constant temperature above that of the
air, the rate at which heat is lost must equal the rate
ELECTRICAL THERMOMETERS EOR AIRCRAFT
at which it is supplied, that is
PR=k(T-T) o (9)
or with k=M/\,
PR=~(T-T„) (10)
The temperature rise due to the heating is then
r-r0=~p/; (ii)
where J is the current and R is the resistance of the ele¬
ment.
The PR loss in the element, calculated from the data
given in figure 12, is equal to approximately 0.05 watt.
The value of M, calculated from the dimensions, densi¬
ties, and specific heats of the parts, is equal to 3.3 watt-
seconds per degree centigrade. Then, for the element
illustrated in figure 15,
r-r0=y^x=o.oi5x (12)
or, from equation (7),
T-T0= 0.015^ (13)
v 1
The observed value of the time lag of the element in
still air with the axis of the tube vertical is 1 15 seconds.
Substituting this value in equation (12), the PR tem¬
perature rise is equal to 1.7° C. From equation (13)
the rise at 50 miles per hour is equal to 0.05° C. Both
the time lag and the PR temperature rise decrease
rapidly with increasing air speed.
Speed correction. — The results of flight tests on high¬
speed airplanes indicate that thermometers exposed in
the air stream give increasing readings with increasing
air speed, the air temperature remaining constant.
The correction C independent of the air density, when
expressed as a function of the indicated air speed, is
C=-SVt2 (14)
where S is a constant, characteristic of the element, and
Vi is the pitot-static indicated air speed. If Vt is ex¬
pressed in miles per hour and C in degrees centigrade,
S for the element illustrated in figure 15 is equal to
approximately 80X10~6. At an indicated air speed of
200 miles per hour, the correction amounts to 3.2° C.
and should be subtracted from the observed readings.
This speed error, which is common to all types of
thermometers, is discussed in reference 8.
Laboratory tests and performance. — Resistance ther¬
mometers are tested for scale errors in an air bath.
The temperature element is placed in a chamber in
which a fan provides a positive flow of air past the
element. The temperature of the air around the ele¬
ment is held constant within narrow limits for several
minutes before each reading. This temperature is£
measured by a calibrated thermocouple placed close
to the resistance element. The scale errors, as deter¬
mined by this method, do not ordinarily exceed 0.5° C.
The method of determining the time-lag constant of
the instrument has been discussed.
The effect of change in temperature of the indicator is
eliminated for all practical purposes when the voltage
is properly adjusted at any given indicator temperature.
SUPERHEAT METERS
The term “superheat” as used in relation to lighter-
than-air craft is defined as the temperature of the lifting
gas minus the temperature of the outside air. The im¬
portance of a knowledge of superheat is evident when
the dependence of the lift of a balloon or airship on this
temperature difference is considered. The additional
lift due to positive superheat is equal to the weight of
the air that is forced out of the envelope by the in¬
crease in temperature. Strother and Eaton (reference
10) discuss the effect of superheat on the lift of an
airship.
The superheat may be determined by separately
measuring the outside air temperature and the gas
temperature, but it is more convenient, and usually
more accurate, to read this temperature difference
directly on a superheat meter. Two general types of
superheat meters have been constructed at the National
Bureau of Standards for use on United States Navy
airships, the thermoelectric type and the resistance
type. Each type will be described.
Thermoelectric type superheat meter. — The essential
details of thermoelectric type superheat meter installa¬
tion using copper-constantan couples are shown in
figure 19. By the use of a selector switch, both forward
and after readings are obtained on the same indicator.
The indicator is a Weston model 440 galvanometer of
3.5 ohms resistance, giving full-scale deflection on
132X10-0 amperes. A photograph of the parts of an
instrument for indication of aft superheat only is given
in figure 20.
Excessive temperature lag at the junctions is avoided
by joining 6-inch lengths of no. 24 gage copper and
constantan wires to the no. 16 gage copper and con-
stantan wires and forming the actual junctions by
joining the smaller wires. It. is essential that the air
junction be protected from the direct rays of the sun.
Calculation of errors. — Fortunately the two largest
errors in a superheat meter of the thermoelectric type
can be made approximately to cancel each other, by
proper proportioning of the copper resistance and con¬
stantan resistance of which the circuit is composed.
These errors arc due to (1) the increase in thermoelectric
power ( lE/dT with increase in air temperature and (2)
the increase in resistance of copper in the circuit with in¬
crease in air temperature. The compensation is based
on the assumption that the galvanometer lead wires
and air junction are at the same temperature. If the
installation cannot be arranged so that this condition is
approximately realized, the errors may amount to as
much as 5 percent.
REPORT NO. 606— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
644
(1) The e. m. f. -temperature relation for a Leeds &
Northrup copper-constantan thermocouple as derived
from test results obtained at the National Bureau of
Standards between the temperatures of —20 and 120° F.
may be expressed as follows:
#=21.4 I2 ( 1 +0.00058 T2) - 2 1 .4 #, ( 1 + 0.00058 1\) (15)
where K is the e. m. f. in microvolts and J\ and T2 are
ment and nearer the temperature at which the in-
strument is calibrated. Substituting AT for (#,__
#i), this equation may be written as follows:
#=21.4 AT [I +0.00058 (2 7\+A#)] (i6)
ft should be noted that AT is the superheat when
the thermocouples form part of a superheat meter. It
Resistance of aft circuit: Ohms
Galvanometer. . . . . . 3. 50
1,120 feet no. 16 copper _ 4.48
Added copper _ _ 2.42
Total copper _ _ 10.40
120 feet no. 16 constantan _ 8.88
Added constantan _ .72
Total constantan _ _ 9. 60
Total resistance _ 20. 00
Resistance of forward circuit: Ohms
Galvanometer _ 3. 50
80 feet no. 16 copper _ _ .32
Added copper _ .26
Total copper _ _ 4.08
80 feet no. 16 constantan _ 5.92
Total resistance _ 10.00
Figure 19. Details of a superheat meter for indicating, on a single indicator, the
superheat in the forward and after gas cells.
the temperatures of the air and gas junctions, respec¬
tively, in degrees Fahrenheit, above a base temperature
of 50° F. A base temperature of 50° F., rather than
O'+F., is chosen because the higher temperature is
nearer the middle of the operating range of the instru-
Figure 20.— A thermoelectric-type superheat meter, complete with air element (A),
gas-cell element (B), and connecting wire (C and D). This instrument was in¬
stalled in an after cell on the U. S. S. Los Angeles.
is seen that E is a function of the air-junction tem¬
perature T i as well as of the superheat AT.
(2) The resistance of the circuit is
R=R50 (1 +Na #,) (17)
where R is the resistance when the entire circuit is at a
temperature 7’, °F. above 50° F., in ohms; R50, is the
resistance of the circuit at 50° F., in ohms; N, the ratio
of the resistance of the copper in the circuit to the total
resistance of the circuit; and a = 0.00222 per degree
Fahrenheit, the temperature coefficient of resistance of
copper, at 50° F. The temperature coefficient of resist¬
ance of the constantan is assumed to be zero.
The indication is also affected in opposite directions
by changes in the temperature of the hairsprings and
permanent magnet of the galvanometer. These two
effects combined may be called the temperature
coefficient of the instrument as an ammeter. It aver¬
ages + 0.0001 per degree Fahrenheit for several in¬
struments which have been tested. Since no definite
information, except that the value is small, is available
on the value of this coefficient for the Weston Model
440 galvanometer, the value will be assumed to be zero.
The galvanometer current 7, in microamperes, as
determined from equations (1G) and (17) is
r#_21.4A#[l +0.00058(2#, + A#)]
R #50(1+0.0022277#,) 1 J
T,=0,
7=
21.4A#(1+0.00058A#)
R
(19)
'50
ELECTRICAL THERMOMETERS FOR AIRCRAFT
The instrument scale is constructed according to equa¬
tion (19). Equation (18) indicates that the calibration
is not independent of Tx. However, if
V- 2X0.00058
0.00222
= 0.52
(20)
the indication, neglecting second-order terms, is correct
for all values of Tx. Thus the resistance of the circuit
should consist of 52 percent copper and 48 percent
constantan. The errors for rather large departures
from this ratio are not serious, but there is no reason why
the ratio cannot be at least approximated. The require¬
ment is not inconsistent with the practice of selecting a
galvanometer that has a resistance equal to that of the
external circuit, since the galvanometer resistance is all
copper and the resistance external to the galvanometer
is mainly constantan.
It is possible to proportion the copper and the
constantan in the aft circuit of the instrument outlined
in figure 19, so that Ar=0.52 and the error in indication
is zero. For the forward instrument the optimum ratio
could not be conveniently attained (without the use of
larger lead wires). For it, Ar=0.41; and the error in
indication is —1 percent of the indication for an air
temperature of 90° F. and +1 percent for an air tem¬
perature of 10° F.
Resistance-type superheat meter. — A resistance-type
superheat meter has several advantages over the
thermoelectric-type instrument, mainly the possibility
of using a more rugged electrical instrument.
The schematic diagram of the essentials of a super¬
heat meter of the resistance type is shown in figure 21.
The temperature elements, e and/, are made of no. 34
gage Driver-Harris Grade A nickel wire and have a
resistance of 30 ohms at a temperature of 0° F. The
temperature coefficient of resistance of this wire has
been determined as described in the section on resistance
thermometers. The resistance of the 30-ohm elements
is
#=30(1 +2.82TX 10-3+2T2X 10-6) (21)
in which T is the temperature in degrees Fahrenheit.
Table III.— RESULTS OF TESTS TO DETERMINE THE
BEST COMBINATION OF RESISTANCES FOR THE
RESISTANCE TYPE SUPERHEAT METER
Errors,
°F., produced by using resistance values as
Air tern-
Super¬
heat
designated in fig. 21
perafure
a = 6=4000
(°F.)
(°F.)
a = b = 500
a =6 = 1500
a = 6=l800
a =6 = 2000
c =77011
c =20012
c =15012
c = 12412
c=012
-40.3
0
0
0
0
0
0
13. 0
-.3
-.3
0
-. 1
. /
27. 0
— . 5
-. 4
— .2
-.2
1.2
40.3
— . 7
-.8
-.4
-.2
1.2
0
-13.3
. i
0
0
0
— . 3
0
0
0
0
0
0
13.2
-. 1
-. 1
_ 2
0
0
20.3
-.3
-.3
. i
-. 1
2
39.3
-.4
-.2
-. l
-. 1
. 1
39.2
-13.0
0
-. 1
0
0
0
0
0
0
o
0
0
12.8
. 1
. 1
2
. 1
0
25. 5
.3
.2
. i
.2
— . 2
38. 1
.4
.3
.3
.3
— . 5
77. 3
-12. 6
-.2
.2
-. 1
- 1
.4
0
0
0
0
0
0
12. 5
. 3
0
-. 1
0
-.5
24.9
.4
. 1
. 1
-. 1
-1. 1
37. 1
.8
_ 2
. 1
-. 1
-.8
645
The circuit shown in figure 21 was established with
dial resistance boxes, setting the resistances e and / to
correspond to various temperatures. The resistance c
in series with the galvanometer was adjusted on each
trial to make the range of the superheat meter —15 to
45° F. The errors determined by this method and re¬
ported in table III show that for certain ratios of the
resistance arms the errors are reduced to negligible
values. It appears from the table that 2,000 ohms each
in the arms a and b, offers the best combination.
Table III shows that the resistance ratios are not
critical, three of the five trials all showing negligible
errors. Low resistances at a and b cause negative errors
at low air temperatures and positive errors at high air
temperatures ; while high resistances at these places cause
errors of the opposite sign. The tests were made with
a Weston Model 301 instrument having a resistance of
approximately GO ohms and a range of 50-0-150 micro¬
amperes. The proposed range of the superheat meter
is —15 to 45° F. The circuit was designed for use on
Figure 21. — The basic circuit of a resistance-type superheat meter. The fixed
resistances of the bridge are a and b; the air and gas elements are e and f.
a 20- to 24-volt battery supply. If designed for 110
volts, with a corresponding increase in resistance, and
decrease of current in the temperature sensitive ele¬
ments, there would be the advantage of relatively less
voltage drop in the long leads sometimes required.
Two superheat meters of the resistance type, which
have been constructed at the National Bureau of
Standards for the U. S. Navy, are shown in figures 22
and 23. The instruments are essentially the same
except that one has space provided inside the in¬
strument for a 22% volt radio B battery while the
other must be supplied with current from an external
source.
Figure 24 is a diagram of connections applicable to
both instruments. The connections are fundamentally
the same as shown in figure 21 with the addition of two
manganin resistances and a triple-pole double-throw
switch arranged for checking the supply voltage. When
the switch is in the “test” position, the temperature
elements in the bridge circuit are replaced by two
646
REPORT NO. 606— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 22. — Resistance-type superheat meter with self-contained battery.
Figure 23.— Resistance-type superheat meter with air- and gas-cell elements.
ELECTRICAL THERMOMETERS FOR AIRCRAFT
647
manganin resistances of 33.48 ohms and 37.15 ohms.
These values are the resistances of the 30-ohm elements
at temperatures of 40 and 80° F., respectively. The
40° F. resistance was selected for the low-value checking
resistance because 40° F. is near the average tempera¬
ture of the air in which an airship operates. The
indicator pointer should be adjusted to stand on the
zero mark with current off. The rheostat serves to
adjust the supply voltage so that the pointer stands on
the 40° F. superheat mark when the switch is in the
test position. The reference marks at 0 and 40° F.
superheat can be seen on the scales of both instruments
(figs. 22 and 23).
It should be noted that the indication at zero super¬
heat is independent of battery voltage and that the
percentage error at other indications is equal to the
percentage variation from the correct voltage adjust¬
ment. Adjustment for battery voltage, as described,
serves to compensate for the effect of variations in the
temperature of the indicator. This fact is obvious
when it is noted that the indicator is adjusted to indicate
correctly at 40° F. superheat regardless of the resistance
of the galvanometer circuit.
The construction of the temperature elements is
similar to that described for the resistance thermometer.
A photograph of the gas-temperature element is shown
in figure 23. The gas-cell element is mounted co¬
axially with a perforated bakelite outer shell. It is
Figure 25. — A potentiometer temperature indicator.
designed to be suspended in the gas cell the superheat
of which is to be measured.
Figure 26.— Engine gage unit incorporating a resistance-type oil-temperature indicator.
REPORT NO. 606— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
648
The length of the copper wires between the indicator
and the gas-cell element are usually longer than those
between the indicator and the air element and their
resistance may be an appreciable part of 30 ohms, but
the temperature coefficient of copper is practically the
same as that of nickel and if most of the wire is inside
the envelope at an average temperature not appreci¬
ably different from that of the gas-cell element, the
error caused by the lead wires will be negligible.
OTHER INSTRUMENTS
Not all types of electrical thermometers in use on
aircraft today are described in this report. Among the
types not described, a potentiometer indicator made
Figure 27.— Diagram of connections of resistance-type thermometer with a voltage
regulator.
by the Lewis Engineering Company might be mentioned.
A photograph of this instrument is shown in figure 25.
This instrument may be used as a standard for testing
thermoelectric indicators in the field and may be used
as the indicator on large aircraft, where the saving in
weight of leads, effected by the use of the potenti¬
ometer instrument, may be enough to warrant the use
of the heavier indicating apparatus.
The Weston Electrical Instrument Corporation has
developed a resistance thermometer of a range suitable
for measuring radiator cooling liquid or oil tempera¬
ture. It is of the unbalanced Wheatstone bridge type.
A photograph of the instrument, built into an engine
gage unit, is shown in figure 26. Figure 27 is a diagram
of connections, showing the details of the voltage regu¬
lator that compensates for variations in battery voltage.
The General Electric Company has used a crossed-coil
ohmmeter type instrument as the indicator in a resist¬
ance thermometer. An instrument of this type was
used on the National Geographic-Army Air Corps
stratosphere flight; it had a temperature element similar
to that shown in figure 17.
National Bureau of Standards,
W ASHiNGTON, D. C., December 15, 1936.
REFERENCES AND BIBLIOGRAPHY
1. Sontag, Harcourt, and Brombacher, W. G.: Aircraft Power-
Plant Instruments. T. R. No. 466, N. A. C. A., 1933.
2. R,oeser, Wm. F., and Wensel, H. T.: Methods of Testing
Thermocouples and Thermocouple Materials. Bur. Stand¬
ards Jour. Res., vol. 14, no. 3, March 1935, p. 247.
3. Roeser, Wm. F., Dahl, A. I., and Gowens, G. J.: Standard
Tables for Chromel-Alumel Thermocouples. Bur. Stand¬
ards Jour. Res., vol. 14, no. 3, March 1935, p. 239.
4. National Research Council: International Critical Tables,
vol. V. McGraw-Hill Book Co., Inc., 1929, p. 58.
5. Stevens, Albert W.: The Scientific Results of the World-
Record Strastosphere Flight. The National Geographic
Magazine, vol. LXIX, no. 5, May 1936, p. 693.
6. Harper, D. R.: Thermometric Lag. Bur. Standards Bub,
vol. 8, no. 4, 1912, p. 659.
7. Henrickson, H. B.: Thermometric Lag of Aircraft Thermom¬
eters, Thermographs and Barographs. Bur. Standards
Jour. Res., vol. 5, no. 3, September 1930, p. 695. ,
8. Koning, C.: The Indication of Thermometers in Moving
Air. Report no. A322 De Ingenieur (Amsterdam) 1932,
no. 45.
9. Smolar, Vaclav: Determination de la Temperature del’Air
Pendant les essais en vol. Aero. Res. Inst., Prague, Czecho¬
slovakia, vol. 6, no. 18, 1932, p. 37. (With French Ab¬
stract.)
10. Strother, D. H. and Eaton, H. N.: A Superheat Meter or
Differential Thermometer for Airships. Tech. Paper No.
359, Bur. Standards, 1927.
Geyer, Wilhelm: A Bridge for Measurement of Temperature
Difference with Electric Resistance Thermometers.
Archiv fur Elcktrotechnik, vol. XXV, no. 7, July 15, 1931.
li. 476.
REPORT No. 607
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE OBTAINED FROM THE
SPINNING BALANCE AND COMPARED WITH RESULTS FROM THE
SPINNING TUNNEL AND FROM FLIGHT TESTS
By M. J. B amber and R. O. House
SUMMARY
A 1 /10-scale model of the XN2Y-1 airplane was tested
in the N. A. C. A. 5 -foot vertical wind tunnel and the six
components of the forces and moments were measured.
The\model was tested in 17 attitudes in which the full-
scale airplane had been observed to spin, in order to deter¬
mine the effects of scale, tunnel, and interference. In
addition, a series of tests was made to cover the range of
angles of attack, angles of sideslip, rates of rotation, and
control settings likely to be encountered by a spinning
airplane. The data were used to estimate the probable
attitudes in steady spins of an airplane in flight and of
a model in the f ree-spinning tunnel.
The estimated attitudes of steady spin were compared
with attitudes measured in flight and in the spinning tun¬
nel. The results indicate that corrections for certain scale
and tunnel effects are necessary to estimate full-scale
spinning attitudes from model results.
INTRODUCTION
General methods for the theoretical analysis of air¬
plane spinning characteristics have been available for
some time. These methods might be used by designers
to predict the spinning characteristics of proposed air¬
plane designs if the necessary aerodynamic data were
known.
In order to provide these data, the N. A. C. A. is
conducting investigations to determine the aerodynamic
forces and moments on airplane models and on the
various parts of airplane models in spinning attitudes.
This report gives a comparison of the results obtained
for a model on the spinning balance with those for the
airplane in full-scale spins and for a model in the free-
spinning tunnel. The XN2Y-1 is the first airplane to
be tested for comparative purposes in these three ways.
The flight tests are reported in references 1 and 2, the
results from the free-spinning tunnel in reference 3,
and those from the spinning balance are given in this
report. Flight and spinning-balance results have been
compared for two other airplanes. (See references 4
and 5.)
The present report gives the aerodynamic forces and
moments acting on the XN2Y-1 airplane model for the
range of probable spinning attitudes with various rud¬
der, elevator, and aileron deflections and in 17 specific
attitudes in which the full-scale airplane had been
observed to spin. These forces and moments are also
given for parts of the model for the 17 flight attitudes.
An analysis of the data and a discussion of the results
of the analysis with respect to flight results and to
model tests in the free-spinning tunnel are included.
APPARATUS AND MODELS
The tests were made in the N. A. C. A. 5-foot vertical
open-jet wind tunnel described in reference (5.
The 6-component balance, as described in reference 4,
was altered to give more accurate results and to allow
for more rapid testing. The balance force system, as
modified to give more accurate readings, is shown in
figure 1. A sleeve to which the model is attached was
installed over the upper end of the vertical spindle, is
fastened to the spindle by a ball-bearing gimbal joint
649
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
650
at the upper end, and is held in position by linkages to
two measuring units at its lower end. This arrange¬
ment allows the rolling and pitching moments (earth
axes) to be measured directly instead of being the small
algebraic sum of two and three relatively large measure¬
ments. Consequently, much greater accuracy may be
obtained with the same variations in balance readings
so that fewer repeat tests are necessary.
This alteration and the direct-indicating force-meas¬
uring system that was installed have reduced the time
required to obtain data. The force-measuring system
consists of an oil pump and six mercury manometers
outside the tunnel, seven slip joints on the lower end of
the turntable shaft, and six measuring units on the
balance head. Each measuring unit consists of a grooved
piston and cylinder and is shown by the small sketch
in figure 1 .
The principle of operation is that the force (see F in
hg. 1) applied to the piston is balanced by oil pressure
in the cylinder. The grooves in the cylinder and in
the piston act as balanced valves, allowing oil to flow
into or out of the cylinder, depending on the location
of the piston in the cylinder. The oil pressure acting
on the piston in the closed end of the cylinder is trans¬
mitted through a slip joint and is indicated by the
mercury manometer.
One oil-pressure line from the pump and one overflow
line connect to all six measuring units. Each unit is
connected through a slip joint to a mercury manom¬
eter; each manometer is provided with a shut-off
valve; and all the valves are operated at the same time
so that all the readings are made simultaneously.
The model, a 1/10-scale reproduction of the XN2Y-1
airplane, was made from dimensions obtained from the
airplane as used for tests in reference 2. Figure 2
shows it mounted on the balance in the tunnel. The
model differed from the airplane principally in that
it had no propeller, the struts were round rods, and the
fuselage and the trading-edge center section of the upper
wing were cut away for attachment to the balance.
The model also differed from the airplane, as tested in
reference 1, in that the airplane had the fin offset and
the fabric sagged between the ribs. The wings,
fuselage, wheels, and stabilizer of the model were of
mahogany, the struts of 3/32-inch brass rod, and the
fin, rudder, and elevator of duralumin. The wings
and the fuselage mounted separately are shown in figures
3 and 4. A small streamline fuselage section was used
to attach the wings to the balance. The tolerances
allowed for the construction were: Wing profile, ±0.003
inch; fuselage cross section, ±0.005 inch; tail surfaces,
±0.003 inch; other dimensions generally, ±0.01 inch;
and angular relationships, ±0.1°.
TESTS
Tests were made at 40°, 50°, 60°, and 70° angle of
attack. At each angle of attack tests were made at
- 10°, 0°, 5°, and 15° angle of sideslip. At each angle of
attack at each angle of sideslip, tests were made with
values of ilb/2Y oi 0.35, 0.50, 0.75, and 1.00. For each
attitude tests were made with the elevator up, rudder
with spin ; elevator neutral, rudder neutral; and elevator
down, rudder against the spin. For each attitude with
elevator up, rudder with the spin, except zero sideslip,
tests were made with ailerons with and against the
spin. Tests were made with elevator up, ailerons
neutral, and rudder positions of 40°, 25°, 17°, 8°, and
0° with the spin at a = 60°, Q.b[ 2Tr=0.75, (3 = 0° and 15°;
and at a = 50°, &b/2V=0.50, and /3 = 5° and —10°.
The control-surface angles for the various settings
were:
Elevator up _ elevators 23° 41' up.
Elevator down _ elevators 25° down.
Rudder with _ rudder 40° to aid the rotation.
Rudder against _ _ _ rudder 40° to oppose the rotation.
Aileron with _ _ ailerons displaced to increase the
rolling.
Aileron against _ _ ailerons displaced to oppose the
rolling.
Aileron deflections were 25° up and 15° down, both
ailerons being deflected in each case.
The radius of the spin for each attitude was com¬
puted from an equilibrium of centrifugal and aerody¬
namic forces. The normal weight of the airplane was
used and the aerodynamic forces were obtained from
the data in reference 7. The resultant force on the
airplane was assumed to be perpendicular to the XY
plane.
Tests were also made in 17 specific attitudes obtained
from measurements of full-scale spins. Table I gives
the attitudes and control positions.
TABLE I.— AIRPLANE ATTITUDES AS TESTED ON THE
SPINNING BALANCE
[Tests 44L through 109L from reference 1. Tests 29F through 36 from reference 2.
All values have been given proper signs for right spins. Right and left spins given
in references 1 and 2. In a right spin inward sideslip is positive.]
Flight
test
(deg.)
/S
(deg.)
V.b
2 V
Sr
(deg.)
se
(deg.) (min.)
<5„
(deg.)
Radius
(ft.)
44 L
53. 1
-0.8
0. 554
-40
-25
30
0
2. 60
52 L
50. 1
1.0
. 453
-40
-25
30
0
3. 70
771.
70.7
9.0
.838
-40
-25
30
0
1 . 30
84 L
69. 1
7.4
.970
-40
— 25
30
0
. 60
107L
57.0
10.8
. 753
-40
— 25
30
With
1. 70
109L
65. 5
9.8
.853
-40
-25
30
Against
.91
29 F
60. 7
13. 7
.593
-40
-23
50
0
1.60
29 G
60. 4
13.0
.622
-40
-23
50
0
1 . 60
20
50. 6
4.3
.598
-40
26
35
0
2. 00
30
52. 4
1.0
.535
-40
26
35
0
2. 30
33
40.2
4.4
. 534
0
-23
50
0
2. 70
31
48.6
-1.9
.390
-17
-23
50
0
3. 50
32C
47.0
.9
.437
-4
-23
50
0
3.90
34 B
44.4
. 4
. 414
-4
-23
50
0
4. 00
27 B
43.0
3.9
.411
-8
-23
50
0
1.70
35
57.4
9. 7
. 523
-18
-23
50
0
2.20
36
50.9
.6
.393
-40
26
35
0
2.30
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
651
Figure 2. — The XN2Y-1 airplane model mounted on the spinning balance.
Figure 3.—' Wings of the XN2Y-1 airplane model mounted on the spinning balance.
Figure 4.— The XX2Y-1 airplane model, with wings removed, mounted
on the spinning balance.
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The model was not changed for the test corresponding
to those given in reference 1, in which the airplane had
the fin offset and the original wing profile on which the
fabric sagged between the ribs. For each test the
controls were set the same as for the flight spins. In
each attitude tests were made with the model complete,
with the fin and rudder removed, with the wings
removed, and with the wings alone. (See figs. 3 and 4.)
In order to insure consistency of results, repeat tests
were made for each condition until individual balance
readings were found to agree within a specified limit or
until a sufficient number of readings had been made to
form a fair average. In each case an average of the
results obtained was used to obtain the coefficients.
The air speeds for the tests varied between 43 and 75
feet per second and covered a range of test Reynolds
Numbers from about 100,000 to 175,000. Early tests
on the spinning balance indicated no scale effects over
this speed range (reference 4). The lower air speeds
were used with the larger values of ilb/2 V because of the
necessarily high rate of rotation.
SYMBOLS
a, angle of attack at center of gravity.
d=sin-1 po angle of sideslip at the center of gravity.
V, resultant linear velocity of the center of gravity.
v, linear velocity along the Y airplane axis, positive
when the airplane is sideslipping to the right,
ft, resultant angular velocity (radians per second).
<5a, aileron deflection.
8e, elevator deflection.
8r, rudder deflection.
a, angle between the vertical and the helix described by
the center of gravity of the airplane.
b, span of wing.
S, area of wing.
g=l/2 pV2, dynamic pressure.
p, air density.
A', longitudinal force acting along the X airplane axis,
positive forward.
Y, lateral force acting along the Y airplane axis, positive
to the right.
Z, norma] force acting along the Z airplane axis, positive
downward.
L, rolling moment acting about the A" airplane axis,
positive when it tends to lower the right wing.
M, pitching moment acting about the Y airplane axis,
positive when it tends to increase the angle of
attack.
A , yawing moment acting about the Z airplane axis,
positive when it tends to turn the airplane to the
right.
Forces and moments with double primes (e. g., A"")
are in the earth system of axes where Z" is positive
downward and X" is along the radius of the spin,
positive toward the center of the spin.
Coefficients of forces are obtained by dividing the
force by q S .
Coefficients of moments are obtained by dividing the
moment by qbS.
771 .. .
p = —^) relative density of airplane to air. Under
standard conditions, g = 13.1 W/Sb.
m — WIg, mass.
kx, kY) kz, radii of gyration of the airplane about the
A", Y, and Z airplane axes, respectively.
b2 Wb2 ... . . .
j- 2 — > — 2 = ~Tn — a\’ pitching- moment inertia parameter.
Kz kx g (U xl)
2 _ h 2 Q _
UA— C— T 10^nS~m<)mon! aRd yawing- moment
inertia parameter.
A—rnkx 2, moment of inertia about the AT airplane axis.
B=mky2, moment of inertia about the Y airplane axis.
C—mkZ) moment of inertia about the Z airplane axis.
RESULTS
Results of the measurements have been reduced to
the following coefficient forms, which are standard ex¬
cept that of the pitching moment, for which the
coefficient is based on the span of the wing:
n X
r Y
'-'X - -Q
qo
Cr~qS
/O' -k
Ll~qbS
r M
m qbS
C,
C
n
Z
"qs
N_
qbS
Pitching-moment coefficients can be referred to the
chord of the wing by multiplying the values given by
7.47. All values of the coefficients are given with
proper signs for right-hand spins. The values of the
coefficients for the series of tests are given in figures 5
to 9. Variations of Ch Cm, and Cn with (3, ftfr/2U, and
control settings for some characteristic cases are shown
in figures 10 to 22.
The differences between the coefficients of flight and
model results (flight minus model) are given in figures
23 to 26. The values of Cn for parts of the airplane
(reference 2) and of the model are given in figure 27.
The values of -yJCx^YCy2 (or CX") Ch Cm, and Cn
for the airplane and for the model, and the values
obtained by adding the coefficients of the wings tested
separately to those of the model with the wings re¬
moved, are given in figures 28 to 31.
The data given are believed to be correct for the
model under the conditions of the tests within the
following limits:
Cz, ±0.02 Cm, ±0.002
Ch ±0.001 Cn, ±0.001
No corrections have been made for tunnel-wall, block¬
ing, or scale effects. The interference caused by the
balance parts would appear to be large, especially at
40° angle of attack where the tail surfaces were very
near the balance, as is shown by figure 2. Inter¬
ference effects, however, are not obvious in the results
given in figures 23 to 31.
Resu liani -force coefficient, \i'Cx.z + Cy.z Resultant- force coefficient, \/Cx.i + CY-
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
653
Figure 5. — Variation of resultant-force coefficient V C.v"2+Cv"2, horizontal plane (earth axes), with angle of attack.
Normal- force coefficient Cz Normal- force coefficient Cz
654
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Angle ofaitack, cL , deg.
Angle of attack,cL ,deg.
Angle ofaitack, U ,deg.
Figure 6. — Variation of normal-force coefficient Cz (bod}’ axes) with angle of attack.
Rolling-moment coefficient, C,
SPINNING CHARACTERISTICS OF THE XN2Y--1 AIRPLANE
655
Figcire 7.— Variation of rolling-moment coefficient Ct (body axes) with angle of attack.
Pitching- moment coefficient, Cm Pitching-moment coefficient, C,
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
656
40 44 48 52 56 60 64 68 12
Angle of attack, cL ,deg.
(body axes) with angle of attack.
Angle of attack, oi ,deg.
Figure 8. — Variation of pitching-moment coefficient C,
Yawing-moment coefficient, C„ Yawing-moment coefficient, Cr
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
657
Figure 9.— Variation of yawing-moment coefficient Cn (body axes) with angle of attack.
s
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
■<■-.08
c
.Qj
.0
$
<u
o
u
X.
c
d)
o
e
Ch
.c
<
o
-.12
-.04
.08
-.12
— I —
i
60°
— c
c
) —
c
15C
f lb
ZV
•X —
— 1 —
■vs r
ci
= 4i
)°c’
*
-8 -4 0 4 8 12
Angle of sideslip, [3 ,deg
Figure 10. — Variation of rolling-moment coefficient
Ci (body axes) with angle of sideslip. 5a=0°;
8«=23°41' Up; 8, = 40° with spin.
Figure 11.— Variation of pitching-moment coefficient
Cm (body axes) with angle of sideslip. So=0°;
8,=23°41' up; a,=40° with spin.
Figure 12.— Variation of yawing-moment coefficient
C„ (body axes) with angle of sideslip. 5a =0°;
5e=23°41' up; 5r=40° with spin.
Figure 13.— Variation of rolling-moment coefficient
Ci (body axes) with Ub/2V. sa= 0°; 8e=23°41' up;
5r=40° with spin.
Figure 14.— Variation of pitching-moment coefficient
Cm (body axes) with Qbl2 V. 8o=0°; 5e=23°41' up;
dr— 40° with spin.
Figure 15.— Variation of yawing-moment coefficient
Cn (body axes) with ilb/2V. <sa=0°; <5,=23°4l' up;
<5r=40° with spin.
G*
-<■
c:
.jj
.u
QJ
8
C
OJ
5
o
e
Ch
C
.04
O
-.04
-.08.
—
r~
, 600
o -
- c
15L
.71
?l
lb
-
X—
rj zv
—
cl =
40
o
_
Again si spin O With spin
Tail selling (e lev a lor and rudder )
Against spin 0 With spin
Tall selling (e/evaior and rudder)
Figure lfi. — Variation of rolling-moment coefficient
Ci (body axes) with tail setting. /3=5°; 5„=0o.
Figure 17.— Variation of pitching-moment coefficient
Cm (body axes) with tail setting. /S=5°; <5„=0°.
Againsf spin
With spin
Tail selling (e/e valor and rudder )
Figure 18. — Variation of yawing-moment coefficient
C„ (body axes) with tail setting. /3 = 5°; o,.=00.
Aileron setting
G
x.-
C
.0
$
dl
o
u
x
b ■
<0
Q
5
I
Ch
-5
L)
.08
.12
.16
.06
-.10
TT
-
6(
r
—
o-
—
—
— C
15
.7.
?}
sib
zv
X-
<|
ci =
40
o
Against spin 0 With spin
Aileron setting
G
.04
.iy
.0
$ 0
4)
8 --02
Hi
t .02
o
5 O
t
Cn
.C
i - 04
^ ' Against spin
n
0°-
J
—
—
1
~;:r~
o
- -
0.501
Rb
X-
— 75|
ZV
—
—
~ — -* 40°
t
i l_
d
O
With spin
Aileron setting
Figure 19. — Variation of rolling-moment coefficient
Ci (body axes) with aileron setting. /3=5°;
8«=23041' lip; 8r=40° with spin.
Figure 20.— Variation of pitching-moment coefficient
Cm (body axes) with aileron setting. /3=5°;
8«=23°41' up; 8r=40° with spin.
Figure 21. — Variation of yawing-moment coefficient
Cn (body axes) with aileron setting. /S=5°;
8e=23°41' up; 5r=40° with spin.
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
659
DISCUSSION OF DATA
General series of tests. — The values of V^v"2+CV"2
(fig. 5) are given because they were used in the analysis.
The values of Cx and CY are not given because they are
small and are probably of no importance for any
analysis of the data.
Figure 22.— Variation of yawing-moment coefficient C„ (body axes) with rudder
setting. 6a=0°; 5,=23°41' up.
Comparison of coefficients from model and flight
results. — The difference in the coefficients in the hori¬
zontal plane (fig. 23) is irregular but shows a general
tendency to be slightly negative (model results smaller
than (light).
Angle of attach, ct ,deg .
Figure 23. — Variation of difference in horizontal-force coefficients of airplane and
model (earth axes) with angle of attack.
Slb/ZV
Figure 24.— Variation of difference in rolling-moment coefficients of airplane and
model ACi (body axes) with 06/21-'.
The difference in the rolling-moment coefficients
ACt shows no general tendency to vary with a or /3 but
shows a slight tendency to decrease as H6/2V is in¬
creased (fig. 24). The average value is 0.02, the same
as that found for the NY 1 and F4B-2 airplanes
(references 4 and 5). The individual values of ACt for
the NY-1 and F4B-2 airplanes are given in figure 24.
Angle of attach, cL ,deg.
Figure 25.— Variation of difference in pitching-moment coefficients of airplane and
model A Cm (body axes) with angle of attack.
Figure 26.— Variation of difference in yawing-moment coefficients of airplane and
model A Cn (body axes) with angle of sideslip.
The difference in pitching-moment coefficients ACm
shows no general variation with /3 or 06/2 Y but shows a
slight tendency to decrease as a is increased (fig. 25).
The average value of the difference is 0.02. The values
of A Cm from the results obtained with the F4B-2 and
the NY-1 airplanes are not sufficiently accurate for
comparison.
The difference in yawing-moment coefficients A Cn
shows no consistent variation with a or 06/2 V but in-
Figure 27.— Variation of yawing-moment coefficient Cn of parts of the airplane and
parts of the model with angle of attack. (Full-scale results from reference 2.)
creases as /3 is increased (fig. 26). The difference is
about 0.005 at slightly negative values of |3, increasing
to 0.02 at 13° sideslip. The values for the NY-1 and
F4B-2 airplanes are included for comparison.
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
()()()
The values of Cn for the fm and rudder were obtained
from the difference in the results obtained from the
tests of the complete model and of the model with the
fm and the rudder removed. The difference between
flight results (reference 2) and model results changes
from zero at 40° angle of attack to 0.003 at 60° (fig. 27).
The values of Cn for the model wings with the struts
and the attachment to the balance are about zero,
while those for the airplane wings are about 0.013.
Undoubtedly this difference is largely due to scale
effects, which may normally be expected. The values
of Cn for the model fuselage were obtained from the
results of tests with the wings removed from the model
^1.2
<vj
■fif0
o -a
k -O
>2 £
,u .6
£
4)
8 4°
~
X
Airplane '
□
Mo
del,
(wir
7 gs
f me
idet
wit
h w
ingt
re
V70V
ed)
X
X
X
■
D
H
@
8
□
%
Lg
o
X
X
X
r
X
~ □
x°
□
8
ft
X
>o
X
X
o
X
~C r
□
D
o |
X
□
44 48 52 56 60
Angle of attack, a ,deg.
64
66
Figure 28. — Variation of horizontal-force coefficient Cx" (earth axes) of airplane and
of resultant-force coefficient V Cx"2JrCy"2 (earth axes) of the model with angle of
attack.
<o
X'
c
,gj
.0
$
QJ
O
U
c
0)
5
0
I
Cn
V
0
JO
.08
.06
.04
.02
O
-.02
X
X
X
Air
at a
ne
o
D
Model \ complete
Model, (winas + m
ode
rno v
/ w
' ed
ith
o
o
w/f
ngs
re
□
□
X
/
X
/
k
1 He
r or
s v\
/ ith
spin!
--O
%
Ailerons
st
oin
X
%
□
X
X
X
X
X
X x
X X
o
o
□
>
On
8
o
13
o
□
°
r
□
b
11
40
44
68
12
48 52 56 60 64
Angle of attack, d , deg.
Figure 29.— Variation of rolling-moment coefficient Ci (body axes) of airplane and
model with angle of attack.
minus the values obtained for the fin and rudder and
are about the same as those obtained in flight at 40°
and 55° angle of attack. Below 58° the values for the
model are more positive and, above 58°, they are more
negative than those obtained in flight.
The yawing moments for parts of the airplane were
obtained in flight from pressure-distribution measure¬
ments on the important fuselage and tail-surface areas;
the measurements included the interference of all parts
of the airplane. The spinning-balance results were
measured without the interference of some parts. This
difference in method of measurement should give some
difference other than that due to scale effects in the re¬
sults and was intended to determine the scale and inter¬
ference effects so that data for individual parts of models
might be combined to give the characteristics of the com¬
plete model or airplane. The results of this part of the
investigation are not sufficiently complete to draw defi¬
nite conclusions because only one airplane is represented.
It does, however, give some indication of the magnitude
of the scale and interference effects that may be ex¬
pected.
The interference effects caused by testing the wings
alone and the model with wings removed for all the
Figure 30. — Variation of pitching-moment coefficient Cm (body axes) of airplane
and model with angle of attack.
Model (wings
+ model
fi with wings
removed) -
'~r pi _ i i i i
48 52 56 60
Angle of attack, ct , deg.
Figure 31. — Variation of yawing-moment coefficient Cn (body axes) of airplane and
model with angle of attack.
coefficients, together with the values obtained for
the airplane, are given in figures 28 to 31. At the
higher angles of attack the values of f°r
the complete model show a tendency to be greater than
for the sum of the parts (fig. 28). The values of Ct for
the complete model are generally more positive, by
about 0.005, than the sum of the parts (fig. 29). The
interference effect on Cm is small (fig. 30). The values
of Cn for the sum of the parts are more negative than
the values for the complete model below 49° angle of
attack; above 49° the effect is reversed (fig. 31).
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
661
ANALYSIS OF DATA
derivation of equations used in computing the spinning
ATTITUDE FROM SPINNING-BALANCE DATA
Since the necessary condition for a steady spin is
that the aerodynamic forces and moments must ex¬
actly oppose the weight, centrifugal force, and inertia
moments of the airplane, the following relations may be
written.
(Because the resultant force on an airplane is not
necessarily perpendicular to the IT plane of the air¬
plane, as it was assumed to be in the computation of
the attitudes, the computed azimuth setting of the
model on the balance had the effect of rotating the
resultant-force vector in the horizontal plane so that
CY" was not zero. Since CY" must be zero in a steady
spin and the resultant force in the horizontal plane must
be exactly opposed by the centrifugal force, the result¬
ant-force coefficient CYC is used instead of
(J x” as might normally be expected.)
1 /2p V2SCZ" = mg (1)
1 l2pV2S^JCx„2+CYA=m92R (2)
l/2pV2SbCm=lj292(A— C) sin 2a cos 2(<t+/8) nearly (3)
1/2 pV2SbCi=Q?(C~B) sin a sin (<rT/3)
cos (cr+) 3) nearly (4)
l/2pV2SbCn=Q2(B~A ) cos a cos (<r-fj8)
sin (cr — (— /3) nearly (5)
where <x is the angle between the vertical and the helix
described by the center of gravity of the airplane.
Relation (3) may be rewritten as
9.b
r
-Cn
-X
2V \ 4 p sin 2 a cos2 (<r+/3)
m j / b2 \ Wb
where and Uj-jg )=jm=
Gz’-fcx2)
v
9 iP— A)
Dividing relation (4) by (3) gives
where
p _ p k 7} ~kY2 tan (<r-f- (3)
mkz2~kx2 cos a
kz2 — kY2 C-B
kz2-kx2 C-A
Dividing relation (5) by (4) gives
'kY2 — kx
Cn=Ci COt,
a
kz2-kC
where
ky-kx2\ B-A
B
/ kY kx \ _ B-
\kz2 — kY2 )~ a
(0)
(7)
(8)
sin '7-=-pF from definition
(9)
sin (j -
V CX"2~\~CY"2
A {>J>
4m2F
from (2) and (9)
(10)
COMPUTED SPINNING EQUILIBRIUM
1. The value of a is obtained for each test condition
by using equation (10).
2. The value of V.b/ 21' required for balance of the
aerodynamic and inertia pitching moments is computed
from equation (6) for each test condition, Cm being
increased by 0.02 for reasons given in the text. These
computed values of ilbj2Y and the values used in test¬
ing the model were plotted against Cm. (See fig. 32.)
The intersection of these curves gives the equilibrium
values of 9b /2V and Cm for each angle of attack at
each angle of sideslip tested.
Slb/2V
Figure 32.— Variation of pitching-moment coefficient, Cm (body axes) with nb/2V
(Value of Sib/ 2 V from tests.) (8= —10°.
3. The value of the rolling moment required for
equilibrium with the inertia moment is found from
equation (7) by using the values of Cm and <r that gave
a balance of pitching moments (par. 2). These rolling
moments, and those from the test data, increased
by 0.02, are plotted against /3 for each angle of attack
in figure 33. Intersection of these curves gives values
of /3 and Ct for spinning equilibrium at each angle
of attack tested.
4. The values of the aerodynamic yawing moment
required for equilibrium are obtained from equation (8)
by using the value of Ct found from paragraph 3,
662
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
40 50 60 70
Angle of atfack,c(,deg.
Finns e 33.— Sample chart showing method of determining'angle of sideslip and angle of attack necessary for equilibrium in spins. 5,=23°41' up; 5r=40° with spin;
kz ^ b*
m=4.74;
;=59.3.
and those obtained from the data (changed according
to fig. 2G for full-scale) at corresponding conditions
are plotted against angle of attack (fig. 33). Equilib¬
rium in a spin is indicated where these curves intersect.
5. The value of Qb/2Y for the attitude found by the
method of paragraph 4 is determined in the following
way: Plot the aerodynamic rolling moments required,
computed for each angle of attack from paragraph 3,
against ttb/2V, from which the value of i2b/2V for each
angle of attack can be found, since the value of Ci
for equilibrium lias been obtained in paragraph 3.
(Fig. 34 is a sample chart.) Plot these values of
ilbj2Y against a and, since the value of a of the spin
is known from paragraph 4, the value of ilb/2V for
the indicated spin is obtained.
This method of analysis is essentially the same as
that given in reference 8, modified for use with the
data from the complete model instead of from only
the wing.
INDEPENDENT VARIABLES USED IN COMPUTATIONS
Computations for estimations of spin characteristics
were made for assumed characteristics of the airplane
for comparison with flight results, and are tabulated
in table II.
Table III gives the assumed airplane characteristics
that were used to estimate spins for a comparison with
the results from the free-spinning tunnel. A model
made to the same dimensions as the model tested on
the spinning balance and with these same parameters
was tested in the free-spinning tunnel.
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
663
TABLE II.— AIRPLANE PARAMETERS
M
1
62
kz'—kr 2
(5a
(deg.)
5,‘
(deg.) (min.)
Sr2
(deg.)
kz2—kx2
kz2—kx2
i
2.5
70
.
1.00
0
-23
41
-40
4.5
70
1.00
0
-23
41
-40
7.5
70
1.00
0
-23
41
-40
10.0
70
1.00
0
-23
41
-40
4.5
50
1.00
0
-23
41
-40
4.5
90
1.00
0
-23
41
-40
4.5
110
1.00
0
-23
41
-40
4.5
70
.50
0
-23
41
-40
4. 5
70
1. 50
0
-23
41
-40
4.5
70
2.00
0
-23
41
-40
4.5
70
2. 50
0
-23
41
-40
4.5
70
1.00
3 Against
-23
41
-40
4.5
70
2.00
Against
-23
41
-40
4.5
70
1.00
* With
-23
41
-40
4.5
70
2.00
With
-23
41
-40
4.74
59. 30
.616
0
-23
41
-40
5 3.91
60. 90
.718
0
-23
41
-40
4.74
73. 73
2.0
0
25
0
40
4.74
73. 73
2.5
0
25
0
40
4.74
73. 73
2.0
0
0
0
0
4.74
73. 73
2.5
0
0
0
0
7.5
70
2.0
0
0
0
0
7.5
70
1.0
0
0
0
0
7 5
70
2.0
0
25
0
40
7.5
70
1.0
0
25
0
40
1 Positive when elevators are down.
2 Positive in a right spin when rudder is against spin.
3 Right aileron up 25°, left aileron down 15°.
4 Left aileron up 25°, right aileron down 15°.
s Corresponds to flight tests 38L, 40L, and 41L of reference 1.
TABLE III.— SPIN-TUNNEL PARAMETERS
M
kz2~ky 2
(5a
(deg.)
be
(deg.) (min.)
Sr
(deg.)
kz2—kx 2
kz2—kx2
4.80
62. 00
0. 558
0
-23
41
-40
4. 90
63.00
.853
0
-23
41
-40
5.00
64.49
1. 147
0
-23
41
-40
5. 09
65. 76
1.440
0
-23
41
-40
5. 19
67.03
1.734
0
-23
41
-40
6. 16
79. 55
.558
0
-23
41
-40
7. 52
97. 13
.558
0
-23
41
-40
7. 52
97. 13
.558
0
0
0
0
7. 52
97. 13
.558
0
25
0
40
7. 52
97. 13
1. 734
0
0
0
0
7.52
97. 13
1.734
0
25
0
40
Under standard conditions at sea level for this air¬
plane, values of n of 2.5 and 10 correspond to wing
loadings of 5.36 and 21.46 pounds per square foot, re¬
spectively. The variables used were chosen to cover
the range for all wing loadings and moments of inertia
likely to be used with an airplane of this type and in¬
cluded some specific values used in flight and in the
free-spinning tunnel.
The results of the analyses are given in figures 35 to
40. Each analysis, with <5e=23°41/ up, was com¬
puted, in addition to <5r=40° with, for rudder settings
of 25°, 17°, 8°, and 0° by using the values of Cn given
in figure 22 and by assuming that the only effect of
moving the rudder from 40° with the spin was to change
C„ and that the value of Pb/ 2U was 0.75 at a=60° and
0.50 at <2=50°. These assumptions are only approxi¬
mate because Cn changes considerably with 126/2 V (see
fig. 15) and Cm changes with rudder movement. The
results are included because they indicate the general
effects of rudder deflections.
ARBITRARY CORRECTIONS TO SPINNING-BALANCE DATA USED IN
MAKING THE ANALYSIS
Full-scale.— Previous investigations (references 4
and 5) and figures 23 to 26 indicate that it is necessary
to correct spinning-balance data when estimating
38548—38 - 43
spins. No correction to Cx» is considered necessary
because ACX» is a small percentage of CX” and rather
large values of A CX" would make but small differences
in estimating spins. The average value of 0.02 has been
added to C\ and Cm because A Ct and ACm show only
slight tendencies to vary with a, or Pb/2V, and the
individual points are scattered. All Cn values were
changed by the amount indicated by the curve (fig. 26)
for this analysis because the curve of ACtl against fi is
well defined and the differences are sufficiently large to
cause large angle-of-attack differences in the estimated
spin.
Free-spinning tunnel. — If the differences between
spinning-balance and flight results were all due to scale
effect, then steady spins estimated from uncorrected
balance data should agree with those obtained in the
free-spinning tunnel. However, the values of 06/2 V
obtained from tests in flight and in the free-spinning
tunnel (references 2 and 3) are very nearly the same
and, since Cm determines to a large extent the curve of
06/2U against a (fig. 34), a correction of 0.02 was
applied to Cm for all estimations of spins used for com¬
parison with the results from the free-spinning tunnel.
DISCUSSION OF RESULTS OF ANALYSIS
ESTIMATED FULL-SCALE ATTITUDES
Increasing ^ increases the angle of attack, makes the
sideslip more positive, and increases the values of
06/2U when the rudder is 25° or more with the spin
(fig. 35). In general, it appears that increased wing
loadings and higher altitudes would make the spin
flatter and recoveries slower and more difficult.
Increasing the pitching-moment inertia parameter
b2l{kz—kx) (decreasing C—A) generally decreases the
angle* of attack, makes the sideslip more outward
(negative in a right spin), and does not appreciably
change 06/2U (fig. 36). The effect on time for recovery
of changing b2f(kz2—kx2) would probably be small.
Increasing the rolling- and yawing-moment inertia
parameter (Jcz2—kY2)/(kz2—kx2), i. e., moving weight
from the center of gravity out along the wings (fig. 37),
increases the angle of attack and 126/2 U and makes the
sideslip more nearly zero. Increasing this parameter
would apparently make the airplane spin faster and
flatter with recoveries probably slower and more
difficult.
This analysis indicates that a large value of n and a
large value of (kz2—kY2)/(kz2—kx3) would make the air¬
plane spin at high angles of attack and very fast. It
was thought that large values of these parameters
might produce spins with the controls neutral or against
the spin. Accordingly, analyses were made with n =
7.5, 62/ {kz — kx2) =70, (kz2-kv2)/(kz2-kx2) = 1.0 and
2.0, and tail surfaces both neutral and against the spin;
but in no case was a spin indicated. Approximately
the same conditions were tried in the free-spinning
tunnel with the same results.
664
REPORT NO. 607— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Moving the rudder, with elevators up, any amount
from full with the spin to neutral in all cases reduces
the angle of attack and ttb/2V and makes the sideslip
more outward.
Equilibrium was impossible in every case in a spin
analyzed with elevator and rudder neutral or both
against the spin. Moving the ailerons from against
the spin to with the spin (fig. 38) decreases the angle
of attack and decreases V.b/2}’ with elevators up and
this analysis are shown in figure 39. The estimated
spins agree very well with flight results when ( kz 2—
kY2)l(kz2—kx2) is equal to 1.4. For other values of this
parameter the disagreement between the results is
considerable. When (kz2—kY2)/(kz2—kx2) is equal to
0.718, the only condition flight-tested both to the right
and left, the flight residts are generally greater or less
than those obtained from analysis, depending upon
whether the airplane was spun to the right or to the
Figure 35.— Variation of estimated values
of angle of attack, angle of sideslip,
and V.b/2V with relative density of air¬
plane. 5o=0°; = 23°41' up; jp£j|^=1.0;
_
k22-kx
Figure 36. — Variation of estimated values of angle of attack,
angle of sideslip, and 06/2Vwith pitching-moment inertia pa¬
rameter
k22—kx2
5a= 0°; 5<=23°41'up; m=4.5;
kz2-kYi
kz2—kx2
= 1.0.
Rollinq- and yawing- ^ z
moment inertia parameter, ~~
Kz
Figure 37. — Variation of estimated values of angle
of attack, angle of sideslip, and ilb/2V with rolling-
fcz2- fcv2
and yawing-moment inertia parameter
1 = 70.
5 a = 0°; 5,= 23°41' up; m=4.5;
b2
kz2—kx2
kd-kx2
70.
rudder full with the spin. With other rudder settings
this effect is reduced and, with 5r = 0° and {kz—kY2)l
(kz2—kx2) = 2.0, the angle of attack and Qb/2V are
increased. Ailerons moved from against the spin
to with the spin generally tend to increase the sideslip
and make the values more nearly the same for all rudder
settings.
COMPARISON WITH FULL-SCALE RESULTS
An analysis for estimation of spins was made for some
flight conditions given in reference 1. The results of
left. There is no doubt but that part of this difference
is due to dissymmetry of the airplane used in the
flight tests. The results of the one test with wing-tip
ballast show considerably different aerodynamic charac¬
teristics than do the results of the tests without ballast
(reference 2); this discrepancy, however, may be due
to the changing of the period of vibration of the wings
by the ballast, thus affecting the rolling and yawing
moments. At the beginning of these tests on the spin¬
ning balance it was found that, under certain conditions,
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
665
the rolling moment (for earth axes) could he varied as
much as 100 percent by changing the tension of a
spring attached to the rolling-moment arm in the balance.
When the rigidity of the wings with respect to the
fuselage was increased, this variation in moment with
spring tension completely disappeared. There can be
little doubt that this variation was aerodynamic
because the balance was carefully checked and a
corresponding condition has been observed in which the
setting of zero is very questionable, as previously
explained, and therefore will not be discussed.
The angle of sideslip for rudder settings of 40° and
17° with the spin is generally within the limits of error
(a degree or so) of the results obtained in the free-
spinning tunnel.
The values of Cn are usually 0.001 to 0.003 too low to
give the angle of attack obtained from the free-spinning
tunnel. This difference indicates that the results from
tail surfaces and wings of a model vibrated during
routine tests in another wind tunnel.
COMPARISON WITH RESULTS FROM THE FREE-SPINNING TUNNEL
The results of the analysis and results of tests from
the free-spinning tunnel are given in figure 40. The
estimated values of (5, 126/2 V, and Cn necessary for
equilibrium in a steady spin are plotted against the
angle of attack; the values obtained from the free-
spinning tunnel were obtained from reference 3 and
from unpublished data. The results agree fairly well
except below 40° angle of attack, in which range the
model could not be tested on the spinning balance
because of interference with the balance. The extrapo¬
lation of the spinning-balance data for the rudder
the free-spinning tunnel are slightly more positive than
those obtained from the spinning balance; however,
this discrepancy may be an indication that the correc¬
tion of 0.02 to the pitching moment was not large
enough, since increasing the value of the correction
reduces the difference.
The fact that the values of 126/2 V are usually slightly
lower than those obtained from the free-spinning tunnel
also indicates that a correction to Cm of the order of
0.021 or 0.022 would have given slightly better agree¬
ment for both 126/2 V and Cn.
The agreement between spins as estimated from
results obtained from the spinning balance and from
those obtained from the free-spinning tunnel is gener¬
ally well within the limits of error except for the neces¬
sary correction to Cm.
Angle of sideslip, /3, deg. ^b/ZV Yawing-moment coefficient, Cn
660
REPORT NO. GOT— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(a) m = 4.8;
(b) m=4-9;
kyi-lcx*
bi
kz2—kx-
=62;
kA-kyi
kA-kx*
= 0.55S.
= 03.3;
kz*-ky
kz^—kx1
V =0.853.
6- kz 2 —
(C ^ = 5-0; A22-A.y2_ 64-49; fcz2_fcx8=1-147-
b2 _
(d. m=5.09; y2=G5.7T>; "fcz2_fcxa=1-44-
x 62
(e)
- 67.03:
fcz2-fcr
k/-—kx
:= 1.734.
(b) m= 7.52; ^3^=97.13;
kA-kyi
kz‘—kx
(0 M
» =0.558.
62 kz2 — 6k2
= fU6: AV-fc**”"9-55: kz^^0 m-
Figure 40 —Variation of angle of sideslip, yawing-moment coefficient, and ii6/2 V with angle of attack. 5a=0°; <5e = 23°41' up.
SPINNING CHARACTERISTICS OF THE XN2Y-1 AIRPLANE
COMPARISON OF SPINS OBTAINED IN THE FREE-SPINNING TUNNEL
WITH THOSE OBTAINED IN FLIGHT AS INDICATED BY THE
SPINNING-BALANCE DATA
The comparison of spins in flight and in the free-
spinning tunnel is based on the necessary corrections to
the data obtained from the spinning balance to give
agreement with results from flight and from the free-
spinning tunnel.
The differences in CX" (force coefficient in the hori¬
zontal plane) and in Cm are not large enough to have an
appreciable effect on the results. The effect of changes
in CX" have been shown in references 7 and 8 and the
changes in Cm have been discussed in this report.
If an arbitrary constant of 0.02 could be added to the
Ci for tests in the free-spinning tunnel, the sideslip of
the model and the airplane should be about the same.
The differences in yawing moments are but slightly
less than those given in figure 26. In the comparison
of spins, however, the difference in yawing moment
required caused by the difference in sideslip between
the model and the airplane must be considered.
The effect of sideslip on the yawing moment required
is reflected as a change in Ci in equation (8):
Cn = Ci cot a
For the model of the XN2Y-1 airplane, Ci would always
be about 0.02 less than for the full-scale airplane
because the aerodynamic rolling moment does not
change much with /3. (See fig. 33.) If (B — A) is
positive, the value of Cn required for the model will
always be less than for the airplane, which gives (in the
analysis) the same effect as adding an increment to the
aerodynamic yawing moment available. The result of
this counteracting effect is that the model may spin at
the same angle of attack and recover in much the same
manner as the airplane. When (7? — El) is negative,
this effect will be reversed and greater discrepancies
between model and airplane spins may be expected.
Also, the aerodynamic yawing moment may be consid¬
erably different because of the difference in sideslip
between the model and the airplane, since the yawing-
moment coefficient varies with angle of sideslip. (See
figs. 12 and 22.) The inference from these comparisons
is that the free-spinning tunnel will, for certain air¬
planes, give reasonable indications of the behavior of
the airplane in the spin but in other cases the beha vior
of the model and of the airplane may be considerably
different.
CONCLUSIONS
1. Scale effects on models, and tunnel and oscillation
effects on the spinning-balance results, make it difficult
to estimate the equilibrium attitude in a full-scale
spin.
2. For the XN2Y-1 airplane the differences in C} and
Cn between full-scale and spinning-balance results
667
agree with the differences found for two other airplanes
previously tested. No comparisons of Cm can be made
with previous results because of the inaccuracy of this
value in the earlier tests.
3. An average difference of 0.02 was found in C\ and
Cm between flight results and spinning-balance results.
The differences in Cn were found to increase with 6
as d became more positive (more inward sideslip in a
right spin). The value of Cn was found to be about
0.005 at slightly negative values of sideslip, increasing
to 0.02 at 13° positive sideslip.
4. Good agreement for steady-spinning attitudes
between results from the free-spinning tunnel and esti¬
mations of spins from spinning-balance data can be ob¬
tained by adding 0.02 to the values of the pitching-
moment coefficients measured with the spinning
balance.
5. This investigation indicates that good agreement
in the attitude for steady spins between results from
full-scale tests and those from the free-spinning tunnel
can be obtained by adding 0.02 to the model rolling-
moment coefficient and an increment that depends on
the angle of sideslip to the model yawing-moment
coefficient.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Ya., April 16, 1937.
REFERENCES
1. Scudder, N. F.: A Flight Investigation of the Effect of Mass
Distribution and Control Setting on the Spinning of the
XN2Y-1 Airplane. T. It. No. 484, X. A. G. A.. 1934.
2. Scudder, X. F.: The Forces and Moments Acting on Parts
of the XX2Y-1 Airplane During Spins. T. R. No. 559,
X. A. C. A., 1936.
3. Zimmerman, C. H.: Preliminary Tests in the NT. A. C. A.
Free-Spinning Wind Tunnel. T. R. No. 557, X. A. C. A.,
1936.
4. Bamber, M. J., and Zimmerman, C. IE: The Aerodynamic
Forces and Moments Exerted on a Spinning Model of the
NY-1 Airplane as Measured by the Spinning Balance.
T. R. No. 456, X. A. C. A., 1933*.
5. Bamber, M. J., and Zimmerman, C. H.: The Aerodynamic
Forces and Moments on a Spinning Model of the F4B-2
Airplane as Measured by the Spinning Balance. T. X.
No. 517, X. A. C. A., 1935.
6. Wenzinger, Carl J., and Harris, Thomas A.: The Vertical
Wind Tunnel of the National Advisory Committee for
Aeronautics. T. R. No. 387, X'. A. C. A., 1931.
7. Bamber, M. J.: Spinning Characteristics of Mings. II-Rec-
tangular Clark 4' Biplane Cellule: 25 Percent Stagger;
0° Deealage; Gap,/ Chord 1.0. T. X'. No. 526, XX A. C. A.,
1935.
S. Bamber, M. J., and Zimmerman, C. II.: Spinning Character¬
istics of Wings. I- Rectangular Clark Y Monoplane Wing
T. R. No. 519, X. A. C. A., 1935.
REPORT No. 608
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
By Paul Kuhn
SUMMARY
The fundamental action oj shear deformation oj the
-flanges is discussed on the basis oj simplifying assumptions.
The theory is developed to the point of giving analytical
solutions for simple cases of beams and of skin-stringer
panels under axial load. Strain-gage tests on a tension
panel and on a beam corresponding to these simple cases
are described and, the results are compared with analytical
results. For wing beams, an approximate method of
applying the theory is given. As an alternative, the
construction of a mechanical analyzer is advocated.
INTRODUCTION
The so-called “semimonocoque” type of construction,
which has been favored by aircraft designers for some
time, presents serious difficulties in stress analysis.
Static tests have proved that the bending action of such
a structure is not always described with sufficient
accuracy by the standard engineering formulas based
on the assumption that plane cross sections remain
plane. It will be necessary, therefore, to devise new
working theories for the action of semimonocoque beams
under bending loads.
In order to arrive at reasonably rapid methods of
stress analysis, it is necessary to make rather sweeping
assumptions. It is obvious that the range of applica¬
bility of any such method is limited. The present
paper concerns itself with beams typical in general
form of one class of beams used in airplane construction,
that is, with fairly shallow, wide beams, having flat covers,
symmetrical about the center line, with two shear webs and
with bulkheads that offer no appreciable resistance to
deformation out of their planes.
Briefly, the action of such a beam under loads applied
at the shear webs is as follows: The transverse shear is
taken up by the shear webs. The flanges attached to
these shear webs furnish part of the longitudinal stresses
required to balance the external bending moment.
The strains set up by these stresses induce shear stresses
in the skin which, in turn, cause longitudinal stresses in
the intermediate stringers attached to the skin until
sufficient longitudinal stresses exist at any section to
balance the external bending moment.
If the skin between stringers did not deform under
the action of the shear stresses, the standard beam
formulas would apply. The thin sheet, however, has
very little shear stiffness and suffers large deformations
under load. As a result, the first intermediate stringer
next to a shear web carries a smaller stress than the
flange of the shear web, the next intermediate stringer
carries less stress than the first one, and so on to the
center stringer, which carries the smallest stress. This
phenomenon of the interdependence between stringer
stresses and shear deformations forms the subject of
the present paper.
Apparently Dr. Younger was the first person in this
country to give serious attention to this subject. In
reference 1 he gives a formula for the efficiency of a box
beam with walls of uniform thickness, which may be
considered as the limiting case of very many extremely
small stringers. Nothing more on the subject was
published until two experimental studies appeared in
1936. Reference 2, dealing with the case of a skin-
stringer panel in edge compression, includes a theoretical
solution for a particular case. Reference 3 deals with a
box beam in pure bending, a problem identical with the
one treated in reference 2. In both studies the stringer
stresses experimentally obtained were used to compute
efficiency factors for the shear stiffness of the sheet.
The most important practical problem is the inverse
of the problem dealt with in references 2 and 3; namely,
given the shear stiffness, to calculate the stringer
stresses. The problem is difficult and complex. In
order to arrive at any solution, it has been necessary to
use a very much simplified concept of the action of the
structure, as suggested in references 1 and 2. On the
basis of this simplified concept, the analytical solutions
for a few very simple cases of axially loaded panels and
of beams are derived in this paper. For other cases,
it will be shown that a trial-and-error method of solution
is feasible.
The analytical solutions as well as the trial-and-error
method apply only to very elementary cases, namely,
to three-stringer panels under axial load and to beams
with a single longitudinal stringer attached at the
center line of the cover sheet. It has been considered
worth while to devote considerable space to the dis¬
cussion of these elementary cases for the following
reasons:
1. The study of these simple cases greatly facilitates
the understanding of the fundamental principles. (It
is very strongly urged that anyone desiring to use the
670
REPORT No. 608— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
proposed method of analysis work, by the trial-and-
error method, at least one example each of a panel under
axial load and of a beam.)
2. The simple cases afford a very convenient way of
experimentally checking the validity of the assumptions
made. Strain-gage tests made for this purpose on a
tension panel and on a beam are described in this paper.
3. The solutions obtained for beams with a single
longitudinal can be used as checks on the degree of
approximation attainable with the “constant-stress
method” proposed later for analyzing actual wing beams.
An additional reason for the lengthy discussion will
only be mentioned in passing. Under certain condi¬
tions, a beam with a single longitudinal stringer may
give useful approximations of the stresses in a beam
with many stringers. Such a simplified substitute beam
makes it possible to obtain some rough ideas on the
influence of bulkheads, an influence that was neglected
in the present discussion.
Two methods are proposed for winglike structures.
One method is the construction of a mechanical ana-
t
(a) Axially loaded panel subjected to shear deformation.
(b) Mechanical model.
Figure 1. — Three-stringer panel.
lyzer permitting a solution that is “exact” within the
assumptions made. The other method is based on the
assumption that the structure is so dimensioned as to
approach the ideal design of constant flange stress along
the span. For this ideal case, the analytical solution
can be obtained. The actual case will have deviations
from the ideal case, which are termed “faults.” These
faults are minimized as much as possible by applying
corrections, and the stresses caused by the corrections
are superposed on the stresses of the ideal case.
SYMMETRICAL THREE-STRINGER PANEL UNDER AXIAL
LOAD
FUNDAMENTAL CONSIDERATIONS
The simplest possible structure in which shear
deformation must be taken into account is shown in
figure 1 (a). Two stringers, A and A' , of equal section,
are connected to an intermediate stringer B by means
of a thin sheet C. The upper edge of this sheet is
reinforced by bars D. The stringers and the sheet are
attached to a foundation F.
The important phases of the elastic action of this
structure may be visualized with the help of the
mechanical model sketched in figure 1 (b). This
model represents one-half the structure, which is per¬
missible because the structure is symmetrical. Helical
springs represent the stringers A and B and their
elastic resistance to longitudinal deformation. Coil
springs represent the elastic resistance of the sheet to
shear deformation. It is assumed that the stringers
carry only longitudinal stresses and that the sheet
carries only shear stresses. For the mechanical model
it is assumed that guides prevent any deflection of the
springs other than that for which they are designed.
The stresses resulting from the load P are shown
qualitatively in figure 2. At the top of stringer A the
Figure 2.— Notation for axially loaded panels.
stress is aA=P/AA, at the top of stringer B it is aB=0.
The shear stresses r acting on the sheet gradually take
the load out of stringer A and transfer it to stringer
B. If the panel has sufficient length and if the sheet
has sufficient shear stiffness, the stresses <rA and <jb will
be very nearly equal at the root.
EQUATIONS OF THE PROBLEM
The equations governing the problem under the
simplifying assumptions can be very easily set up.
Figure 3 shows a strip of length dx cut from the panel
FA+dFA FB + dFB
Figure 3.— Element of panel.
and Separated into its component parts. The equation
of equilibrium gives
dFA=dSc=-dFB (1)
(See list of symbols, appendix A.)
It should be noted that these equations are written
for the structure as shown in figures 1 (b), 2, and 3,
which is one-half the original structure in figure 1 (a),
so that AB is one-half the area of stringer B as shown in
figure 1 (a). The sign convention used throughout this
paper is that tensile forces and stresses are positive and
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
671
that shear forces and stresses in the sheet are positive
when caused by positive stresses in the loaded stringer
A (or in the flange F in the case of beams).
The elastic deformation of the structure is shown in
figure 4. Two corresponding points 1 and 2 are dis-
////7///7Z/77/Z7
Figure 4.— Elastic deformation of panel.
placed to new positions 1' and 2'. The total displace¬
ments are given by
°A
E
dx and uB=
The shear strain is given by
uA—uB
y = -T-
and since
where Ge is the effective shear modulus, these relations
may be combined into
The last equation may be written
dT=j^(<TA — aB)dx (2)
Equations (1) and (2) may be combined into a differ¬
ential equation (see appendix B) which, together with
the boundary conditions, defines the problem com¬
pletely. If there are more stringers, a system of
simultaneous differential equations results.
SOLUTION OF THE EQUATIONS
For the fundamental case of a symmetrical three-
stringer panel of constant cross section, the analytical
solutions are given in appendix B for two cases: The
panel attached to a rigid foundation and loaded at the
free end, and the panel free in space strained by displac¬
ing the ends of the stringers a known amount. Com¬
bining the two solutions makes it possible to calculate
loaded panels attached to an elastically yielding
foundation.
For the analysis of three-stringer panels in which the
stringer areas and the shear stiffness of tfie sheet vary
along the axis, a trial-and-error method has been found
feasible.
The recommended procedure for the trial-and-error
method is as follows:
Divide the length L of the specimen into a suitable
number of bays. Tabulate the average values of t, Aa,
and Ab for each bay.
Assume values for the increment of shear ASC in
each bay. According to equation (1)
AFa= — AFb=ASc
With the assumed values of AFa and AFb and the
known values F A—P and FB= 0 at the end of the panel,
calculate for all stations along the length of the panel
the forces in the stringers and then the stresses in the
stringers. From these values calculate the shear stresses
and the shear forces in the sheet. The method of tabu¬
lation is shown in table I. In this example, the values
of Aa, Ab, and t are constant and need not be tabulated.
The calculated values of ASC will not, in general, agree
with the originally assumed values. Change the assumed
values and repeat the entire process until a satisfactory
agreement is reached between the assumed values of
ASC and the calculated ones.
In the choice of the first set of values for ASC, the
analyst must be guided by previous experience. The
only condition known at the outset is
Sc<
P Ab
Aa-\-A
B
because this is the maximum possible force that would
he transmitted to stringer B only if the shear deforma¬
tion were reduced to zero.
The most difficult step, and the one upon which the
success of the method hinges, is to compare the cal¬
culated ASC curve with the assumed one and, on the
basis of this comparison, to derive a new curve modified
in such a way that the repetition of the entire calculation
will yield a calculated ASC curve that agrees with the
assumed one. No general ride can be given concerning
the method beyond stating that decreasing the assumed
ASC values at any point will raise the calculated ones and
vice versa. Some practice is necessary to develop the
skill required for this step. Five trials should be suffi¬
cient, in general, to obtain an agreement to 1 or 2 per¬
cent for five or six bays unless the variations of areas are
extreme.
It should be emphasized that the method is a trial-
and-error one and not a method of successive approxi¬
mation, i. e., the calculated ASC curve cannot be used
as the assumed curve for the next cycle.
EFFECTIVE SHEAR STIFFNESS AND EFFECTIVE STRINGER AREAS
Two quantities must be determined before an analysis
can be started — -the effective shear stiffnesses and the
effective stringer areas.
The shear stiffness of a flat sheet is equal to the shear
modulus G of the material. If the sheet buckles into a
diagonal-tension field and the edge members are rigid,
the shear stiffness is the theoretical shear stiffness of a
diagonal-tension field Ge—%G (for duralumin or steel).
38548 — 38 - 44
672
REPORT No. 608 — NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
von Karman’s
in the form
formula for effective width was used
2w= 1.9-
IE
t
%x/% duro/
strip
{ 4^ -
0.016 dural sheet
ee-
Section A- A
Figure 5.— Test panel.
V
where vo is the effective width (on one side of the
stringer) and a the stress in the stringer. This formula
is probably always conservative in the range in
question.
COMPARISON BETWEEN TEST AND CALCULATED RESULTS
In order to check the validity of the method thus far
developed, a test specimen was built to represent a
structure corresponding to figure 1 (a). A sketch of the
actual test specimen is shown in figure 5. Pin-end steel
bars (not shown in the figure) spaced 3 inches apart
were used to separate the edge stringers from the cen¬
tral stringer and to take up the transverse component
of the diagonal-tension field that developed under load.
In each bay between these bars, the strains in the
stringers were measured with 2-inch Tuckerman strain
gages on both sides of the specimen. This precaution
proved necessary because the stresses on the two sides
differed so much at some stations that readings on only
one side would have been almost useless.
The load was increased from zero to the maximum
of 4,800 pounds in five steps. With a very few minor
exceptions, the points for any one gage fell on straight
lines. For each station, the results obtained on the
front and the back of the specimen were averaged and
the average values are plotted in figure 6.
The condition of a pure diagonal-tension field is not
reached, however, until the buckling shear stress has
been considerably ex¬
ceeded. Consequently,
values intermediate be¬
tween G and %G will
occur at stresses not
too greatly in excess of
the buckling stress (i. e.,
3 to 5 times), provided
that the edge members
are sufficiently stiff. If
the edge members are
not sufficiently stiff or
well braced to take the
transverse component of
the diagonal tension and
particularly if the sheet
carries edge compression
in addition to shear, the
shear stiffness may drop
to very low values.
Values as low as Ge=
0.1 G have been reported
(reference 3); although
the numerical accuracy
of this particular anal¬
ysis has been questioned, it serves at least as a useful indi¬
cation of what may be expected, remembering that this
test was stopped long before
reaching the ultimate load. ^600Q
Quantitative information on ct
this subject is scarce. Fortu¬
nately, as will be shown later,
the shear stiffness need not be
very accurately known to obtain
reasonable accuracy in the
stringer stresses.
It is clear that the sheet will
not only act as a shear member in
accordance with the theory but
will also assist in carrying longi¬
tudinal stresses. The following
assumptions have been used:
1. For a sheet carrying ten¬
sion in addition to shear, it was
assumed that the sheet is fully
effective in tension; i. e., the
sheet up to a line halfway be¬
tween the stringers is added to
the stringer proper when com¬
puting the cross-sectional area
of the stringer. This assump¬
tion is obviously somewhat un¬
safe and should be modified when
the stringer stresses are high.
2. For a sheet carrying com- Distance from top, percent
pression in addition to the shear, Figure 7.— Comparison between calculated and experimental results for compression test panel. (Data from reference 2.)
20 25 30
Distance from top, in.
Figure 6. — Comparisons between calculated and experimental results for tension test panel.
tO, OOO
8,000
.C
6*
b
q
«0
lo
Q)
k
<o
6,000
4,000
2,000
O
— 1 i r- 1 i i i rn f
o Experimental dota, edge stiffener
} *
= /0
x/Os
>
N. -
A
n
" , center »
Calculated, Ge = 0.2 G
// n - n —
o
C
O"-' ,
-*e
A
—
P,
P
/
— ^
/
A /
/
/
/
!/
X -
P= 2,000 lb.
1 _
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
The calculations were made for the two different
assumptions of the shear stiffness indicated on the fig¬
ure. The second assumption of Ge=%Gin the top part
was based on the experimentally observed fact that one
well-developed diagonal-tension fold showed in the top
of the panel on each side, in agreement with the cal¬
culation showing that at the maximum load the shear
stress in this region was about six times the buckling
stress.
The second assumption gives perfect agreement be¬
tween calculated and test results for the stress in the
central stringer. The agreement is not quite so good
on the edge stringer, the discrepancy occurring chiefly
at the root. Several explanations of the discrepancy
may be offered. An error of several percent may be
caused by an error in the value of E assumed to convert
strain readings to stress readings. The simple theory
used may break down to some extent near the root and,
finally, jig deflection may cause errors. The steel
triangle used on the lower end is not a rigid foundation,
and a slight elastic deformation of this steel triangle
under the edge stringers would relieve the edge stringers
of some load and throw it into the sheet and possibly
into the central stringer. A deformation of about
0.0003 inch would be sufficient to make the calculated
stringer stresses equal at the jig end. Undoubtedly the
assumptions of effective areas, effective shear stiffness,
and jig deflection could be varied within their possible
limits to give a much better agreement with the experi¬
mental points.
A similar analysis was made for the panel tested in
compression as described in reference 2. The results
are shown in figure 7. It will be noted that fair agree¬
ment with the experimental points is obtained by assum¬
ing that the effective shear stiffness is onlv 0.2 the shear
modulus, in marked contrast to the tension panel. The
curves calculated with Ge= G are also given to show
the extent to which possible variations in Ge affect the
stringer stresses.
BEAMS WITH ONE LONGITUDINAL
BEAM OF CONSTANT DEPTH
The simplest case of a beam subjected to shear defor¬
mation of the flange is shown in figure 8. For simplicity
of the sketch the flange material on the side not under
consideration is assumed to be concentrated at the shear
web. This assumption does not influence the analysis
when the cover is flat.
For convenience of discussion, the material concen¬
trated at the top of the shear web will be referred to as
the “flange” throughout this paper, while the stringer
attached to the cover sheet will be referred to as the
“longitudinal.”
It is again assumed that the longitudinal is cut along
the line of symmetry (fig. 8 (b)). The force acting on
this halved longitudinal is denoted by FL, the force on
the (tension) flange by Ff. The shear force in the web
Fl
Figure 8.— Beam with flat cover and one longitudinal.
is denoted by Sw] the sliear force in the
by Sc.
cover sheet,
The governing equations are
dFF=Swdf-dSc
(3a)
00°
II
ks
1
(3b)
dr=—^(aF—aL) dx
(3 c)
with the auxiliary equations
<JF= = <sv= F; dSc= rtdx
A? Aijr,
The solution of the resulting differential equation is
given in appendix B, Case 3 (a).
COMPARISON BETWEEN TEST AND CALCULATED RESULTS
The test panel that had been used in the previously
described tension test was slightly modified and
attached to two duralumin I-beams to form an open
674
REPORT No. 608— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
(a) Closed side.
(b) Open side.
Figure 9.— View of test beam, showing strain gages.
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
675
Figure W.— Set-up for testing beams.
676
REPORT No. G08— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
box beam. Figure 9 shows photographs of the beam
with the strain gages in place for a test run; figure 10
shows the test set-up. The cross section of this beam
is shown in figure 11.
It should be noted that the cover sheet and the longi¬
tudinal were not attached to the bulkheads except at
the root. The flange material of the I-beams (includ¬
ing the cover strips riveted to them and the sheet
material effective in tension) was replaced, for the pur¬
pose of analysis, by equivalent concentrated flanges
with a centroidal distance of 2.80 inches (effective depth
h of beam, fig. 8 (a)). The calculated stresses are
therefore valid for the flange centroids. For compari¬
son with the measured stresses, the calculated flange
stresses were corrected to the outside fiber stresses
under the assumption that plane cross sections remain
plane for the I-beams with cover strips.
Figure 12 shows the experimental points, the curves
calculated for three different assumptions of the shear
stiffness, and the stresses calculated by the ordinary
bending theory. It can be seen that the experimental
points group fairly well about the curve for Ge=% G ,
particularly when this curve is corrected for an esti¬
mated jig deflection by the formula in appendix B,
case 2. Close to the root, however, discrepancies are
again observed as in the case of the tension panel.
The high flange stress at the station nearest the root
may perhaps be explained by nonlinear stress distri¬
bution in the I-beams caused by the method of attaching
them to the jig, which was not designed for this test.
The reduction in shear stiffness of the sheet as compared
with the stiffness developed by the same sheet in the
tension panel can be ascribed to numerous initial
buckles present in the beam but not in the tension
panel.
Inspection of figure 12 shows that very large varia¬
tions of shear stiffness have only a relatively small
influence on the bending stresses. This result is due
to the fact that, even when the shear stiffness increases
to infinity, the bending stresses never exceed a finite
limiting value. In many actual structures, the shear
stiffness provided is sufficiently large to permit the
limiting stress to be approached within a few percent.
Practically speaking, this fact means that the shear
stiffness need not be very accurately known to obtain
the necessary accuracy in the bending stresses.
BEAM OF VARIABLE DEPTH
In a beam with variable depth, the only change in the
equations is introduced by the fact that the vertical
components of the flange forces balance part of the
applied shear, so that the shear in the web now becomes
M
Sw=Sa — -r (tan tan 7) (5)
where /3 and 7 are the angles of inclination of the
tension flange and of the compression flange.
The analytical solution for a special case of a beam
with variable depth is given in appendix B as Case 3 (6).
CONSTANT-STRESS SOLUTION FOR BEAMS WITH ONE
LONGITUDINAL
The analytical solutions presented thus far, together
with the trial-and-error method, are reasonably ade¬
quate for dealing with beams having one longitudinal.
There appears to be but slight possibility, however, of
extending these solutions to the practical cases of beams
with a number of longitudinals. An approximate
method will now be developed that can be extended to
such beams. The method will first be developed for a
beam with a single longitudinal because comparisons can
be made with the exact solution to gain some idea of the
reliability of the approximate method.
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
The approximate method is based on the following
reasoning. It is the aim of the designer to dimension
the structure so that the stress in it is uniform for the
given loading. For several reasons this ideal is never
reached, but there is usually an effort made to taper the
dimensions so as to approach the dimensions of the ideal
design. Now the solution for constant stress along the
span can be very easily obtained. It is possible, there¬
fore, to consider the actual condition as a super¬
position upon the ideal case, which can be calculated
exactly, of some additional disturbing cases or “faults.”
These faults can be calculated only approximately, but
if they are of minor importance compared with the ideal
case, the resulting error of the total solution will be
small.
The detailed development of the method is as follows:
The fundamental equation
dT — -j^(aF— aL)dz (6)
can be integrated once, if o> and aL are constant as
assumed, to give
(aF—aL)
Eb
f Gedx=
Jo
(o> — <tl)xGx
Eb
(7)
where Gx is the shear stiffness averaged over the
distance x = 0 to x = x, and the x origin is taken at the
root. Integrated again to give the total shear force in
the cover sheet
Sc=f^Txtdx=K1(aF— <rL) (8)
For example, if Ge and t are constant along the span,
GetL-
2 Eb
Equation (8) furnishes one relation between o> and aL.
One more relation is needed to complete the solution.
There are infinitely many conditions from which to
choose this relation. At any station along the span, the
internal bending moment should equal the external
bending moment. The root section has been chosen
because in a number of trials it always proved, by far, to
be the best choice. Equating the internal and external
moment (applied at the root) gives the relation
(d f A Fq~\~ ffjr A/,0) A() = AAzq (9)
Now remembering that
Sc — O' L A
O' L-tlLo
equations (8) and (9) can be solved for the bending
stresses
= _ M,KX
°L h o [AF{)AL() -f Kx (AFq + ALq) ]
(10a)
M0(Al0A~Ki)
<Jf b()[AFoAL() + Kx (AFq + A Lq) ]
(10b)
Substituting equations (10a) and (10b) into equation
(7) gives
677
T =
xGxMq
Ebh ,
A
H)
A
L0/J
(10c)
Equations (10a), (10b), and (10c) constitute the “pure
constant-stress solution” for a beam with a single
longitudinal.
The internal bending moment at any station along
the span can now be calculated
Mint — (o'Ahr o-^/1/J h
and, in general, this internal moment will not be equal
to the applied moment Ma. This difference constitutes
the first fault of the constant-stress solution and will
be called the “moment fault.”
In order to remove this fault, additional (corrective)
bending moments must be added, which are at any
station
M' —Ma Mint
the prime denoting corrective moments. The stresses
caused by these corrective moments must be computed
and added to the stresses of the pure constant-stress
solution.
The method of computing the stresses caused by the
corrective moments will be approximate and arbitrary
as thus far no exact solutions of this problem have been
found. The following method was chosen because the
underlying assumption is the most obvious one and
because the method is very convenient, eliminating the
necessity of computing the internal moments, the cor¬
rective moments, and the corrective stresses separately.
From equations (10a) and (10b) it follows that the
ratio
The assumption is now made that this ratio remains con¬
stant (r=r0) along the span and that it holds not only
for the stresses caused by the “ideal” moments but also
for the stresses caused by the corrective moments.
Under this assumption, the direct stresses at any station
are given bv
From these stresses the shear stresses are obtained by
using the fundamental relation (2) and integrating from
the root toward the tip
r= f ^g(o>— <rL)dx (12c)
The moment fault has now been removed; that is, the
internal moments equal the applied moments when the
stresses as given by equations (12a) and (12b) exist in .
678
REPORT No. 608— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the flange and in the longitudinal. But equation (12c)
follows directly from equations (12a) and (12b) and the
stresses given by (12a) and (12c) will not, in general,
fulfill the fundamental equation (3a) of equilibrium of
the flange element. Equation (3a) requires that, lor
Figure 13.— Correction factor, C\.
equilibrium of the flange element, the increment of
shear force in the cover should be
AScs=^Ax-AFf (13)
where the additional subscript S denotes the increment
required for static equilibrium. The increment of shear
force actually developed is
ASCE=rtAx (14)
where the subcript E refers to the fact that this incre¬
ment is provided by the elastic deformations of the
flange and the longitudinal. Failure of the shear-force
increments given by equations (13) and (14) to be
identical constitutes the second fault of the constant-
stress solution, the so-called “shear fault.”
Static equilibrium for the flange elements would be
restored if corrective shear-force increments were in¬
troduced equal to the differences of these two sets of
shear-force increments
A8c' — A Scs~~ (15)
where the prime again denotes a correction. The cor¬
rective shear force Sc' at any station is obtained by
integrating from the tip to the desired station, the force
being zero at the tip. The corrections to be added to
the stresses would then be given by
Sc/
A F
gl
■Sc'
A Sr
A,
t Ax
(Care must be taken in determining the signs of the
corrective stresses. The safest method is to compare
their direction with the direction of the stresses given
by the pure constant-stress solution.)
Introducing these corrective stresses would restore
static equilibrium but would again upset the basic
elastic relation given by equation (6). A compromise
must therefore be made bv using only a fraction (\
of the correction
/ _ /7 Sc'
o> — Ci .
/Ip
gl
-Ci
Sc/
A,
'=CX
A Sg'
tAx
(16)
These stress corrections are added to the stresses
obtained from equations (12a), (12b), and (12c) to
obtain the final corrected stresses o> , aL , and
r corr’ u corr >
T COTT'
Values of Cx may be established by comparing a
number of exact solutions with the corresponding
constant-stress solutions; an averaged curve is shown
in figure 13.
In order to gain some idea of the range of applicability
of the constant-stress solution, a series of related beams
was calculated. The characteristics of three of these
beams are given in table II. The first set of calculations
was made by using t lie analytical solutions given in
appendix B for beam A and by using the trial-and-
error method for beams B and C. The second set of
calculations was made by using the constant-stress
solution as described. The results of the calculations
are shown in figures 14 to 16.
F or beam B, the stresses given by the pure constant-
stress solution are also shown. Beam B is a constant-
stress beam when analvzed by the ordinary bending
theory and has zero moment fault. The complete
analysis for this beam is given as an example in
appendix C.
It is to be expected that, in general, there will be
smaller differences between the constant-stress solu¬
tion and the exact solution for beams with small moment
fault than for beams with large moment fault. This
expectation is borne out by the results. Beam B,
rr
Figure 14.— Stresses in beam A.
which comes close to the ideal case, shows smaller
differences than beam A, which is further from the
ideal case because the areas AF and Ah are constant
along the span. Beam C, which corresponds to an
actual case, as far as variation of AF, AL, t, and h along
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
679
the span is concerned, shows also good agreement for
the bending stresses. The agreement is not quite so
good for the shear stresses.
Considering all the factors involved, it seems safe to
assume that the constant-stress solution will give
satisfactory results in practical cases for the maximum
stresses, provided that the correction introduced by the
shear fault is not larger than about 20 percent of the
stress given by the pure constant-stress solution.
BEAMS WITH MANY LONGITUDINALS
YOUNGER’S SOLUTION
Actual wing structures are built as box beams with
many longitudinals, and the depth of the beam as well
as all cross-sectional areas varies along the span.
The first attempt at obtaining a solution for a multi-
stringer beam was made by Younger (reference 4). He
considered the limiting case of infinitely many longi¬
tudinals (i. e., a plate cover as shown in fig. 17) and
assumed the box to be of constant section; for the dis¬
tribution of the bending moments he assumed a cosine
law.
Younger’s solution and its extension to arbitrary
moment curves are given in appendix B. It should be
noted that this solution does not fulfill the equation of
equilibrium for the flange element (the differential
Figure 15.— Stresses in beam B.
equation does not hold along the flange) so that a shear-
fault correction is necessary, as discussed in connection
with the constant-stress solution for the beam with a
single longitudinal.
CONSTANT-STRESS SOLUTION
The usefulness of Younger’s solution is so limited by
the assumption of constant cross section along the
Sfaf/ons
Figure 16. — Stresses in beam C.
span that a more general method appeared desirable.
The constant-stress solution was developed to fill this
need of practical stress analysis.
The principles of the constant-stress solution have
been discussed in detail for beams with a single longi¬
tudinal. The extension of the solution to beams with
many longitudinals is given in appendix B. The
practical procedure of applying it is essentially identical
with the procedure outlined for beams with a single
longitudinal. The constant K2 is computed and used
to compute the constant K3 for the root section, using
equation (B-27). The stresses at a number of stations
along the span are then obtained by the formula
M cosh K?ly ...
7 - ~xf - \ W)
h[AF cosh f\:.b 4- sinli KJ>)
where y varies from y= 0 for the center line of the beam
to y=b for the flange. The shear stress in the cover
sheet next to the flange is obtained by integrating from
the root outward the expression
(rlr) = E°fKz tanh R-zb (18)
where o> is obtained from equation (17) by setting
y—b. Equation (18) is obtained from equations (B-20)
and (B-25).
680
REPORT No. 608— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The increments of corrective shear force are obtained
by using equations (13), (14), and (15). After the
integration of (15) in from the tip to obtain the correc¬
tive shear force Sc', the correction to the flange stress
is calculated by the first expression of (16); the correc-
Figure 17.— Notation used for beams with orthotropic cover plates.
tion to the shear stress is calculated by the last ex¬
pression of (16).
The calculation of the correction to the stress aL is
somewhat more complicated because it varies along
the chord. The total force on all longitudinals, using
equation (17), is given by
Fl = Jo <y~^dy= ~ (Jcl sinh K3b (19)
where aCL denotes the stress at the center line of the
beam obtained from equation (17) by setting y— 0.
In accordance with (16), only a part of the corrective
shear force is applied so that the corrected total force
on the longitudinals is
FLcoTT=FL-CxSc' (20)
Assume now that the corrected stresses in the longi¬
tudinals are distributed chordwise according to the law
<TcorT=<rcLCOTT cosh Yy (21)
The unknown Fean be found from the equation
tanh Yb_ FLcorr /rio^
Yb ALaFcnrr
" r COTT
which is based on the premise that
° ^corr G F cott
for y=b. After Y has been found, the corrected stress
at the center line is found from
acLC0TT=(rFC0Tr sech I b
and equation (21) can then be used to calculate the
stresses at intermediate values of y. The right-hand
side of equation (22) is the ratio of the average stress
in the longitudinals to the stress in the flange. In
general, this ratio will be less than unity; however,
figure 16 shows that for a beam with a single longi¬
tudinal the stress in the longitudinal may be larger
than the stress in the flange over a part of the span, and
similarly the right-hand side of equation (22) some¬
times may exceed unity. In such a case, equations (21)
and (22) may be replaced by
(Tcorr=<TcLCOTr( 2 — cosh Yy) (21a)
/0 sinh Yb\
V (22a)
(2 — cosh Yb) ALaFcorr
After Y has been found, the corrected stress at the
center line is found from
° CLcorr
COTT
(2 — cosh Yb)
and equation (21a) can then be used to calculate the
stresses at intermediate values of y.
The solution of equations (22) and (22a) can be
effected by inspection of tables. For practical pur¬
poses it should be sufficient to use the curve given on
figure 18.
As examples, beams A and B were analyzed under
the assumption that longitudinals with the total cross-
sectional area AL are distributed uniformly along the
chord. The results are shown in figures 19 and 20.
It will be seen that the stress at the center line of the
beam is very low. If all longitudinals are of the same
cross section, they must be designed to the stress in the
first longitudinal adjacent to the flange. Consequently,
Figure 18. — Graph for auxiliary parameter Yb.
the longitudinals near the center line are very in¬
effectively used. In this connection, attention might
be called to the fact that the longitudinals need not be
of the same cross-sectional area along the chord. The
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
681
assumption of AL being uniformly distributed may be
fulfilled, for instance, by using longitudinals of large
cross-sectional area but widely spaced near the flange
and longitudinals of small cross-sectional area but
closely spaced near the center line. Although such an
arrangement would not increase the over-all structural
efficiency, it might under certain conditions offer
man u f ac tu ring ad va n tages .
MECHANICAL ANALYZE!!
The constant-stress solution is always approximate.
When the moment and shear corrections are large,
doubts may arise as to whether the solution is suffi¬
ciently accurate. It might be advantageous to con¬
struct a mechanical analyzer to deal with such cases.
One possibility for such an analyzer would be actually
to build units representing the mechanical model
sketched in figure 1 (b). The springs might be canti¬
lever springs, so that their stiffnesses could be varied by
changing their lengths. Each unit would represent
one bay of the trial-and-error method of solution and
would have one spring to represent the stringer stiffness
and one spring to represent the shear stiffness of the
sheet attached to one side of the stiffener.
The chief difficulty in the design of such an analyzer
would probably be in reducing the friction between the
units and the guides necessary to aline them. A fairly
large number of units would be necessary to represent
a wing cover, which would mean a fairly expensive
instrument. This disadvantage is counterbalanced by
O'
T
40,000
8,000
30,000
20,000
in
in
<b
L
in
/ 0,000
J
Root 6
4
S ta tions
6,000
.C
Cr-
$
4,000
2,000
Figure 19.— Stresses in beam .4 with At uniformly distributed along chord.
the possibility that the instrument would offer in a
comparatively short time quite an exact analysis,
including the effects of bulkheads and of yielding
supports. The main errors in this solution would be
those caused by the finite1 length of bays.
CONCLUSION
The art of stress-analyzing shell structures is of recent
origin, and any methods of analysis proposed must go
through a process of trial and development.
Development of the method of shear-deformation
analysis is desirable in several directions; e. g., exact
Root 6 4 2 Tip
Stations
Figure 20.— Stresses in beam B with . i r. uniformly distributed along chord.
solutions should be found to replace the constant-stress
solution and methods should be devised to calculate
the influence of bulkheads.
Rough approximate calculations on bulkhead effect
can be made bv assuming that all the longitudinals
are relocated at the center line of the beam. For
beams with a single longitudinal, the effect of bulk¬
heads can be calculated. A series of systematic com¬
parisons between the extended solution of Younger and
Case 3 (a) of appendix B indicates that for a certain
range the single-longitudinal assumption may yield
acceptable approximations when used in conjunction
with suitable correction factors. The comparisons
are not given, however, because they might be mis¬
leading in view of the shear fault of Younger’s solution.
Calculations made thus far indicate that in practical
cases the effect of the bulkheads is very small.
It should be emphasized that analyzing shell struc¬
tures is an art rather than a science. The arithmetic
of analyzing highly redundant structures can be re¬
duced to manageable proportions only by making
assumptions that will be valid only within a certain
range. This fact leads to the unfortunate, but inevi¬
table, conclusion that the analysis of such structures
cannot be made entirely by handbook and formula but
must be guided by engineering judgment.
Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., June 3, 1937.
APPENDIX A
LIST OF SYMBOLS
A, cross-sectional area (sq. in.).
E, Young’s modulus (lb. per sq. in.).
F, internal force (It).).
O, shear modulus (lb. per sq. in.).
K, constant.
L, length of panel or beam (in.).
M, bending moment (in. -lb.).
P, external load (lb.).
S, shear force (lb.).
b, spacing of stringers (in.). (See figs. 3 and 4.)
b, half width of beam (in.). (See fig. 8.)
c , camber of cover (in.).
h, depth of beam (in.).
t, thickness of cover sheet (in.).
u, displacement of point (in.). (See fig. 4.)
iv, running load (lb. per in.).
y, shear strain.
a, direct (normal) stress (lb. per sq. in.),
r, shear stress (lb. per sq. in.).
682
Subscripts have the following significance:
A, loaded stringer A shown in figures 1, 2, 21, and 22.
B, unloaded stringer B shown in figures 1, 2, 21, and 22.
C, cover sheet.
F, flange of beam.
L, longitudinal of beam.
W, shear web.
a, applied shears and bending moments.
e, effective.
0, root section.
c, compression.
t, tension.
ini, internal.
corr, corrected.
S, static equilibrium.
E, elastic equilibrium.
CL, center line.
APPENDIX B
SOLUTIONS OF DIFFERENTIAL EQUATIONS FOR SYMMETRICAL STRUCTURES OF CONSTANT
CROSS SECTION
SIGN CONVENTIONS
Forces and stresses in stringers are positive when
tensile. Shear forces and stresses in the sheet are posi¬
tive when caused by positive stresses and strains in the
loaded stringer A in the case of axially loaded panels
or in the flange Fin the case of beams.
CASE 1— THREE-STRINGER PANEL ON RIGID FOUNDATION WITH
AXIAL LOAD
The two possible cases shown in figures 21(a) and
21(b) can be mathematically treated by taking one-
half the panel, as shown in figure 21(c), which also
////////////////////// ■/////////, . . ,
KV/Z////.A
A
B
b — =
(a) (b) (c)
Figure 21.— Axially loaded panels.
gives the notation to be used. The derivation of the
fundamental equations is given in the main body of
this paper. Slightly modified for the purpose of deriv¬
ing the basic differential equation, these equations are
/_ rt , rt
<j a — a anct a B — a
n
r 1 1 ’ ( \
T — EKCa <Tb
(B-l)
(B-2)
where the primes denote differentiation with respect to x.
Differentiating equation (B-2) again and substituting
into the result from equation (B-l),
Grt/ 1
'''-4\i+£>=o
The boundary conditions are
at x=0 , -=0
P
(B-3)
at
x=L , a A
Aa
and a b — 0
(B-4)
The result is
P G, sinh Kx
A A EbK cosh KL
*—(■
A .4+ Ab) \
<7 a
(
cosh Kx\
cosh KL /
_P _Ab
<7 A — A A G B
^1j XX a
(B-5)
where
In reference 2 the formula
2Prcosh px— tanli pL sinh px
(B-6)
where
9 _ 25 Get
v 2 ArhE
is given for the special case where the area of the edge
stiffener is twice the area of the central stiffener. Tak¬
ing account of the differences in notation and coordinate
systems used, this result agrees with the general formula
given under (B-5).
It should be noted that the final formulas (B-5) be¬
come invalid when either t or Gc approaches zero be¬
cause in these cases the equation (B-3) becomes invalid.
The solution for such cases is obtained by using the
fundamental equations (B-l) and (B-2) directly.
An analogous procedure must be used for Cases 2
and 3.
CASE 2— THREE-STRINGER PANEL STRAINED BY MOTION OF
SUPPORTS
The differential equation for the case of figure 22 is
I
(aj (b) (c)
Figure 22.— Panels strained by motion of supports.
the same as for Case 1. The boundary conditions are
now ;
at z=0 , <7.i=0 and <rB=0
at x~L , t=t Ce=r0
The result is
cosh Kx
r=r°cosh KL
(B-7)
<7.4 =
t sinh Kx
t°KAa cosh KL
t sinh Kx
aB=T°KAB cosh KL
where K has the same meaning as in (B-6).
(B-8)
(183
REPORT No. 608— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
684
CASE 3— CANTILEVER BEAM WITH ONE STRINGER
(a) Uniform depth, concentrated load at tip.
(b) Depth decreasing lineally to zero, uniformly dis¬
tributed load.
Figure 8 shows the notation used for both cases.
(Note that the x origin is at the tip.) The funda¬
mental equations are for Case 3 (a)
a/AF=-, - rt
P
h
’ AL=rt
GP
F = — -g| (o>— (T/,)
which gives the differential equation
„ Get / 1,1 \ . PGe _
r -TEb\AF+AL)+^m-0
The boundary conditions are
at x=(), aF= 0, and aL= 0
at x=L, t— 0
The result is
(B-9)
(B-10)
(B-ll)
_ P / cosh Kx
~ cosh KL
P / sinh Kx \
aL~h{AL+AF)\x~K cosh KLJ
UM*
aF~AF\ hx
(B-12)
w here K has again the same meaning as in (B-6) with
AF and Al substituted for Aa and AB.
In Case 3 ( b ), wLj 2 is substituted for P; h in this
case is the depth at the root.
Figure 23. — Cantilever beam with concentrated load not at tip.
The case of a beam loaded by a concentrated load
not at the tip is a simple problem in indeterminate
structures. The beam is cut just outboard of the load
(fig. 23) and the stresses in the cantilever part are cal¬
culated (Case 3 ( a )). From these stressss, the distortion
of the beam section at the cut; i. e., the relative dis¬
placement of the tips of the flange F and the longi¬
tudinal L, can be calculated. A system of forces Ar
is then applied to equalize the distortion of the can¬
tilever tip and of the inboard end of the “overhang,”
utilizing the formulas of Case 2.
CASE 4— CANTILEVER BEAM WITH ORTHOTROPIC COVER PLATE
Younger’s solution for a beam of constant section.—
The beam and the coordinate system used are shown in
figure 17. It should be noted that the x direction is
opposite to that used in Cases 3 and 4.
Under the assumptions that the transverse stresses
and strains are negligible (Poisson’s ratio equal to zero),
and that Ge is independent of E, the differential equa¬
tion of the cover is
d2u
dy2
Eb2u
Ge
(B-13)
where u is the displacement of any point on the cover in
the x direction.
The boundary conditions are
. An
x = 0 , u—i) and =0
at
T ^U—0
X~L’ dx °
n d U
2/=°’ 3;, = °
dy
(B-14)
This equation was established by Younger (reference
4, pp. 36-47). For the solution he assumed that the
external bending moment (on the wdiole beam) is
given by
M=M0 cos AP (B~15)
and obtained for the longitudinal stress in the cover
M0 cosh cos op
2 hi AF cosh 7
irb
2KL
and for the shear stress
MM sinh
Al 2 KL . . Tb \
T ~K~smhWL)
ttV . irX
2KL sm 2 L
hE
2 KAF cosh YEEp
where K is defined by
K2=
irb , 4 K2tL .
7T
sinh -
irb
2 KL
(B-16)
Ge
E
(B— 17)
Extension of Younger’s solution. — Younger’s solution
can be somewdiat extended. The external bending
moment can be represented by a superposition of
several terms:
M--
+
M
7 rX , ?>TTX , , CnU
l COS 2T + M3 COS 7) j- + AL5COS
Cn rX
~r
Mm COS
rrnrx
2 L
(B-18)
w here the rn’s are odd integers.
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
685
The values Mx . . Mm are chosen so that the sum of
the terms equals the given external bending moment at
m points other than the tip, where it is assumed that
M— 0. In order to make comparisons with Case 3, the
bending moment caused by a tip load was expressed by
M=PL ^0.821 cos H+0.101 cos
+ 0.045 cos |^+0.033 cos 7~) (B-19)
The stresses corresponding to the mth term are given
by
VlTTX
Mm cosh cos
& m '
, rrnrb . +/
2/d Af cosli +
T m
lit n
1 777 11 C
li E
irnr
2KL 1 6
. , m iry
Slnh ML
2 KL . , m-rrb \
81nh Ml)
sm
rmrx
2L
(B-
16a)
(2
2 KAf cosh
rrnrb
2 KL
AlAK2L . , rmrb\
smh Ml)
brd'i
The assumptions of Poisson’s ratio being zero and G
being independent of E are, strictly speaking, incom¬
patible. The physical picture conforming to these
assumptions is not a plate but a system of stringers
carrying only longitudinal stresses tied together by a
sheet carrying only shear stresses. This picture is
realized very nearly in practice by a skin-stringer cover,
the only difference being that the total cross-sectional
area of the stringers is not necessarily equal to the area
of the sheet, as in the case of the plain cover sheet. All
the equations written for the plain cover sheet apply,
therefore, to the skin-stringer cover if only (B-17) is
replaced by
Me
K2=R
E
(B-17a)
where H is the ratio of sheet area to area of longi¬
tudinals.
Constant-stress solution. — The coordinate system is
that shown in figure 17. Under the assumption that
<7= constant for each longitudinal, the fundamental
relation
(It GeAa
dx EAy
(B-20)
can be integrated once to give
G4x=ftyG‘ <B-21>
where Gx is the shear stiffness averaged over the distance
x=0 to x=x. Integrating again
In any given case this integration can be performed
and the result is
Sc=IiM (B— 22)
where
II
<
L~Gxtdx
o E
Now
Sc~
p al ,
!„ c~b~dy
(see fig. 24) or
dSc
Al
(B-23)
dy
a b
Figure 24. — Free-body diagram of cover plate.
Differentiating (B-22) and equating to (B-23)
Pa
(hr
A L _ n
cbKp
(B-24)
assuming that K2 is independent of y.
The boundary conditions are
(1) at y— 0, r=0 for any x. Therefore ^=0
(2) at any desired reference station R, the internal
moment equals the external moment MR.
The solution is
Mr cosh Kzy
/ ^
jt Af cosh Kzb + sinh Kzb
Tt
r=a-pJK3x tanh K:iy
(B-25
(B-26)
where Kz is defined by
Iu2-
1 1
bKo
(B-27)
It may be noted that if Ge and t are not varied along
the span, the constant Kz is identical with the corre¬
sponding constant of Younger’s solution except for a
10 percent difference in the numerical factor, namely,
-v'2 against +2.
APPENDIX C
ANALYSIS OF BEAM B
The dimensions and the loading of the beam are
shown in table II.
ORDINARY BENDING THEORY
M _ 2,800,000
a*—ai-(r^}t(AF+AL)~24:(l .875+1.875)
31,100 lb. per sq. in.
CONSTANT-STRESS SOLUTION
Since Ge is assumed constant along the span, Gx—Ge
and, from equation (7),
, _ .xQ,
TX — ' 17 F
From equation (8)
SC — (&F Gl) *0 ^ 1 Xj)^X
=-(aF—aL) Jq .r(\~ L}l.r
— (o> 0+
0.2X0.040
24
— 4.3 5(o> (Tl)
Ad =4.35
JT'O-ss)*
From equation (10a)
_ _ 2,800,000X4.35 _
at_24[l. 875X1.875-4.35(1. 875+ 1.875)]
=25,550 lb. per sq. in.
From equation (1 0b)
2,800,000(1.875+4.35)
<Tp 24 [1 .875 X 1 .875+4.35(1.875 + 1.875)]
= 36,500 lb. per sq. in.
686
Substituting in equation (7) for the shear stress at
the tip
r mo x = (36,500—25,550)
280X0.2
24
-25,560 lb. per sq. in.
The calculation of the shear correction is shown in
table III.
T RIAL- A ND-ERR O R SOLUTION
Take A# =40 in
SwAx wxLAx U'L
71.4X280X40 u
= ftt Ax= - ox/rt , - =16, bit) lb.
2 h0x 2 ho 2X24
Ai+= 16,670— ASC
GeAx , \
Ar=-g^- (o>— <r+
0.2X40
24
(a> — (Ti) =0.333 (o' F — ax)
A typical cycle of the calculation is shown in table IV.
REFERENCES
1. Younger, John E.: Miscellaneous Collected Airplane Struc¬
tural Design Data, Formulas, and Methods. A. C. I. C.
No. 644, Materiel Division, Army Air Corps, 1930.
2. White, Roland J., and Antz, Hans M.: Tests on the Stress
Distribution in Reinforced Panels. Jour. Aero. Sci., vol.
3, no. 6. April 1936, pp. 209-212.
3. Lovett, B. B. C., and Rodee, W. F.: Transfer of Stress from
Main Beams to Intermediate Stiffeners in Metal Sheet
Covered Box Beams. Jour. Aero. Sci., vol. 3, no. 12,
Oct. 1936, pp. 426-430.
4. Younger, John E.: Metal Wing Construction, Part II—
Mathematical Investigations. A. C. T. R. ser. no. 3288,
Materiel Division, Army Air Corps, 1930.
STRESS ANALYSIS OF BEAMS WITH SHEAR DEFORMATION OF THE FLANGES
687
TABLE I.— ANALYSIS OF TENSION PANEL WITH SHEAR DEFORMATION
,4.4=0.403 A r— 3fi Fb=2ASc . G.Ax . .
A 8 = 0. 220 F?-2 400-ZASr Fb Fb Eb ^)^.522 {aA ob)
f =0. 016 1 2fr* p , au~ A b~0. 220 r = 2A r
6=4.60 <T'1S=T4=(T403 G,/E=0. 4 ASc=r/Aa:=0. 096 t
Station
By trial-and-error method
By formula 1
A Sc
(lb.l
Fa
(lb.)
O A
(lb./sq. in.)
Fb
(lb.)
OB
(lb./sq. in.)
O’ A (T B
(lb./sq. in.)
At
(lb./sq. in.)
T
(lb./sq. in.)
A Sc
(lb.)
O A
(lb./sq. in.)
OB
(lb./sq. in.)
T
(lb./sq. in.)
0 _
2, 400
5,960
0
0
5, 960
0
5, 230
1 . .
376
3, 887
373
2, 024
5, 020
376
1,708
3,312
1,730
5, 022
1,717
2, 885
2 . . .
210
2, 157
214
1, 814
4,500
586
2, 662
1,838
960
4, 502
2,670
1,584
3 _ _
112
1, 197
115
1,702
4,224
698
3,170
1, 054
550
4,220
3, 186
856
4 _
60
647
62
1,642
4,075
758
3,444
631
329
4,070
3, 461
442
5 . . . .
29
318
30
1,613
4, 005
787
3,575
430
224
3,996
3, 595
187
6 _ _
9
94
9
1,604
3, 980
796
3,618
362
189
_
3,968
3, 630
0
1 Appendix B, Case 1,
TABLE II.— CHARACTERISTICS OF BEAMS
The beams are assumed to be half beams as shown in fig. 8 (a) .
All beams:
ft=24 in. at root. 6 = 24 in.
6=0 at tip. X=280in.
Ge!E= 0.2. W=71.4 lb. /in.
Beam
Af=Al
(sq. in.)
1
(in.)
0
Root
Tip
Root
Tip
A _
1.875
1.875
0.040
0. 040
0.
B _
1.875
0
.040
. 000
0.
C. _
1.880
.470
.040
.010
0.
TABLE III.— CALCULATION OF SHEAR-FAULT CORRECTION FOR BEAM B
AX=40 X <tf'=0.5^— o =25,550 -fox'
Fp=oFAp=30,500Ap t=25,o60-^ Af f Lco *, ASC'
AScs=S„¥-AF °-5*i; /-t+tAC
h A Sc - A Scs A Sce =36.500+<7b' corr +
r corr
Station
X
from
root
(in.)
Af=Al
(sq. in.)
h
(in.)
t
(in.)
c, A.r
ow -T-
h
Ff
(lb.)
A F
(lb.)
A Scs
(lb.)
(lb./sq.
in.)
A Scf.
(lb.)
A Sc'
Ob.)
Sc'
0b.)
of’
(lb./sq.
in.)
ol'
(lb./sq.
in.)
a’fccrr
(lb./sq.
in.)
° Feorr
(lb./sq.
in.)
Tr
(lb./sq.
in.)
T corr
(lb./sq.
in.)
o
1
260
0. 334
.268
.402
.536
.669
.804
.937
1.072
1. 205
1.340
1.473
1.608
1.740
1.875
1.71
0. 00286
16, 600
9, 800
6,860
23, 740
2,720
4, 140
18, 100
41,840
9,800
4, 140
7,720
-7, 720
44, 220
17, 840
9
220
5. 14
. 00857
16, 660
9, 800
0,860
20, ngO
6,880
-20
-30
20, 050
19, 600
4, 120
3, 840
-3, 840
40, 340
21,720
3 .
180
5. 86
. 0143
16, 660
9, 800
6, 860
16, 440
9, 400
-2, 540
-2, 220
14, 220
29, 400
1,580
980
-980
37, 480
24,580
4
140
12. 00
.0200
16, 660
9, 8C0
6, 860
12, 780
10, 220
-3, 360
-2, 100
10,680
39, 200
-1,780
-830
830
35, 670
26, 390
5
100
15. 42
. 0257
16, 660
9, 800
6, 860
9, 130
9, 400
-2, 540
-1,230
7,900
49, 000
-4, 320
-1,610
1, 610
34, 890
27, 170
6
60
18.87
.0314
16, 660
9, 8C0
6, 860
5, 480
6, 880
-20
-10
5,470
58, 8C0
-4, 340
-1,350
1,350
35, 150
26,910
20
22.28
.0371
16, 660
9,800
6, 860
1,826
2,710
4,150
1,400
3,226
68, 600
-190
-50
50
36,450
25, CIO
TABLE IV.— TRIAL-AND-ERROR SOLUTION FOR BEAM B
i Station
x from
root (in.)
Af=Al
(sq. in.)
tAx
A Sc
(lb.)
Fl
Ob.)
(lb./sq. in.)
0 _
280
0
0
0
260
0. 1142
3, 730
1 . .
240
.268
3, 730
13, 920
220
• . 3426
7, 440
1 9
200
.536
11, 170
21,740
180
.571
8, 680
! 3
160
. 804
19, 850
24, 700
140
.799
8, 670
4 . .
120
1.072
28, 520
26, 620
100
1.028
8, 070
j 5 _
80
1.340
30, 590
27,300
60
1.255
6, 360
6
40
1.608
42, 950
26, 700
1
20
1.485
3, 130
0
1.875
46, 080
24, 560
A Ff
Ff
OF
OF— OF
At
T
ASc
0b.)
(lb.)
(lb./sq. in.)
(lb./sq. in,)
(lb./sq. in.)
(lb./sq, in.)
(lb.)
0
0
0
12, 940
32, 896
3, 755
12, 94 C
48,280
34, 300
11,453
9,230
21,443
7, 340
22, 170
41,400
19, 660
6, 553
7, 990
14, 890
8, 500
30. 160
37, 500
12, 800
4,267
8,000
10, 623
8, 490
38, 160
35, 600
8, 980
2, 993
8, 600
7, 630
7,840
46, 760
34, 880
7,580
2, 527
10,310
5, 103
6, 400
57, 070
35. 470
8, 770
2, 923
13, 540
2, 180
3, 240
70, 610
37, 640
13, 080
4, 360
.
sftsgaii-aa
esm
REPORT No. 609
EXPERIMENTAL INVESTIGATION OF WIND-TUNNEL INTERFERENCE ON THE
DOWNWASH BEHIND AN AIRFOIL
By Abe Silverstein and S. Katzoff
SUMMARY
The interference of the wind-tunnel boundaries on the
downwash behind an airfoil has been experimentally inves¬
tigated and the results have been compared with the avail¬
able theoretical results for open-throat wind tunnels. As
in previous studies, the' simplified, theoretical treatment
that assumes the test section to be an infinite free jet has
been shown to be satisfactory at the lifing line. The experi¬
mental results, however, show that this assumption may
lead to erroneous conclusions regarding the corrections to be
applied to the downwash in the region behind the airfoil
where the tail surfaces are normally located. The results
of a theory based on the more accurate concept of the open-
jet wind tunnel as a finite length of free jet provided with a
closed exit passage are in good qualitative agreement with
the experimental results.
INTRODUCTION
A comprehensive theoretical treatment of wind-tunnel
interference exists at present. The theory includes all
the major effects attributable to the limited boundaries
of the air stream and provides stream-angle corrections
both at the airfoil and in the region behind the airfoil.
Experimental verification of this theory has, in general,
been satisfactory, although mainly confined to the cor¬
rections at the lifting line of the airfoil. The present
investigation is concerned with the interference in the
region behind the wing, a problem of importance in the
testing of airplanes or airplane models, since the induced
boundary effects at the wing and at the tail surfaces are
usually different. A particular purpose of the present
investigation was to provide correction factors for air¬
plane test data obtained in the N. A. C. A. full-scale
wind tunnel.
The theory of wind-tunnel interference on the down-
wash at the tail surfaces has been given in references 1,
2, and 3. Reference 3 also contains an evaluation of
the correction factors for square and rectangular tun¬
nels. These studies have indicated that the effect in
the region of the tail surfaces is of the order of twice
that at the wing. The work is based, however, on the
assumption that the air stream is of infinite length.
This assumption is permissible for a closed wind tunnel
but is very questionable for an open tunnel because the
actual open test section is usually only about one tunnel
diameter long. The boundary condition for free jets,
namely, uniformity of pressure over the surface of the
jet, thus applies over only a short section; the boundary
condition for closed tunnels, zero velocity normal to the
surface, applies in front of and behind the open section.
The disturbing effect of the exit cone is clear since,
upon entering it, any inclination of the free jet induced
by the lift on the wing must be so reduced that the air
will follow more nearly the horizontal flow direction in
the closed tube (fig. 1). From some recent boundary-
Figure 1. — Effect of exit cone on downwash behind an airfoil.
interference calculations (reference 4) for a circular
open tunnel of finite length, it was concluded that the
assumption of an infinitely long open jet would lead to
very serious error in the region of the tail plane but to
very little error at the wing. The results from reference
4 are reproduced in figure 2.
Conditions were particularly favorable for experi¬
mental investigation of the downwash corrections in the
N. A. C. A. full-scale wind tunnel, as a hs-scale model of
the tunnel was available. The procedure consisted in
measuring the downwash angles behind small airfoils in
the model tunnel and comparing them with the meas¬
ured downwash angles behind the same airfoils in the
full-scale wind tunnel. The full-scale wind tunnel is so
large in comparison with the airfoils that the boundary
interference is negligible. The correction factors thus
obtained should be directly applicable to downwash
data obtained behind large airfoils in the full-scale
tunnel for there is little reason to expect an appreciable
scale effect on the induced-velocity distribution. The
689
REPORT NO. 609— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
690
free-stream downwash data obtained from the meas¬
urements in the full-scale tunnel with the small airfoils
should be valuable as standards for comparison with
similar measurements in other tunnels. By a compari¬
son, such as was made in the present work, the bound¬
ary-interference factors may be derived.
O .5 1.0 1.5 2.0 25 3.0
Distance behind airfoil lifting line, in tunnel radii
Figure 2. — Theoretical jet-boundary corrections for finite and infinite jets.
MODEL-TIJNNEL TESTS
Apparatus. — The model tunnel used in these tests
is a lb-scale replica of the N. A. C. A. full-scale wind
tunnel. A complete description of the small tunnel and
its equipment is given in reference 5. A wire balance
was devised to measure the lift on the airfoils. The
models were suspended from an overhead platform
scale, and counterweights were provided below to
maintain tension in the system. The angle of attack
was changed by an adjustable quadrant on the scale
platform.
The tests were made with two rectangular Clark Y
airfoils, one with a 5-inch chord and a 30-inch span and
the other with a 10-inch chord and a 30-inch span.
The 5-inch-chord airfoil in the 2- by 4-foot jet of the
model tunnel corresponds in the 30- by 60-foot jet
of the full-scale wind tunnel to a 6.25- by 37.50-foot
airfoil, which represents the average size of the airfoils
tested in the large tunnel. The 10-inch-chord airfoil
was chosen to exaggerate the effects investigated and
the results from the measurements made with it are,
perhaps, of greater academic than practical value.
The airfoils were constructed of laminated mahogany,
varnished and then polished to a smooth surface.
The downwash angles were measured by means of a
calibrated yaw head consisting of two total-head tubes,
each inclined at a 42° angle with the horizontal to
form a Y with an 84° included angle. The inclination
of the air stream was indicated by the pressure differ¬
ence p between the two prongs of the Y and was
measured by means of an alcohol manometer. The
yaw head was calibrated in terms of the dynamic pres¬
sure q of the air stream, and the stream angle in degrees
was obtained from a calibration chart showing pjq
Figure 3.— The four test conditions of the model tunnel.
(a) Normal tunnel.
(b) Tunnel with balance house.
(c) Tunnel with ground board.
(d) Tunnel with exit-cone flare removed.
against e, the angle of downwash. For measurements
of dynamic pressure a small Prandtl-type pitot head
was used.
Tests. — Test data were obtained with the model
tunnel in four different conditions (fig. 3) as follows:
1. Normal tunnel condition.
INVESTIGATION OF WIND-TUNNEL INTERFERENCE ON THE DOWNWASH BEHIND AN AIRFOIL 691
2. Normal tunnel condition with a model balance
house to simulate the balance house of the full-scale
tunnel.
3. Normal tunnel condition with a ground board 32
inches wide extending between the lower surfaces of the
entrance and exit cones.
4. Flare removed from the exit cone, increasing the
length of the open jet from 44 to 56 inches.
Conditions 1 to 3 simulate possible operating condi¬
tions of the full-scale tunnel; condition 4 was studied
to determine whether increasing the length of the open
section would appreciably affect the downwash at the
tail. Tests were made for each of the four tunnel
conditions with the 10- by 30-inch airfoil; only condi¬
tions 1 and 2 were studied with the 5- by 30-inch airfoil.
Figure 4.— Diagram of self-synchronous motor balance for small-airfoil tests in the
full-scale tunnel.
For all the test conditions the air-stream angles in
the tunnel at all the stations were obtained with the
airfoils removed from the jet. The actual downwash
angles were then taken as differences between the air-
stream angles with the airfoil present and removed.
Downwash surveys were made at three lift coefficients
for each airfoil. The lift forces were measured in all
cases over a range of angles of attack that included
the angles of zero and maximum lift. The downwash
surveys were limited to the plane of symmetry of the
wing since tail surfaces do not normally extend a great
distance on either side of this plane. Measurements
were made between 4 inches above and 9 inches below
the longitudinal axis through the quarter-chord point
of the airfoils, at 1.0 and 1.65 chord lengths back of the
trailing edge for the larger airfoil, and at 1, 2, and 3
chord lengths back of the trailing edge for the smaller
airfoil. An air speed of about 60 miles per hour was
used for all the tests.
FULL-SCALE WIND-TUNNEL TESTS
Apparatus.— Free-air data (free of tunnel-boundary
interference effects) for the airfoils were obtained by
tests in the full-scale tunnel (reference 6). Owing to
the small forces encountered in measuring the lift, it
was necessary to construct a special balance, a schematic
diagram of which is shown in figure 4. The airfoil
was supported on the balance by means of a forked
Figure 5.— The experimental set-up in the full-scale tunnel.
frame, this frame being supported in turn on a pair of
flat cantilever springs. Vertical forces on the balance
deflect the cantilever springs and the motion is con¬
verted into rotation of one of a pair of small self-
synchronous motors by means of a thin strip of spring
steel attached to its shaft. Remote recording of this
motion was obtained on the complementary self-
synchronous motor, placed in the balance house below
the jet. By means of a calibrated dial and a pointer
attached to the motor shaft, the lift forces on the air¬
foils could be observed directly. Effective damping
was obtained by means of an oil dashpot. The entire
balance was enclosed in a streamline fairing and
REPORT NO. 609 —NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
692
attached to one of the normal balance supports (fig. 5).
Downwash angles and dynamic pressures were meas¬
ured with the same instruments used in the model-
tunnel tests. These instruments were attached to
the survey apparatus in the tunnel (reference 6).
Tests. — Preliminary measurements in the full-scale
wind tunnel, with the airfoil removed, consisted of
surveys of air-stream angle and dynamic pressure and
the determination of tare lift forces on the balance.
For each airfoil, the lift forces were measured over
the range of angles of attack between zero and maxi¬
mum lift, and the downwash angles were measured
for three lift coefficients. As in the model-tunnel
tests, surveys were made only in the plane of symmetry
of the airfoil. A slightly larger area was surveyed in
Figure 6. — Comparison of lift curves for the 5- by 30-inch airfoil in the normal model
tunnel and in the full-scale tunnel.
the full-scale tunnel than in the model tunnel. Down-
wash measurements were made between 8 inches
above and 12 inches below the longitudinal axis, from
1 to 5 chord lengths back of the quarter-chord point
for the smaller airfoil, and from 1 to 4 chord lengths
back for the larger airfoil.
RESULTS
Representative experimental data are plotted in fig¬
ures 6 to 9. The final derived jet-boundary corrections
are given in figures 10 to 13, in which is plotted the
coefficient hT used in the usual boundary-correction
formula
Act — 0/ .3
in which S and Care the areas of the airfoil and jet cross
section, respectively, and A a is the induced downwash
angle in degrees due to the influence of the bound¬
aries. The coefficient bT represents the total jet-
boundary effect rather than the increase in the correc¬
tion over that at the wing; i. e., in which
8W is the correction factor for the wing and 5A is the
additional factor for the tail. Accordingly, in the
application of the results, it must be remembered that,
if the angle of attack of the airplane has already been
corrected for the jet-boundary effect at the wing, the
correction factor for the tail will be only the difference
between the bT values at the tail and at the wing.
The tunnel-boundary effects at the airfoils were
obtained directly from the lift curves (fig. 6) as the
difference between the full-scale and model-tunnel
angles of attack at a particular lift coefficient. Fig¬
ures 7, 8, and 9 illustrate some intermediate steps in
the derivation of the boundary-interference corrections
behind the airfoil. Figure 7 comprises contour maps
of the downwash measured in the full-scale tunnel;
figures 8 and 9 compare plots of the downwash meas¬
ured in the model tunnel and in the full-scale tunnel.
The corrections were primarily obtained for applica¬
tion to tests performed in the full-scale wind tunnel
and are accordingly plotted against distance down¬
stream in full-scale dimensions (figs. 10 to 13). Points
are shown that correspond to each of the two airfoils
at each of two lift coefficients. These points are not
actual experimental values but were obtained after
some interpolation, as the measurements in the two
tunnels were made at slightly different lift coefficients
and at slightly different positions back of the wing.
For comparison with the theoretical values calculated
for an infinitely long open jet, the corrections of refer¬
ence 3 are included with the experimental data (figs.
10, 11, and 13).
The scattering of the experimental points on some of
the curves is very noticeable. Although theoretical
reasons exist for expecting that the four cases would not
exactly check, they appear insufficient to explain the
observed amount of variation. The experimental error
may possibly have exceeded the estimated value of
0.15°.
DISCUSSION
The results of greatest interest are those for the
normal tunnel (fig. 10). It is seen that, whereas the
correction at the wing has the theoretical value, the
corrections on the longitudinal axis back of the wing
not only do not approach twice that at the wing, as
given by the theory, but actually decrease rapidly after
the first 20 feet behind the wing (about 3 chord lengths).
This effect is due to the exit cone. It is therefore appar¬
ent that the conception of the open jet as one of infinite
length may lead to gross error in applying corrections
at the tail surfaces. The curves show a marked re¬
semblance to the one theoretically obtained considering
the jet to be of finite length. (See fig. 2 taken from
reference 4.)
INVESTIGATION OF WIND-TUNNEL INTERFERENCE ON THE DOWNWASH BEHIND AN AIRFOIL 693
Longitudinal distance from quarter-chord point, in.
Longitudinal distance from quarter -chord point, in.
(a) 5- by 30-inch airfoil; a, —3.8°; Cr., 0.25.
(d) 10- by 30-inch airfoil; a, —1.8°; Cl, 0.21.
Longitudinal distance from quarter-chord point, in.
(b) 5- by 30-inch airfoil; a, 3.2°; Cl, 0.74.
(e)10-by 30-inch airfoil; a, 5.0°; Cl, 0.59.
Longitudinal distance from quarter -chord point, in.
(c) 5- by 30-inch airfoil; a, 9.2°; Cl, 1.09.
(f) 10- by 30-inch airfoil; a, 11.2° \Cl, 0.91
Figxjke 7.— Downwash-angle contour lines from surveys in the full-scale wind tunnel on two airfoils of Clark Y section.
694
REPORT NO. 609— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
_ _ CL fA 0 9
7 chord length 2 chord 3 chord
Figure 8. — Comparison of model and full-scale tunnel down wash;
5- by 30-inch airfoil; normal model tunnel.
Figure 9.— Comparison of model and full-scale tunnel downwash; 10- by 30-inch airfoil;
ground board in model tunnel.
Figure 10.— Jet-boundary correction against distance behind entrance cone; tunnel
normal.
Figure ll.— Jet-boundary correction against distance behind entrance cone; tunnel
with balance house.
INVESTIGATION OF WIND-TUNNEL INTERFERENCE ON THE DOWN WASH BEHIND AN AIRFOIL
The differences between the experimental and theo¬
retical values are least in the region 4 to 8 feet below
and 12 to 20 feet behind the wing. For a high-wing
monoplane the tail is in this region at high lift coeffi¬
cients; so in this case the theoretically calculated effect,
assuming an infinitely long section, will not usually be
in error by as much as 1°. For low-wing or midwing
monoplanes the tails will lie relatively higher and some¬
what above this region. For these cases it may be
sufficiently accurate to assume that the correction is
uniform over the entire airplane and equal to the
theoretically calculated effect at the wing.
Removal of the exit cone causes somewhat closer
approach of the experimental to the theoretical results
(fig. 13); it is clear, therefore, that the proximity of the
closed section forming the exit cone of the jet contributes
considerable inaccuracy to the results of a theory that
assumes an infinitely long free jet.
The downwash results when the ground board was
used (fig. 12) are, on the other hand, in agreement with
the results of the theoretical treatment for an infi¬
nitely long jet with bottom boundary. For a long 2:1
rectangular jet, which is open on three sides and closed
at the bottom, the theory predicts relatively small
Figure 12. — Jet-boundary correction against distance behind entrance cone; tunnel
with ground board.
A point of interest is that the observed jet-boundary
effect is not symmetrical with respect to the horizontal
center plane of the tunnel. This dissymmetry is
probably due to the fact that the trailing vortices do
not extend straight back from the wing but are inclined
downward, owing to the downwash. No theoretical
treatment has yet taken this feature into account,
although the calculations for a wing placed below the
center line should be somewhat comparable and they
do indicate the same type of dissymmetry in the down-
wash. (See fig. 25 of reference 3.)
The results with the model balance house in place
(fig. 11) are, as expected, about the same as those with¬
out it, except possibly in that portion of the jet closest
to it.
38548—38 - 45
Distance behind entrance cone, ft.
Figure 13.— Jet-boundary correction against distance behind entrance cone; tunnel
with exit-cone flare removed.
tunnel-wall corrections in the region of the axis. The
experimental results verified this prediction, although
the agreement is somewhat fortuitous since (1) the jet
is not quite rectangular, (2) it is not infinitely long, and
(3) the ground board did not extend across the entire
width. The lift curves were practically the same as
those obtained in the full-scale tunnel, as were the down-
wash angles in the region of the tunnel axis. Near the
ground board, however, the deviation from the free-
stream downwash becomes very large, owing to the fact
that the inclination of the stream must approach zero
at the board.
In all the model-tunnel experiments, the lifting line,
assumed to be located at the quarter-chord point of
the airfoil, was placed 16 inches back of the entrance
REPORT NO. 609— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
cone on the horizontal center line. The results are
then strictly applicable to the full-scale tunnel only
when the airplane wing is 20 feet behind the entrance
cone and on the horizontal center line. This location
is approximately the usual one of the wings tested in
the tunnel.
The boundary corrections for other wind tunnels may
be found by using the downwash contours of figure 7,
which are for free-stream conditions. By a comparison
of the data obtained in the full-scale wind tunnel
with those obtained in other tunnels behind similar
airfoils at the same lift coefficients, the boundary-
interference corrections may be directly obtained. This
method assumes that the scale effects on the down-
wash contour map and on the jet-boundary effect are
negligible.
CONCLUSIONS
1. For an open-jet wind tunnel the boundary cor¬
rections at the wing itself may be predicted from the
simplified theory, which assumes the jet to be of infinite
length; however, the theory gives erroneous results
downstream. In the region of the tail surfaces, the
jet-boundary corrections are less than those predicted
by the simplified theory but are in good qualitative
agreement with the results of a theory that considers
the jet to be of finite length.
2. For the case of an open rectangular tunnel with
ground board, the experiments substantiate the theoret¬
ical prediction that in such a tunnel there is relatively
little jet-boundary effect either at the wing or at the.
tail.
3. With special reference to the full-scale wind
tunnel, the experiments shcnv that the presence of the
balance house below the jet has no appreciable effect
on the corrections. Removal of the exit bell improved
the agreement between the experimental downwash
and that predicted by the simplified theory.
Langley M emorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., June 4, 1987.
REFERENCES
1. Glauert, H., and Hartshorn, A. S.: The Interference of Wind
Channel Walls on the Downwash Angle and the Tailsetting
to Trim. R. & M. No. 947, British A. R. C., 1925.
2. Lotz, Irmgard: Correction of Downwash in Wind Tunnels of
Circular and Elliptic Sections. T. M. No. 801, N. A. C. A.,
1936.
3. Silverstein, Abe, and White, James A.: Wind-Tunnel Inter¬
ference with Particular Reference to Off-Center Positions
of the Wing and to the Downwash at the Tail. T. R. No.
547, N. A. C. A., 1935.
4. Weinig, F.: Der Strahleinfluss bei offenen Windkanalen.
Luftfahrtforschung, Bd. 13, Nr. 7, 20. Juli 1936, S. 210-213.
5. Theodorsen, Theodore, and Silverstein, Abe: Experimental
Verification of the Theory of Wind-Tunnel Boundary Inter¬
ference. T. R. No. 478, N. A. C. A., 1934.
6. DeFrance, Smith J.: The N. A. C. A. Full-Scale Wind
Tunnel. T. R. No. 459, N. A. C. A., 1933.
REPORT No. 610
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY
WIND TUNNEL
By Eastman N. Jacobs, Robert M. Pinkerton, and Harry Greenberg
SUMMARY
A recent investigation of numerous related airfoils
indicated that positions of camber forward of the usual
location resulted in an increase of the maximum lift. As
an extension of this investigation, a series of forward-
camber airfoils has been developed, the members of which
show airfoil characteristics superior to those of the airfoils
previously investigated.
The primary object of the report is to present fully
corrected results for airfoils in the useful range of shapes.
With the data thus made available, an airplane designer
may intelligently choose the best possible airfoil-section
shape for a given application and may predict to a reason¬
able degree the aerodynamic characteristics to be expected
in flight from the section shape chosen.
For airfoils of moderate thickness, the optimum camber
position was found to correspond to that of the N. A. C. A.
23012 section. A discussion is included concerning the
choice of the best thickness and camber for full-scale
applications depending on specific design conditions.
Data to assist in the choice of the optimum section for a
design using split flaps were obtained by testing some of
the better sections with trailing -edge split flaps.
INTRODUCTION
The well-known airfoil-section investigations in the
N. A. C. A. variable-density wind tunnel have been
directed toward studies of the effects of variations of
airfoil-section shape. Such studies are intended to
determine the range within which the best possible
section shapes for any given application will generally
be found. With the data thus made available, an
airplane designer may intelligently choose the best
possible airfoil-section shape for a given application
and may predict to a reasonable degree the aerodynamic
characteristics to be expected in flight from the section
shape chosen.
The first investigation of this series (reference 1)
gave comparable data from the standard large Rey¬
nolds Number tests in the variable-density tunnel,
which were considered as representative within the
flight range, for related airfoils covering section-shape
variations in the neighborhood of commonly used
airfoils. A subsequent investigation (references 2 and
3), covered by this report, deals with airfoil sections
differing from those commonly used in that the camber
occurs farther forward, i. e., nearer the leading edge.
The desirability of this shape characteristic was indi¬
cated by the first investigation.
After the mean-line shape designated 230 had been
found to be near the optimum (reference 2), an airfoil
having the N. A. C. A. 23012 section was tested in the
N. A. C. A. full-scale tunnel to verify the superiority
of its characteristics over those of commonly used air¬
foils (reference 4). This and other tests (references 5
and 6) in the full-scale tunnel also provided valuable
data on which to base an interpretation of the variable-
density-tunnel data as applied to flight. In addition,
a selected group of the related airfoils has been tested
over a wide range of values of the Reynolds Number.
The results of this investigation (reference 6) provided
the information needed to apply the standard variable-
density-tunnel airfoil data to flight at any particular
value of the flight Reynolds Number.
Aside from the presentation of the important section
characteristics fully corrected for application to flight
at the standard value of the Reynolds Number
(effective Reynolds Number approximately 8,000,000)
for all the forward-camber series of airfoils tested, one
object of the present report is to consider possible im¬
provements of the N. A. C. A. 23012 section. This
possibility was investigated by an analysis of test
results for a number of airfoils, the shape of which
varied systematically from the N. A. C. A. 23012.
Finally, several airfoils within the most useful range of
shapes were investigated to provide data for the various
airfoils that may be chosen as most efficient in par¬
ticular applications.
697
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
698
The airfoils developed in the variable-density-tunnel
investigations have been designated by numbers having
four or more digits. As explained in reference 1, the
maximum ordinate of the mean line is called the
“camber” and the position of the maximum ordinate
is called the “position of the camber.” The airfoils
reported in reference 1 were designated by a number
having four digits. The first digit indicated the camber
in percent of chord; the second, the shape of the mean
line as indicated by the position of the camber in
tenths of the chord from the leading edge; and the last
two, the maximum thickness in percent of the chord.
The extension of the investigation to the forward-
camber airfoils presented herein (including the airfoils
in references 2 and 3) necessitated an extension of the
designation numbers to cover the new mean-line
shapes. As before, the first digit indicates the relative
magnitude of the camber; but the second has been re¬
placed by a pair of digits, which together indicate the
mean-line shape for which position of camber is one of
the parameters; and the last two, as before, indicate
the thickness of the airfoil section. The camber, the
mean-line shape designation, the corresponding values
of camber, and the position of camber for these forward-
camber airfoils are given in the following table.
^X Mean-line shape designation
\ (second and third digits)
\
10
20
30
40
50
GamberX
desig- \
nation \
(first digit) \
\
Position of camber,
percent of chord
5
10
15
20
25
(Actual camber in percent of
chord)
2. _ _
1. 1
1.5
1.8
2. 1
2.3
3. _
2.3
3. 1
2. 8
3. 1
4 _
3. 7
4.2
6 . . __ _ _ _ . ..
4.6
5. 5
6.2
The table thus indicates, for example, that the N. A.
C. A. 230 — airfoil has the camber 1.8 percent of the
chord at 0.15c behind the leading edge.
The airfoils designated by both the four and the
five digit numbers have only one form of thickness
variation. Changes in the form of the thickness va¬
riation made by altering the leading-edge radius and the
position of maximum thickness (see reference 7) have
been designated by appending two additional digits
separated by a dash from the basic airfoil designation.
The first of these two digits indicates the relative magni¬
tude of the leading-edge radius and the second indicates
the position of the maximum thickness in tenths of
the chord from the leading edge. The significance of
the leading-edge radius designation is given below:
0 designates sharp leading edge.
3 designates one-fourth normal leading-edge
radius.
G designates normal leading-edge radius.
9 designates three or more times normal leading-
edge radius.
The complete system of airfoil designation is illus¬
trated by the following examples: The N. A. C. A. 2212
(reference 1) has a camber of 2 percent of the chord
at 0.2 of the chord from the leading edge and a thickness
of 12 percent of the chord. The N. A. C. A. 0012
(reference 1) is a symmetrical airfoil having a thickness
of 12 percent of the chord. The N. A. C. A. 24012
(reference 2) has a camber of approximately 2 percent
of the chord (actually 2.1 of the chord, see table I)
at 0.2 of the chord from the leading edge and a thickness
of 12 percent of the chord. It will be noted that the
N. A. C. A. 2212 and the N. A. C. A. 24012 have prac¬
tically the same camber, camber position, and thickness;
however, the shapes of the mean-camber lines, desig¬
nated by the digit 2 in one case and 40 in the other, are
entirely different. Finally the N. A. C. A. 0012-64
is a symmetrical airfoil having a normal leading-edge
radius and the maximum thickness at 0.4 of the chord
from the leading edge. The N. A. C. A. 24012-33 has
the same mean line and thickness as the N. A. C. A.
24012 but has a leading-edge radius one-fourth the
normal and the maximum thickness at 0.3 of the chord
from the leading edge.
The scope of the present investigation is best indi¬
cated by figure 1, which gives the profiles of the air¬
foils tested. Of the airfoils of 12 percent thickness
there are included a group of increasing camber: 00,
230, 330, 430, and 630; a group of varying camber posi¬
tion: 210, 220, 230, 240, and 250; and some variations
of camber position for airfoils more highly cambered
than the 230 series. From the results of these tests,
the camber position corresponding to the series 230,
430, and 630 appeared to be best, so that in most cases
variations of section thickness are included only for
these mean-line shapes and for the symmetrical airfoils.
Some variations of thickness distribution are included,
and also some of the more interesting airfoils with a
high-lift device consisting of a 20-percent-chord full-
span split flap.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 699
0006
0009
0012
0015
0021
21012
22012
23012
24012
25012
23006
23012 43012 63012
23015 43015
63015
23018 43018
63018
23021
43021
63021
64021
Figure 1.— N. A. C. A. airfoil profiles.
700
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
DESCRIPTION OF AIRFOILS
The thickness variations of the airfoils are given in
references 1 and 7. The cambered airfoils have mean
lines of the form given in reference 2. Profiles of all
the airfoils presented herein are shown in figure 1.
The models are of 5-inch chord and 30-inch span, of
rectangular plan form, and are constructed of duralumin
as explained in reference 8.
APPARATUS ANI) METHOD
The variable-density wind tunnel, in which the tests
were made, is described in reference 8. Routine meas¬
urements of the lift, drag, and pitching moment were
made at an effective Reynolds Number of approxi-
and to the “blocking effect” of the model in the tunnel.
These errors have since been investigated (see the
appendix of reference 6) and have been eliminated by
correcting the manometer settings used in fixing the
tunnel air speed. Other errors mentioned in reference
1 have been somewhat reduced.
RESULTS
The data are presented (figs. 2 to 51) in a manner
that is a slight modification of the standard graphic
form used in previous reports. The left-hand portion
of the plot presents the test data in the usual standard
form for rectangular airfoils of aspect ratio 6. In¬
cluded also are the airfoil profile, the table of ordinates,
Figure 2.— N. A. C. A. 0006 airfoil.
mately 8,000,000 (tank pressure 20 atmospheres). In
addition, for most of the airfoils, measurements of lift
in the neighborhood of maximum lift were made at an
effective Reynolds Number of approximately 3,800,000,
obtained by running at reduced speed with a tank
pressure of 20 atmospheres.
The discussion of precision in reference 1 points out
certain errors in the velocity measurements due to a
change in the apparent density of the manometer fluid
with a change in the tank pressure from atmospheric
and a portion of the lift curve in the neighborhood of
maximum lift obtained at a reduced Reynolds Num¬
ber. The right-hand portion of the plot presents the
section characteristics derived from the experimental
data and fully corrected for turbulence and tip effects,
as explained in reference 6.
In addition to the graphic form of presentation, the
most important characteristics, fully corrected, are
presented for each section in table I. The three columns
on classification are explained in references 6 and 9.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS
IN THE VARIABLE-DENSITY WIND TUNNEL
701
Figure 3.— N. A. C. A. 0009 airfoil.
Figure 4. — N. A. C. A. 0012 airfoil.
02
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 6— N. A. C. A. 0012-64 airfoil.
Angle of attack for infinite aspecf ratio, a0 (degrees) Angie of attack for infinite aspect ratio. or„ ( degrees )
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 703
38548—38 - 46
Angle of attach for infinite aspect ratio, c/0 (degrees)
704
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 9.— N. A. C. A. 0018 airfoil.
Figure 10. — N. A. C. A. 0021 airfoil.
Angle of attach for infinite aspect ratio, a0 (degrees) Angle of attach for infinite aspect ratio, a0 ( degrees )
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL
Figure 11. — N. A. C. A. 21012 airfoil.
"0
4.
o
<
0
V
o
T:
<0
CD
SI a.
Up’r.
L'w 'r.
O
-
O
IPS
2.84
-I.I0
2.5
3. 76
- 1.60
5.0
4.97
-2.17
7.5
5. 7/
-2.68
10
6.22
-3.15
15
6.80
-3.89
20
7. II
- 438
25
7.23
-4.66
30
7.22
-4.80
40
6.85
-4. 76
50
6.17
-4- 42
60
5.2 7
-3.85
70
4.19
-3.14
80
2.99
-2. 26
90
1.63
-1.26
95
.89
- .71
100
(■/ 3)
(-J3)
mo
—
O
C*
0) 5
S’ <
a o
-20
10
o
-10
ax
20 40 60 80 100
Percent of chord
24 \
20
£
20 ^
40
o
cJ.
60
0
u
Id
t>
u
12 o
80
o
<
o
4:
5 o
too
o
* c
A <D
.0
0
A
CD
o
Qr
0.
-4
-8
.026
.024
.022
.48 .020
.44
.40
.36
.32
.28
C
,24§.
u
■20°
Ch
J6 0
.0/8
■£. 016
.<D
1.0/4
8 012
o
P.0/0
D
~S J.OOfl
0
£. 006
.004
-8 -4
Airfpif.N.A.C.A. 220/2
Size: 5"x.30" Ve/(ff./sec.j: 69./ .
Pres. (sfnd. atm.): 20.6 Date: 4-23-34
Where tested: L.M.A.L. Test: V.D.T.//25
Corrected for tunnel-wall effect
O 4 ~~8 /£ /6 ~20 24
Angle of attack, oc ( degrees )
o Q
.6 u .12
u
.002
A'4 .08
0
.2 .04
1 ’
‘9V**0
o 0
-.2
-.2
0
o
~-3
-.4
CD
| -4
!
L
\
\
■
\
\
V
\
k
Y
L
\
""'I
C 4
\
\
^0.1
r1
>
o.c.
c t
r*'
0
TC.
>r
0.0/3 c ahead o
f c/4
,05c above chord
T
r
r
LL
r
Airfoil: N.A.C.A. 22012 R.N.ifff): 8.320.000
D
ate: 4 -23-34 Test: V.D.T. 1 125
or rected to infinite aspect ratio ^
C
52
48
44
40
4)
<0
36
32
28
o
o
24 L
a>
Q
20 lo
o
16
c
s:
12 -
u
4-8
n v.
u 0
-4 Ch
c
-8
-12
-16
-.4 -.2 0
.4 .6 .8 1.0
Lift coefficient, c,
t.2 t.4 t.6 18
Figure 12.— N. A. C. A. 22012 airfoil.
706
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 14.— N. A. C. A. 23009 airfoil.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL
Figure 15.- N. A. C. A. 23012 airfoil.
Angle of attack, cc (degrees) Lift coefficient, c,o
707
Figure 16.— N. A. C. A. 23012-33 airfoil.
708
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
S/a.
dp’r.
L'w'r.
O
-
O
1.25
253
-1.30
2.5
3.41
-1.61
5.0
4.53
-2.00
7 5
5.4/
-2.27
10
6.00
-2.50
15
6. 70
- 3.02
20
7.04
-3.55
25
7.23
-3.96
30
7.37
-4.29
40
7.32
-4.66
SO
6.93
-4.70
60
6.21
-4.42
70
5.17
-3. 79
80
3. 78
-2.86
90
2.09
-1.63
95
/.IS
- .90
lOO
U3)
(-. /3)
100
O
L.E. Rod.: / .58
chord: 0.305
10
ttv'0
"
a.t
r
•
-1
-
1
1
j
0 20 40 60 80 100
Percent of chord
**»
0
0
Q;
. c
4 <0
.0
Is
n 111
u ^
.5
~4 d
-8
Eff. R.N.
1
8,400,000-
/
3,940,000
/
A
I
I
1 /
1/
c.
p
e—
*
L-
V’
X
WDy
_
1
cD
—
U-
-8
N.A. C.A. 23018-64 R.N..-3, 180,000
Size: 5"x30 " Ve/. (ft/sec.): 69.0
Pres. (st'nd.atm.): 20.6 Date:2~B-35
Where tested: L.M.A.L. Test: V.D.T. 1222
~ Corrected for tunnel-wall effect
0 4 8 to 16 20 24
Ang/e of attack, oc ( degrees )
2.0
1.8
1.6
t.4
'■2
V
,Cj
<u
o
.026
.024
.022
.020
.018
-r.OI6
C
,<D
•$.0/4
$
<u
0.0/2
o
.44
.40
.36
.32
C
.28-% S.010
•Sj
■24 9 L.008
dj v
• 20 o ?006
Ch
.16 0
Q
.004
.6 ^ .12
.002
%
.4^ .08
0
.2 .04
a
<S - /
0 0
8sT
0) -.2
-.2
0
0
- -.5
-.4
<b
I -.4
T
— 1
-
! —
1
“T
\
\
\
\
\
t --
\
\ .
*c
i0
7 \
s
0.1 Cd
<*■
Cm
—
X-
C
7.C.
0.0/0 c ahead of c/4
04c above chord
±
- -
52
48
44
40 2
<U
Is
16 ^
A
^3
32
28
24
28 32
-.4 -.2
0
N.A. C.A. 230/2-64
Dofe:2-2-35 Test: V. D.T. !222
Corrected to infinite aspect ratio
.2 .4 .6 .8 ~To 12
Lift coefficient, c,
.o'
4s
0
Is
Ss
(J
Qj
20 §■
0
16 $
x
3
12 9
Is
d'S
<
O
•K
o
0 v
o
. -3}
Cri
c
-8 ^
-16
!4 16 1.8
Figure 18— N. A. C. A. 23012-64 airfoil.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 709
Figure 19.— N. A. C, A. 23015 airfoil.
Figure 20.— X. A. C. A. 23018 airfoil.
710
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
"6
C.
o
<
o
o
c
«J
4<9"5
6
S
c.
a.
c
-
20 40 60
Percent of chord
100
0
24 f 20
20 ^
o
*
5 *
* J2§
s -5
60
80
>•*.
o
CD
8^/00
C
<U
u
Is
<u
CL
po J 1.80
1 25\t?. Q5
-8.30
-8. 76
- 895
-8.83
—
— I —
i JO
40 J
ruo
1.43
— —
50
60
70
0.40 \
8 90'
7.09
- 8.14
- 7.07
-5.72
80
90
95
tool
100 \
5.05
9. 76
-4 13
-P.30
.
_ J
1.53 -1.30
(.22) " (-.22)
- i o
/
/
L .E. Rad.: 4.85
—
_
/
Slope of rod/us
through end of
chord: 0.305
! Eff. R.N.
•
3,800,000
8,2/0,000
.
- -
c
P
i -
x-
X —
X -i
X
:
*cL
—
L/D
/
/
°i
u
.024
.020
.44
.40
.36
.32
.018
016
.0)
8 -012
-4
-8
1
Airfoil: N.A. C.A. 23021, R.Nr.3, / / 0,000
Size: 5"x30" Vel(ft./sec.): 63. 7
Pres.(sfnd. aim.): 20.6 Date: 8~!7-35
Where tested: L.M.A.L. Test: V.D.T. 1285
Corrected for tunnel-wall effect
1.2^
!.0%
.0
<u
o
.6 u
.4^
.2
* *
■ 2S^ 8-0/0
,j>
j».008
u o
■20 8 ih-006
.004
On
,/6 CD
Q
0
-.2
.12
.08
.04
O
CD
o
u
-.4
-e -4 0 4 5/4 /5 40 44
Angle of attack, cc ( degrees )
.002
0
6
e
\ -■/
.2
.3
28 32
-.4
T 4
/
/
t
/
1
I
V
.
T
/•
1
L
1
Cd
b
t
V
<
^0
y
"''CU Cd
c.
a c
-7c
1
a.c
T"
0.023c
ahead of c/4
.07c above
chord
L
54
45
44
40 Q>
<D
k
36 ^
54
45
44
o
0)
40 8
0
16
12
.C
u
CD
-4
O
Airfoil: N.A.C.A . 23021, R.N.(Eff)8,2 / 0,000
Date: 847-35 Test: 7. D. T. 1285
Corrected to infinite aspect ratio
.2 .4 .6 .8 10 1.2 1.4 7.6 7.8
Lift coefficient, c,
4
0\
Qj
C
-8
-12
-16
Figure 21.— N. A. C. A. 23021 airfoil.
Angle of attack, cc ( degrees ) Lift coefficient, c,o
Figure 22.— N. A. C. A. 24012 airfoil.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE
VARIABLE-DENSITY WIND TUNNEL
711
Figure 23.— N. A. C. A. 25012 airfoil.
Figure 24.— N. A. C. A. 32012 airfoil.
712
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 25— N. A. C. A. 33012 airfoil.
Figure 26. — N. A. C. A. 31012 airfoil.
Angle of attack for infinite aspect ratio, cx0 ( degrees )
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 713
Figure 27. — N. A. C. A. 42012 airfoil.
Figure 28.— N. A. C. A. 43009 airfoil.
714
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 29.— N. A. C. A. 43012 airfoil.
Figure 30.— N. A. C. A. 43012A airfoil.
Angle of attack for infinite aspect ratio, cx0 (degrees) Angle of attack for infinite aspect ratio, a0 (degrees)
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL (
Figure 32.— N. A. C. A. 43018 airfoil.
716
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 34.— N. A. C. A. 44012 airfoil.
Angle of aiiack for infinite aspect ratio, tt0 (degrees)
TESTS OF RELATED
FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY
WIND TUNNEL
Sto.
Up'r.
L’w r.
0
—
0
t.25
8.12
-0.70
2.b
9.39
- .97
5.0
11.05
- / .27
7.5
12.08
-2.14
to
12.80
-3.58
/b
13.67
-5.06
20
14. 12
-5.97
2b
14.26
-6.56
30
14. !2
-6.89
40
13.30
- 7.02
50
7/. 92
-6.63
60
tO. !2
-5.88
70
8.0/
- 4.80
80
5.70
-3.5/
90
3-09
-2.00
9b
1.69
-I./4
too
(.22)
(-.22)
mo
—
0
V5
g o
i- o
U- o
3-.
c
t
2.C
•
*
0 20 40 60 80 100
Percent of chord
U ir fo //: N.A.C.A. 6202/ 6. N.: 3, 190. 000
Size : S"x 30 " VeL ( ft, /sec.) : 68. 7 I - £>
Pres, (st'nd. atm.): 20.8 Date: /0~/0~ 35 \
Where tested: L.M. A. L. Test: V.D.T. 1311
" Corrected for tunnel-wall effect
-8 -4 0 4 8 /2 16 20 24
Angle of attack, ct ( degrees )
28 32
Figure 35.— N. A. C. A. 62021 airfoil.
718
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
\Sto. \Up'r.
10 -
/.25 4.46
2.5 ! 5.84
5.0 7.77
7.5 907
10 9.99
15 10.96
20 1 1.03
25' 10.91
30 40.66
40 . 9.80
50 8.64
60 i 7.24
70 5.69
80 3.9 7
90 2.12
95 1.14
100
100 _ _ _
I L.E.Rad.: 7.58
5/ope of radius
through end of
ychord: 0. 9/5
.026
.024
20 40 60 80
Percent of chord
too
- .99
-1.38
- 1.84
-1.97
- 1.90 .
~/.6£
-1.28
- 79
- .48
(./3J\ (-./3)\
0
A — 1
^ 20 5 40-
i e
S' 16^60-
% 3q/00
<L/D
•5
1 -
—
n
/
Eff.
H.t
00
IOC
t.
8,
290,
3 70/
0
\3t
1
t
i\
1
i y
f
**
c.
P
/
t
j.
x —
x —
/(
~1
i
*5
L
— 1.2,4
28^ p .0/0
.9? ~c5
24 £ u.008
fll ^
.4
.2
0
Airfoil: N.A. C.A. 630/2, R.N.-.3, 140,000 '
Size: 5"x30" Ve/.(ff./sec.): 69.3\-p
Pres. (st’nd.ofm.): 20.6 Dale: 9-/8~ 35 j
Where tested: L.M. A. L. Test'VD.T 1299
Corrected for tunnel-wall effect -4
fc
.002
'J .08
0
tj
.04
2 -./
0
u -.2
o
u
^ ~-3
01
| -.4
0 027c ahead of c/4
■ 13c above chord
Airfoil: N.A.C. A. 630/2, R.N.(Eff)8, 29 0,000
Date : 9- 18-35 Test: V. D. T. 1299
Corrected to infinite aspect ratio
-8 -4 0 4 8 /2 /6 20 24
Angle of attack, cz ( degrees )
28 32
-.2 0 .2 .4 .6 .8 tO !2 /.4 L6 /.8
Lift coefficient, c
-12
-16
Figure 37— N. A. C. A. 63012 airfoil.
Figure 38.— N. A. C. A. 63015 airfoil.
TESTS OF RELATED
FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL
719
Figure 40.— N. A. C. A. 03021 airfoil.
720
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 42. — N. A. C. A. 0012 airfoil with 0.2c split flap deflected 60°.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 721
Sta.
0
1.25
2.5
5.0
7.5
10
15
Up'r
2.04
2 83
3.93
4.70
5.26
5.85
L’w 'r.
O
-0.9/
-U9
- 1.44
-/.63
-1.79
-2./ 7
20 40 60 80
Percent of chord
0
20
40
80 h
100
25
3C
4C
5C
6C
7C
8C
9C
95
/OC
IOC
6. II
6-05
5.65
5. OS
4.32
3.42
2.4/
1.3/
.72
(.10
-
-2.80
-2.96
-3.03
-2.86
-2.53
\ -2.08
-1.5/
- .86
- .50
f-./OJ
0
Eff. R.N.
8,240,000
3,670,000.
i
i
i
i
i
L.E. Rad.: 0.89
Slope of radius
through end of
Chora: 0.305
c.
k
r
_
Vv
p
-*
-K-J
CD
/
7
h
—
/D
L'/
r-
N.A.C.A. 23009* R. N. : 3, 120, 000
_.5ize: 5“x30" Vet (ft./sec.): 69.7 A
Pres, (sf’nd. atm.): 20.4
Tested: L.M.A.L. Test: V.D.T. 1386
Corrected for tunnel-wall eff.'
-R2 - 8 -4 0 4 8 12 /6 20 24
Angle of attack, oc ( degrees I
* With split
flop deflected
R.N. (Eff.): 8,240,000
— _ - Test: V.D.T 1386 .
Corrected to infinite aspect ratio [
.8 !.0 1.2 1. 4 7.6 1.8 2.0
Lift coefficient, c,
’ 'o
Figure 43.— N. A. C. A. 23009 airfoil with 0.2c split flap deflected 60°.
Figure 44.— N. A. C. A. 23012 airfoil with 0.2c split flap deflected 60°.
22
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 46.— N. A. C. A. 23012 airfoil with 0.2c split flap deflected 75'
Angle of attack for infinite aspect ratio. a0 (degrees)
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 723
Figure 48.— N. A. C. A. 23021 airfoil with 0.2c split flap deflected 75'
724
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
~8 -4 0 4 8 /8 /6 20
Angle of attack, or ( degrees )
flop deflected 75c
.024
1
\
, npp
—
V
—
■4-
f?
\
\
pn
1 J
1 n
.1 <
*-
~
N,
/
r
4l
T-'i
0
L ■ f4»
<l>
^■0/6
c:
.0)
.<j.0/4
$
<9
o .012
Ci
0.0/0
? ^
r i.oo<9
^006
.004
32 T
28 -S
C3
24 £
u
CD
40 §■
0
/6
c
\
3
T"
\
\
\
\
h
\
\
\\
-
L _
—
Airfoil without flap
X'
XT
<
|
x
\
;
5cO
o
4 0
0
0‘S
4)
-4 CJi
C
>
— /
✓
T)
-
.
>
<*o
_ 1
A
—
i-
"6U
0.1 c,
ic
— |
—
s
*-x
—
- s — =
<9 -.2
0
0
—
- 1 ]
"X4i
—
— —
~Q
—A
K
-X.
(c
l c
oc
>n
m(°
c*>
X
X"
-12
-16
-20
J
—-“r
—
0.008c ahe
1 of c/4
X
X
4
■ 06 c above chord
1
Airfoil: N.A.C.A 4?nnQ* R N (Fff)- Ft If
in nn
n
-
Oate: 9-8-36 " Test: V.'o.T.'/388\
Corrected to infinite aspect ratio
Lift coefficient, c,
Figure 49.— N. A. C. A. 43009 airfoil with 0.2c split flap deflected
Sto- Up'r. L'w’r. Y*
1
rm
-t
^'C')n
I
\ 7
52
0 20 40 60
Percent of chord [
Eff. R.N.
1.6. Rod.: 1 .58
5 lope of radius
ihrough end of
chord: 0.6/0
24
60
.o
8,240,000 '''
3.830,000 ■
C,
L/D
.56
.52
.48
.44
2.0
/. 8
.28'
1.2, s. 24-9.
4,0 £ .20?
.$>
.6
O
.16 p
it:
.12
.4^ .08
if
.04
■8
■ N.A.C.A. 430/2* R.N. -. 3,120,000
Size: 5"x30" Vet. (ft/sec.):69.t \
_ Pres, fst'nd. atm.): 20. 9
Tested:/. HA. L. Test: V.D.T./296
Corrected for tunnel-wall ef A
-.4
~I2 - 8 -4 0 4 8 12 16 20
Angle of attack, a (degrees)
24 * With
flop deflected 75
.024
T-
1
.022
1
r
.020
t
— 1-
r
0
.1
ote-
1
»
:.0I6
1
1
.014
1
1
.0/2
—
V
\
\
\o/o
\
\
\
,
.008
s_ .
*
r
.006
A
rfoi
ithouf flap
\
^ —
004
✓
X
/
>
002
^0
-
X
.
11 c
)— \o-
'
^0
M-
a
*
T~
"T
fX
i —
—
X-
L
— c.
'
—
—
- J
—
— 1
- 1
(o.c.j
J
4
--
--
0
U/Uc ahead of c/4 T' j
1
“f
0 7c
obove
chord 1
— [
Airfoil: At. A C A 430/2* RN (Fff )■ R PAn
nnr
- 5
[
Date: 9- 14-35
Test: v n’r IP.QR
J
L
Corrected to infinite aspect ratio
48
44
<9
36 £)
C*
A)
32 $
28
-20 S
-- 12
-16
-20
Lift coefficient, c,
Figure 50.— X. A. C. A. 43012 airfoil with 0.2c split flap deflected 75°.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 7
25
CHOICE OF BEST CAMBER POSITION
The first results of an investigation of the effects of
placing the camber forward of normal positions were
reported in reference 2. These results showed that air¬
foils with the camber well forward had improved char¬
acteristics and that the 0.15c position was probably the
best except for the apparently high maximum lift of the
N. A. C. A. 21012 airfoil. (See fig. 15 and table II of
reference 2.) Subsequently, the investigation was ex¬
tended to higher cambers. These results (fig. 52) indi¬
cate that the 0.15c position is best for airfoils of mod¬
erate thickness (12 percent c). Furthermore, when the
data for this report (including the data in references 2
and 3) were being prepared, an error was discovered in
figure 15 and table II of reference 2. The value of the
uncorrected maximum lift for the N. A. C. A. 21012
airfoil plotted in figure 15 should have been 1.52 instead
of 1.62 and the corresponding value of CLmax in table II
corrected for the tip effect should have been 1.57 instead
of 1 .67. The basis for the qualified conclusion of reference
2 that stated the maximum lift coefficient of simple
mean-line airfoils to be unaffected by positions of cam¬
ber less than 0.15c is thus removed. The optimum
position of camber may now be definitely placed at
O. 15c; that is, the position corresponding to the mean¬
line shape designation 30.
The rest of this discussion will therefore be concerned
with the effects of airfoil shape on the aerodynamic
characteristics of those airfoils whose camber position
2.2
2.0
Cl„
Ci„
I.B
/. 6
300
" 260
in
220
.OIO
n.008
.006,
•
do
mbe
r
c
ies/gnat
* o
/o
n
V
?
••
-• -
■T
□
4
-v
— —
— J
—
—
3 -
3—
- -
— \ —
—
Y-
O .04 .08 .12 .16 .20
Comber position in fraction of chord
.24
Figuke 52.— Variation with camber position of maximum lift, minimum drag, and
the ratio of maximum lift to minimum drag for the 12 percent thick airfoils.
is at 15 percent of the chord back of the leading edge
and will be concluded with a discussion of the choice
of the best thickness and camber.
a.c. position,
percent c ahead of c/4
726
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 53.— Variation of minimum drag with thickness.
i
Comber
c
res
'9'
A
X
□
70/
2
/Or
)
-
3
$
4
H
.
f
6
J
_
O .04 .08 .18 J6 .80
Maximum thickness in fraction of chord
Figure 54.— Variation of position of aerodynamic center with thickness.
Figure 55.— Variation of maximum lift with thickness.
VARIATION OF AERODYNAMIC CHARACTERISTICS WITH
SECTION SHAPE
Tlie variation with thickness of the characteristics of
the airfoils reported herein agrees approximately with
previous findings, although the present results are
slightly different owing to their greater accuracy. The
added accuracy of the section characteristics is princi¬
pally the result of corrections for turbulence and tip
effects (reference 6), which may also be applied to the
results presented in reference 1. The minimum drag
coefficient increases in accordance with the relation
cd(. =£+0.0050 +0.0033f -(-0.lt2 (fig. 53), where t is
the thickness ratio and k (which is approximately con¬
stant for sections having the same mean line) repre¬
sents the increase in cd above that of the symmet-
rical section of corresponding thickness. The lift-curve
slope decreases slightly for the thicker airfoils, and the
position of the aerodynamic center moves slightly for¬
ward with increasing thickness (fig. 54). The pitching-
moment coefficient and the optimum lift coefficient
decrease numerically with increasing thickness.
The maximum lift coefficient is highest for moder¬
ately thick sections, as shown in figure 55. The greatest
value of maximum lift occurs at a thickness near 13
percent for the symmetrical and 230 series but at a
lower thickness for the 430 and 630 series.
Tests made to determine the optimum position of
maximum thickness for an airfoil showed that the usual
N. A. C. A. thickness distribution is better than thick¬
ness distributions having positions of maximum thick¬
ness farther back. This conclusion is substantiated by
the results shown in figure 56.
The effect of filling out the concave portion of the
lower surface near the nose of the N. A. C. A. 43012
airfoil and thickening the upper surfaces so that the
mean line is unchanged may be seen by examining the
data given in table I. The N. A. C. A. 43012 is seen to
be aerodynamically better than the N. A. C. A. 43012A.
A comparison of the results given in table I for the N.
A. C. A. 23012 with the N. A. C. A. 23012-33 and those
for the N. A. C. A. 23012-64 with the N. A. C. A.
23012-34 shows that the effect of decreasing the lead¬
ing-edge radius below its normal value is to decrease
the maximum lift, which confirms the results of ref¬
erence 1.
The effects of camber changes upon the aerodynamic
characteristics of the airfoils shown in figure 1 also
agree with previous findings. The minimum drag
increases with camber. (See fig. 53.) The angle of
zero lift is proportional to camber and agrees with the
theoretical value (see reference 1) to within 0.2° for
airfoils of moderate thickness. The comparison of the
angle of zero lift with the computed theoretical value
is shown in figure 57. The diving moment is propor¬
tional to the camber and increases with a rearward
movement of the position of the camber as predicted by
TESTS OF RELATED
FORWARD-CAMBER AIRFOILS IN THE
VARIABLE-DENSITY WIND TUNNEL
727
theory but is smaller in magnitude than the theoretical
value (fig. 58). These and other differences between
theory and experiment agree with the findings in refer¬
ence 1 but have since been adequately explained.
(See reference 10.)
Figure 56.— Variation with position of maximum thickness of maximum lift, mini
mum drag, and the ratio of maximum lift to minimum drag.
0
10
3
-.4
-.8
-t.2
Camber position in fraction of chord
.04 .08 .12 .16 .20 .24
—
.
r
+
L
r
i
Thich
nest
> (per
cent c)
— Theoretical
o 12
L i 1
+
ct
i —
TX
mil
Figure 57.— Variation of angle of zero lift with camber position.
Figure 58. — Variation of pitching moment with camber position.
The maximum lift increases for moderate amounts of
camber, but this effect is less noticeable with thicker
airfoils (fig. 59). It may be mentioned that the in¬
crease of maximum lift with camber is more pronounced
at reduced values of the Reynolds Number. (See ref¬
erence 6.)
The addition of the split flap may be considered as
giving a maximum-lift increment. This maximum-lift
increment increases with thickness, as shown in figure
60, but does not change appreciably with camber.
CHOICE OF BEST THICKNESS AND CAMBER
In the selection of a member of this airfoil family for
a given application, the choice of the best thickness
and camber to be used depends on several factors.
The Reynolds Number at which the airfoil is to be used
will be one of these factors. By means of the scale-
Figure 59.— Variation with camber of maximum lift, minimum drag, and the
ratio of maximum lift to minimum drag.
effect classification given in table I and explained in
references 6 and 9, the variation of maximum lift and
other characteristics with Reynolds Number for any
airfoil can be found.
For simplicity, the following discussion is based on
airfoil section characteristics corresponding to the
standard conditions (effective Reynolds Number,
8,000,000). Such an analysis will apply approximately
to an airplane such as a medium-size transport, which
lands at Reynolds Numbers near 8,000,000.
38548-38-
47
728
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
If a high cruising speed for a given landing speed is
of primary importance, the ratio of maximum lift to
the drag at cruising speed Cimax/cdo, known as the “speed-
range index,” is a useful criterion of airfoil efficiency.
Figure CO. — Variation of maximum lift with thickness.
Although other performance characteristics, such as
rate of climb and length of take-off run, depend less on
the airfoil section characteristics than does the speed
range, the same criterion may also serve as a rough
indication of these characteristics. In such cases, the
drag coefficient in the ratio Cimax/cdQ should be taken at
a lift coefficient corresponding to the best rate of climb
or to the shortest take-off run, respectively.
Inasmuch as the cruising speed generally occurs near
the lift coefficient corresponding to the attitude of
minimum profile drag, the ratio Cimax/cd0min may be used
as a measure of merit. The variation of this ratio with
thickness and camber is shown in figure 61, which
indicates that for thicknesses near the optimum (that
is, somewhat less than 12 percent c) the N. A. C. A.
airfoils can be arranged in the following decreasing
Figure 61 —Variation of <7 /c,/„ with thickness.
*- max u ) . •
order of merit as shown by the speed-range index:
230 series, 430 series, symmetrical series, and 630
series. For thicknesses only slightly greater than the
optimum, however, the index for the symmetrical series
becomes greater than for the 430 series and nearly equal
to that of the 230 series. Attention should perhaps be
called to the fact that the curves presented in figures 61,
62, and 63 are drawn to agree with cross plots of the
characteristics against thickness. Points are included
to show the experimental values.
TESTS OF RELATED FORWARD-CAMBER AIRFOILS IN THE VARIABLE-DENSITY WIND TUNNEL 729
Owing to the wide use of split flaps and other high-
lift devices in landing, the speed-range index should
preferably be derived from the maximum lift coefficient
with the high-lift device. Figures 61, 62, and 63 each
include curves showing the ratio of the maximum lift
coefficient with flap deflected to the drag coefficient with
flap neutral. The addition of split flaps does not affect
the optimum camber of the airfoils since the maximum-
lift increment is practically independent of camber at
flap deflections of 60° and 75°. The addition of split
flaps will tend, however, to increase the optimum
thickness of the airfoils, since the maximum-lift incre-
O .04 .08 .12 .16 .20 .24
Maximum thickness in fraction of chord
Figure 62.— Variation of ci ten,.. . with thickness.
‘max u0(c;=0.4)
ment with flaps increases with thickness. (See fig. 60.)
Thus the thickness for the highest value of ct Jcd
max Vjnin
for the 230 series increases from 9 to 11 percent (approxi¬
mately) with the addition of the flap. (See fig. 61.)
Particular design conditions, such as high-altitude
flight, high wing loadings, and long-range flight, require
that the airplane fly most efficiently at a certain lift
coefficient that may be higher than Cigp(. For such
applications the useful criterion is the ratio Ctmax/Cd0
where ca is taken as the value corresponding to this
certain lift coefficient.
A comparison of the N. A. C. A. forward-camber air¬
foils, based on their drags at a lift coefficient of 0.4, is
given in figure 62. The order of decreasing merit for
thicknesses between 1 0 and 1 2 percent is then changed and
becomes 430 series, 230 series, 630 series, and symmetri¬
cal series. As before, the addition of a flap will not
markedly affect the relative merit of the airfoils for any
given thickness but will increase the value of optimum
thickness for any given camber.
It may also be desirable to compare these airfoils on
the basis of a cruising speed corresponding to a lift
coefficient of 0.6. The results, which are shown in
Figure 63.— Variation of q led with thickness.
‘max ao(fi=0.6)
figure 63, indicate that the 430 series now becomes supe¬
rior to the 230 series over the entire range of thicknesses
tested and the symmetrical series becomes definitely
inferior.
Finally, structural considerations will dictate the
choice of an airfoil thickness and a wing shape that will
efficiently support the aerodynamic loads. This re¬
quirement will lead to the choice of an airfoil that is
thicker, in general, than one selected solely on the basis
of aerodynamic requirements. The final selection of
the best thickness and camber will result in a compro¬
mise between the demands of aerodynamic and struc¬
tural efficiency.
730
REPORT NO. 610— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The general factors determining the choice of the
best thickness and camber have been only briefly
discussed. The requirements of any particular airplane
design will determine exactly what airfoil will be best
suited to that application. It should be emphasized,
for instance, that for small airplanes landing at Reyn¬
olds Numbers much below 8,000,000, section char¬
acteristics should be corrected by means of the method
given in reference 6 to the design Reynolds Number
before comparisons to determine the optimum sections
are made. Such a comparison will show that the
optimum camber is considerably higher at the lower
Reynolds Number than that indicated by the preced¬
ing analysis. For most purposes, a camber of 2 to 4
percent and a thickness slightly above that of the
maximum speed-range index will usually be chosen.
Some unpublished investigations of particular cases
indicate that it is inadvisable, in any case, to depart
very much from the optimum airfoil shape dictated by
purely aerodynamic considerations unless structural
considerations definitely justify the departure.
fj angle y Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., December 5, 1936.
REFERENCES
1. Jacobs, Eastman N., Ward, Kenneth E., and Pinkerton,
Robert M.: The Characteristics of 78 Related Airfoil
Sections from Tests in the Variable-Density Wind Tunnel.
T. R. No. 460, N. A. C. A., 1933.
2. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests in
the Variable- Density Wind Tunnel of Related Airfoils
Having the Maximum Camber Unusually Far Forward.
T. R. No. 537, N. A. C. A., 1935.
3. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests of
N. A. C. A. Airfoils in the Variable-Density Wind Tunnel.
Series 230. T. N. No. 567, N. A. C. A., 1936.
4. Jacobs, Eastman N., and Clay, William C.: Characteristics
of the N. A. C. A. 23012 Airfoil from Tests in the Full-
Scale and Variable-Density Tunnels. T. R. No. 530,
N. A. C. A., 1935.
5. Platt, Robert C.: Turbulence Factors of N. A. C. A. Wind
Tunnels as Determined by Sphere Tests. T. R. No. 558,
N. A. C. A., 1936.
6. Jacobs, Eastman N., and Sherman, Albert: Airfoil Section
Characteristics as Affected by Variations of the Reynolds
Number. T. R. No. 586, N. A. C. A., 1937.
7. Stack, John, and von Doenhoff, Albert E.: Tests of 16
Related Airfoils at High Speeds. T. R. No. 492, N. A.
C. A., 1934.
S. Jacobs, Eastman N., and Abbott, Ira H.: The N. A. C. A.
Variable-Density Wind Tunnel. T. R. No. 416, N. A.
C. A., 1932.
9. Jacobs, Eastman N., and Rhode, R. V.: Airfoil Section
Characteristics as Applied to the Prediction of Air Forces
and Their Distribution on Wings. T. It. to be published,
N. A. C. A., 1938.
10. Pinkerton, Robert M.: Calculated and Measured Pressure
Distributions over the Midspan Section of the N. A. C. A.
4412 Airfoil. T. R. No. 563, N. A. C. A., 1936.
TABLE I.— CHARACTERISTICS OF FORWARD-CAMBER AIRFOILS
Airfoil
Classification
Effective
Reynolds
number
(millions)
Fundamental section characteristics
Derived and additional characteristics that may be used for structural design
Chord
f’D
SE
( I. max
c,
‘ max
al
*0
(deg.)
no (per
deg.)
Clopl
% •
min
c
mu.c.
a. c. (percent c
from c/4)
C i
» max
vr
min
c. p. at
r,
1 max
(per¬
cent c)
Wing character¬
istics A = 6,
round tips
Thickness (percent e) at •
Camber
(per¬
cent c)
Ahead
Above
vh (per
radian)
CD .
m\n
0.15c
0.65c
Maxi¬
mum
N. A. C. A.
C1)
(')
0)
0)
(5)
O')
(6)
(6)
(8)
0006 _ _
A
A 10
A
i)
8. 47
0. 91
0
0.098
0. 00
0. 0054
0
0.7
2
169
35
4. 28
0. 0054
5.35
4. 13
G
0
0009... _
A
1310
R0
A
8. 29
1. 39
0
.098
.00
. 0064
0
1.0
5
217
26
4.28
.0064
8. 02
6. 20
9
0
0012... _
A
CIO
CO
A
8.37
l.CC
0
.099
.00
.0069
0
.6
3
241
26
4.32
. 0009
10. 69
8. 27
12
0
0012-63 _
A
CIO
CO
A
7.87
1.62
0
.098
.00
. 0068
0
1.0
6
238
25
4.28
.0068
10.82
8.58
12
0
0012-64 _
A
CIO
CO
C
7.95
1.56
0
.094
.00
. 0069
0
1.5
5
226
24
4. 14
. 0069
9.72
9.87
12
0
0012-65 _
A
CIO
B8
C
8.21
1.36
0
.084
.00
.0077
0
3.5
6
177
23
3.78
.0077
9. 01
11.22
12
0
0015 _ _ _
A
1)10
DO
A
8.61
1.66
0
.097
.00
.0077
0
1.2
4
216
25
4. 24
.0077
13. 36
10. 33
15
0
0018 _ _ _
A
E 10
E0
A
7. 84
1.53
0
.096
.00
.0088
0
1.7
4
174
25
4.20
. 0088
16. 04
12. 40
18
0
0021 . . . . .
A
E10
El
A
8. 34
1. 48
0
.093
.00
.0100
0
3.0
6
148
24
4. 11
. 0100
18. 71
14.40
21
0
21012 _
A
C12
D3
C
8.37
1.63
-.6
.099
.04
.0070
.001
1.5
0
233
25
4. 32
. 0070
10. 69
8. 26
12
1. 1
22012 _
A
C 12
1)2
C
8. 32
1.72
-.9
. 100
. 10
. 0071
-.005
1.3
5
242
25
4.34
. 0072
10.69
8.24
12
1. 5
23006 _
A
A12
A
D
8. 29
1. 17
-1. 2
. 100
. 15
.0061
-. 012
1.0
8
192
26
4. 34
. 0062
5. 34
4. 13
6
1.8
23009 _ _ _
A
Ji 12
C2
A
8. 26
1.66
-1. 1
. 099
.08
.0065
-.009
.9
7
255
25
4. 32
. 0066
8. 02
6. 21
9
1.8
23012 _
A
C 12
D2
A
8.37
1.74
-1.2
. 100
.08
.0070
-.008
1.2
7
249
25
4. 34
.0071
10. 69
8.25
12
1.8
.23012-33 _ _ _
A
R 12
B6
R
8. 53
1.52
-1.2
.097
.25
.0071
-.010
, 7
7
214
27
4. 24
.0073
10. 48
8.60
12
1.8
23012-34 _
A
R12
R3
C
8. 60
1.49
-1. 2
. 094
. 13
.0072
-.011
. 9
4
207
26
4. 14
. 0073
8.98
9. 87
12
1.8
23012-64 _ _ -
A
C 12
1)2
A
8. 40
1.71
-1.0
.095
.10
.0072
-. 010
1.0
4
237
26
4. 18
.0073
9. 72
9. 88
12
1.8
23015 _
A
1)12
D2
A
8. 37
1.73
-1. 1
.098
. 10
.0081
-. 008
1. 1
6
214
24
4. 28
.0082
13. 36
10. 35
15
1.8
23018 _
A
E12
E2
R
8. 16
1.58
-1. 2
.097
.08
. 0091
-. 006
1.7
6
174
24
4. 24
. 0091
16.04
12.39
18
1.8
23021.. _ _ _ _
A
El 2
E2
R
8.21
1.50
-1. 2
.092
.07
. 0101
-.005
2.3
7
149
24
4.07
. 0102
18. 70
14.44
21
1.8
24012 _ _
A
C 12
C3
C
8. 26
1.71
— 1. 5
. 100
.08
.0072
-.013
1.3
6
238
26
4.34
.0073
10.71
8.25
12
2. 1
25012 _
A
C 12
C3
C
8. 24
1.67
-1.6
100
. 10
.0074
-. 019
1. 1
7
226
27
4. 34
. 0075
10. 72
8. 28
12
2.3
32012 _
A
C 12
D3
A
8. 40
1.74
-1. 2
. 100
. 15
. 0075
-. 005
1. 1
6
232
24
4. 34
.0077
10.69
8.23
12
2.3
33012 _ _
A
C 12
D3
A
8.37
1.80
-1.7
. 099
. 10
. 0074
-.014
1.0
6
243
25
4. 32
.0075
10. 68
8. 28
12
2.8
34012 _ _
A
C12
D3
A
8.37
1 80
-2. 1
. 100
.20
.0075
-.022
.6
5
240
27
4.34
.0077
10.71
8.25
12
3. 1
42012 _
A
C 12
D4
A
8. 42
1.76
-1.8
. 100
.20
.0078
009
1. 1
0
226
26
4.34
.0079
10. 72
8.28
12
3. 1
43009 _
A
R 12
B4
A
8.08
1. 72
-2.4
. 100
. 18
.0068
-.021
.8
G
253
26
4. 34
.0073
8.02
6.21
9
3.7
A
C 12
D4
A
8.39
1.84
-2.3
. 100
.26
.0079
-. 019
1. 0
7
233
27
4.34
.0081
10.69
8. 26
12
3.7
43012A _
A
C 12
E4
A
8. 26
1. 78
-2. 2
. 102
.29
.0081
-.017
1. 2
7
220
26
4. 41
.0085
11.90
8. 26
12
3.7
43015 _
A
1)12
D4
A
8. 31
1.76
-2.3
. 101
. 18
.0085
-.015
1.2
5
207
20
4. 37
.0086
13. 36
10.32
15
3.7
43018 _ _ _
A
E 12
E4
C
8.34
1. 63
-2.4
.090
. 16
.0095
-.013
1.8
6
172
26
4. 20
. 0097
16. 03
12. 40
18
3.7
43021 _
A
F 12
E6
A
8. 40
1. 48
-2.4
. 093
. 10
.0108
-.010
2. 4
7.
137
25
4. 11
. 0108
18. 70
14. 50
21
3. 7
44012 _ _
A
C12
1)4
A
8.50
1.82
-2.8
.098
. 25
.0080
-. 028
.5
5
227
28
4. 28
. 0081
10.70
8. 24
12
4. 2
62021 _
A
F12
E4
D
8.42
1.52
-3. 1
. 094
. 12
.0110
-.006
3. 2
8
138
25
4. 14
.0111
18. 73
14. 47
21
4.6
63009 _ _ _
A
R 12
C6
A
8. 10
1. 77
-3.5
.098
. 57
.0081
-.042
2.6
7
219
27
4.28
. 0204
1 1. 05
0. 22
9
5.5
63012 _ _
A
C12
D6
A
8. 29
1.84
-3.5
. 100
.40
.0086
-.033
2.7
13
214
26
4. 34
.0100
11. 03
8.27
12
5.5
63015- _ _ _ _
A
D12
E6
A
8. 29
1.76
-3.5
.098
.25
.0093
-.024
1.6
0
189
26
4. 28
.0097
13. 35
10. 33
15
5.5
63018 _
A
E 12
E7
A
8.24
1.63
-3.4
.097
. 15
. 0099
-. 020
2. 1
6
165
20
4. 24
. 0100
16. 04
12. 44
18
5.5
63021 _ _ _
A
F 1 2
E8
A
8. 18
1.48
-3.6
. 097
. 21
.0113
-. 018
3. 1
6
131
25
4. 24
.0115
18. 68
14.52
21
5.5
64021 _ _
A
F12
Ell
A
8. 16
1. 46
-4. 2
. 094
. 13
.0115
-.031
2.7
8
127
26
4. 14
.0116
18. 68
14.53
21
6. 2
n
fs)
(10)
00
nm 9: 60°, 0 2c split llap. _
A
CO
A
S. 11
2. 35
-13. 1
.091
. 167
-.220
.6
3
341
35
4.04
10.69
8. 27
12
0
23009; 60°, 0.2c split flap -
A
C2
A
8. 24
2. 31
-14.0
. 092
. 166
-.223
.9
7
355
35
4. 07
_ _ __
8. 02
6.21
9
1.8
A
1)2
A
8. 18
2. 48
-14.3
. 088
. 160
-. 236
1. 2
354
35
3.93
10.69
S. 25
12
1.8
vsneti- 7S° n 9 r snlit. flan
A
C2
A
7.98
2. 30
-15. 1
. 089
. 205
-. 210
.9
354
34
3. 96
8. 02
6.21
9
1.8
23012; 75°, 0.2c split flap -
A
—
D2
A
8. 10
2. 54
-15.6
.085
—
.201
-.228
1. 2
7
363
34
3.82
—
10.69
8. 25
12
1.8
23015; 75°, 0.2c split flap -
A
_
D2
A
8. 21
2. 70
-16.2
.086
.
. 198
-.245
1. 1
6
333
35
3. 86
_ _ _ _
13. 36
10.35
15
1.8
92A91- n 9r <;nl if. flan
A
E2
A
8. 13
2. 74
— 16.5
.094
. 191
— . 300
2. 3
7
271
35
4. 14
18.70
14.44
21
1.8
dinoo- 7R° n 9c snlit flan
A
114
A
8. 10
2. 35
-17.5
. 080
. 207
-. 208
.8
0
346
34
3.64
7.52
0. 20
9
3. 7
43012; 75°, 0.2c split flap -
A
D4
A
8.24
2. 65
-17.3
. 082
.200
-. 225
1.0
7
335
34
3. 72
_ _ _ , _ _
10. 68
8.20
12
3.7
63009; 75°, 0.2c split flap -
A
C6
A
8.21
2. 40
-19.0
.078
. 207
230
2. 6
7
295
34
3. 57
11.05
6. 23
9
5.5
hJ
M
co
H
co
O
W
W
>
H
a
*3
O
st
>
rC
O
I
o
>
s?
i— <
tc
H
SC
>■
H- H
SC
O
HI
HI
CO
HH
3
H
Hri
H-4
M
<j
>
SC
I— I
>
a
t-1
K
w
i — i
H
3
O
H
cj
K
-vj
CO
2 Type of pressure aisinounon. oee rtueienee a.
2 Type of scale effect on maximum lift. A signifies practically no scale effect.
For other designations see reference 6, fig. 44.
» Type of lift-curve peak as shown in the sketches.
5 Turbulence factor is 2.64.
0 These data have been corrected for tip effect.
7 Angle of zero lift obtained from linear lift curve approximating experimental lift curve.
8 Slope obtained from linear lift curve approximating experimental lift curve.
9 Value of the drag that applies approximately over the entire useful range of lift coefficients.
12 The value of c is taken about the aerodynamic center of the airfoil without the flap.
m a • c*
11 Values of Cd used in computing this ratio arc taken from tests of the airfoil without the flap.
Qmin
REPORT No. 611
WIND-TUNNEL INVESTIGATION OF TAPERED WINGS WITH ORDINARY AILERONS
AND PARTIAL-SPAN SPLIT FLAPS
By Carl J. Wenzinger
SUMMARY
An investigation was made in the N. A. C. A. 7- by
10-joot wind tunnel to determine the aerodynamic 'proper¬
ties of tapered wings having partial-span flaps for high
lift and ordinary ailerons for lateral control. Each of two
Clark Y wings , tapered 5:1 and 5:3, was equipped with
partial-span split flaps of two lengths and with ordinary
ailerons extending from the outboard ends of the flap to
the wing tips . Measurements of wing forces and moments
and of aileron hinge moments were made for the two condi¬
tions of flaps neutral and deflected.
With split flaps of equal length both wings had practi¬
cally the same CLmax. If 30 percent of the flap outer span
were removed for the installation of ailerons , a reduction in
CLmax of the tapered wings with flaps might be expected of
the order of 4 to 7 percent.
Ailerons of the same span were found to give higher
rolling-moment coefficients together with greater adverse
yawing-moment coefficients on the 5:3 tapered wing than
on the wing tapered 5:1. In addition, ailerons of the
same span on the tapered wings tested gave greater rolling-
moment coefficients and smaller adverse yawing-moment
coefficients at the same lift coefficient when the partial-span
flaps were deflected than when they were neutral.
INTRODUCTION
Full-span high-lift devices are seldom used on air¬
planes at the present time because of the difficulty of
obtaining satisfactory lateral control with the lift-
increasing device extending along the entire trailing edge
of the wing. Several control devices adaptable to wings
with a full-span flap have been investigated (references 1
and 2) and a few have shown considerable promise. How¬
ever, each one has apparently had some disadvantage
sufficient to prevent its general use. An arrangement
commonly used in practice consists of partial-span flaps
extending along the inner portion of the wing span for
increasing lift combined with ordinary ailerons extend¬
ing from the outboard ends of the flap to the wing tips
for lateral control. Naturally, such an arrangement
does not take advantage of the full potential value of the
flap in decreasing the landing speed and steepening the
gliding angle at landing.
Some research has already been completed concerning
the aerodynamic effects of flaps extending along different
portions of the wing span for both rectangular and
tapered wings (references 3, 4, and 5). In addition,
considerable data are available concerning the charac¬
teristics of different sizes of ordinary ailerons on wings
of various plan forms (references 6, 7, and 8). There is
a scarcity, however, of information regarding the aero¬
dynamic characteristics of wings combined with partial-
span flaps and ordinary ailerons.
The investigation described in the present report was
made to determine the aerodynamic effects of combina¬
tions of flaps and ailerons of various spans. The tests
included wings of medium and high taper having split
flaps and ordinary ailerons of different spans.
APPARATUS
MODELS
The two models used have been previously tested in
connection with the wind-tunnel research described
in references 4 and 8. One wing is tapered 5: 1 and the
other 5:3, the slopes of the leading and trailing edges
being equal (figs. 1 and 2). The Clark Y profile is
used at all sections along the span, and the maximum
ordinates of all the sections are in a horizontal plane
on the upper surface. The models are constructed of
laminated mahogany; each has a span of 60 inches and
a geometrical aspect ratio of 6.0.
The ailerons tapered with the wings, the chord of
each aileron at any longitudinal section being 25 percent
of the wing chord (cw) at the same section. The spans
of the ailerons first tested were the same as those used
in previous tests, 50 percent 6/2 and 41 percent 6/2 for
the wings tapered 5:1 and 5:3, respectively. The
spans were then reduced to 30 percent 6/2 for each
aileron tested, this latter length being considered the
shortest desirable. Since earlier tests (reference 6)
had shown that the moments caused by both the right
and left ailerons could be separately found and added
to give the total effect with satisfactory accuracy, the
present models were equipped with ailerons only at
the right wing tip.
733
REPORT NO. Gil— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
734
All the ailerons were arranged to lock rigidly to
the wing at a given deflection or to rotate freely about
their hinge axes, the gap between aileron and wing
being sealed with a light grease. Hinge moments of
the ailerons were measured by the calibrated twist of a
long slender steel rod extending along the hinge axis
Figure I.— The 5 :1 tapered Clark Y wing with 0.25c„ tapered ordinary ailerons and
O.lotv, tapered partial-span split Haps.
from the aileron to the balance frame outside the air
stream.
Simple split flaps that tapered with the wing were
used with each model, the flap chord at any longitudi¬
nal section being 0.1 5cw at the same section. In each
case the flaps extended along the trailing edge of the
wing from the center section to the inboard end of the
ailerons, so that partial-span flaps of 0.50, 0.59, and
0.706 were used. Each of the flaps was built of fl6-inch
steel plate and was fastened to the wing model by
screws and blocks at an angle of 00°. This angle was
the one that gave the highest CL with the 0.1 5cw
tapered flap in earlier tests (reference 4).
WIND TUNNEL
The N. A. C. A. 7- by 10-foot wind tunnel in which
the tests were made had an open jet and a closed return
passage. The tunnel and regular 6-component balance
are described in detail in reference 9. On this balance
the six components of aerodynamic forces and moments
are independently and simultaneously measured with
respect to the wind axes of the model.
TESTS
The dynamic pressure was maintained constant
throughout the tests at 16.37 pounds per square foot
corresponding to an air speed of 80 miles per hour at
standard sea-level conditions. The average test Rey-
nolds Number was 609,000 based on the mean wing
chord of 10 inches; the effective Reynolds Number
(test Reynolds Number X the turbulence factor of the
wind tunnel) was 609,000X1.4=853,000. (See refer¬
ence 10.) The angle-of-attack range covered from
zero lift to beyond the stall of the wing. Aileron
deflections covered from 30° to —30° and were meas¬
ured in a plane perpendicular to their hinge axes.
(Positive deflections are downward and negative,
upward.)
Force tests were made first with full-span flaps on
the wings as a basis for comparison with the partial-
span flaps. Lift, drag, and pitching-moment coeffi¬
cients were measured for flap deflections of 0° and 60°.
The flaps wrere next cut to the shortest spans used so
that the longest ailerons could be tested first. With
this arrangement no alterations to the original models
were required. Lift, drag, and pitching-moment co¬
efficients were again measured for flap angles of 0°
and 60°, ailerons neutral, and then rolling-, yawing-,
and liinge-moment coefficients of the ailerons were
measured for the same two flap deflections. In all
these tests the aileron gaps were sealed with a light
grease to prevent any leakage because even a small
gap considerably reduces the aileron effectiveness.
Figure 2. --The 5:3 tapered Clark Y wing with 0.25cK tapered ordinary ailerons
and 0.1 5Cw tapered partial-span split flaps.
For comparison with results for the aileron gap
sealed, a few tests were made with the long aileron
having the gap unsealed on the 5:1 tapered wing. In
this case rolling-, yawing-, and hinge-moment coeffi¬
cients of the aileron were measured only for the flap-
neutral condition. These data also served for com¬
parison with similar data from the same model obtained
about 3 years earlier.
TAPERED WINGS WITH ORDINARY AILERONS AND PARTIAL-SPAN SPLIT FLAPS
735
The ailerons were then cut to the shorter spans and
the flaps were lengthened. Tests similar to those for
the longer ailerons were again made, except that the
aileron gaps were always kept sealed.
RESULTS AND DISCUSSION
FORM OF PRESENTATION OF DATA
The test results are given in the form of absolute
coefficients of lift and drag, and of pitching, rolling,
yawing, and hinge moment:
C
D
a
(a.c.)0
drag
qS
[of plain wing
pitching moment about aerodynamic center
qcS
n / _ rolling moment
1 ~ qbS
/r , yawing moment
Cn qbS~~
Ch
hinge moment
qcafe>a
where S is the wing area.
b, the wing span.
c, the mean geometric chord of the wing.
Sa, the area of one aileron.
ca, the root-mean -square chord of a tapered
aileron; i. e., the square root of the mean
of the squares of the aileron chords along
its span.
q, the dynamic pressure.
All coefficients, except those of hinge moment, were
obtained directly from the balance and refer to the wind
(or tunnel) axes.
The data were corrected for tunnel effects to aspect
ratio 6.0. The standard jet-boundarv corrections were
applied,
S
Aa=5^C7X57.3, degrees
where C is the jet cross-sectional area. A value
5= — 0.165 for the open-jet 7- by 10-foot wind tunnel
was used in correcting the test results. An additional
correction to the drag data was necessitated by the
static-pressure gradient in the open jet. This gradient
produced an additional downstream force on the model
corresponding to A CL of 0.0019 for the wing tapered
5:1 and A CD of 0.0017 for the wing tapered 5:3.
EFFECT OF FLAP SPAN ON WING CHARACTERISTICS
Lift and drag coefficients for the 5 : 1 tapered wing
with various spans of tapered split flap are given in
figure 3, and pitching-moment coefficients in figure 4.
Similar data for the 5:3 tapered wing are given in
figures 5 and 6. Values of CLmax and of CD and LjD
Figure 3.— Lift and drag coefficients of 5:1 tapered wing with tapered split flaps of
various spans deflected 00°. Aileron neutral.
Ang/e of attack, cl , degrees
~/6 -!2 -8 -4 0 4 8 /2 !6 20
Figure 4— Pitching-moment coefficients of 5: 1 tapered wing with tapered split flaps
of various spans deflected 60°. Aileron neutral.
at CLmax for different flap spans on both the 5 : 1 and
5:3 tapered wings are plotted in figure 7.
Some aerodynamic characteristics of the tapered
wings with split flaps of various spans are compared in
table I with similar data for a rectangular wing. (The
data for the rectangular wing were taken from reference
3 and corrected for tunnel effects.) It will be noted
REPORT NO. 611— NATIONAL ADVISORY COMMITTEE FOR AREONAUTICS
736
Figure 5.— Lift and drag coefficients for 5:3 tapered wing with tapered split flaps
of various spans deflected 60°. Aileron neutral.
Angle of attack, ct , degrees
-16 -12 -8 -4 0 4 6/2/6 20
C 0
o
si
O
U
■+'-3
C J
Qj
§■*
i
o
r
\
+-
- A-
o •
+-+~f-+-f + — =H~+— +
o-a- •
°fo--o n;
C3- — q.
--A-jA-A. A
— CUD- C
No flap
0./5cw by 0.59b flap
.15" " .70" » _
" LOO- "
- .15
-°==r
- + -+V.
wV -A~
-o-6-q XIjT 1— “r
A-o-
Aerodynamic center:
x= 0.061c back of root quarter chord
-(/ - 0.059c below root chord
1 1 I i I 1 .1 1 1 I I
Figure 6. — Pitching-moment coefficients for 5:3 tapered wing with tapered split
flaps of various spans deflected 00°. Aileron neutral.
Figure 7.— Effect of partial-span split flaps on Cl and on Cd and L/D at Ct
The 5:1 and 5:3 tapered wings with 0.15 cw tapered split flaps deflected 60°.
(a) Aileron gap closed. (b) Aileron gap open.
Figure 8.— Rolling- and yawing-moment, coefficients of o.25c„, by 0.50 2 tapered aileron on 5:1 tapered wing. Flaps neutral.
TAPERED WINGS WITH ORDINARY AILERONS AND PARTIAL-SPAN SPLIT FLAPS
737
that the CL of the plain wings increases slightly
with increasing taper but, with full-span flaps deflected,
the CL decreases slightly with increasing taper.
Reducing the flap span from 100 to 70 percent on the
5:1 tapered wing reduced the lift increment &Cr
by about 11.5 percent although the actual CL was
reduced about 4 percent. On the 5:3 tapered wing
and on the rectangular wing the values are roughly 17
percent reduction in A CL and 7 percent in CL
1 max 1 7 71 ax
AILERON CHARACTERISTICS, 5 : 1 TAPERED WING
Rolling- and yawing-moment coefficients due to the
0.2 5cw by 0.50 6/2 tapered aileron, gap closed, are given
in figure 8 (a) at five angles of attack for the flap-
neutral condition. The results for the gap open
between aileron and wing are plotted in figure 8 (b).
Comparison of these two figures shows that the rolling-
moment coefficient for a given aileron deflection is
decreased when the gap is left unsealed, indicating that
no leakage should be permitted between aileron and
wing for the maximum rolling effect. Comparison of
the data for the unsealed aileron (fig. 8 (b)) with those
obtained with the same aileron in tests made about 3
years earlier (reference 8) shows good agreement.
The effect on aileron rolling- and yawing-moment
coefficients due to deflecting the 0.1 5c,*, by 0.506 split
flap 60° is shown in figure 9. For the two conditions
Figure 9. — Rolling- and yawing-moment coefficients of 0.25c,, by 0.5o g tapered
aileron on 5: 1 tapered wing. The 0. 1 5c„ by 0.505 tapered split flaps deflected 00°.
of flap neutral and flap deflected, the rolling moments
due to the up aileron increase directly with aileron
deflection to about 20° after which they taper off.
-32 -24 ~16 -8 O 8 16 24 32- ,-24 -16 -8 O 8 16 24 32
Aileron deflection, 6a, degrees
(a) Aileron gap closed. (b) Aileron gap open.
Figure 10. — Hinge-moment coefficients of 0.25c„ by 0.50 r, tapered aileron on 5:1 tapered wing. Flaps neutral.
Figure 11. — Hinge-moment coefficients of 0.25c,, by 0.50 | tapered aileron on 5:1
tapered wing. The 0.15c„, by 0.506 tapered split flaps deflected 60°.
The moments due to the down aileron increase directly
to an aileron angle of about 15° after which they also
begin to fall off. In general, when the flap is deflected,
the rolling-moment coefficients are increased above the
values for the flap-neutral condition. Hinge-moment
coefficients of these ailerons increase almost directly
with aileron deflection (figs. 10 (a), 10 (b), and 11)
for the range tested.
Rolling- and yawing-moment coefficients due to the
0.25cw by 0.30 6/2 tapered ailerons are given in figure 12
for the flap-neutral condition and in figure 13 for the
0.15cw by 0.706 split flap deflected 60°. Hinge-moment
coefficients for the two conditions are given in figures 14
and 15. The variation of rolling moment with aileron
deflection is quite similar for these ailerons to that of
the longer ones, but the values are considerably less for
a given deflection at a given angle of attack. In fact,
REPORT NO. 611— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
788
the reduction in rolling-moment coefficient is almost
directly proportional to the decrease in the span of the
aileron.
<0
.B
.0
$
0)
o
■k V
CTf*
nj
T
I
6-C
1-,
I
Fig v be 12.-
— | — 1
- 1 - 1
v = -5.0°
■ = -0.2°
■ - 4.6 °
- = 9.4 °
/ - /4
C '
+ -
t
□ -
8f =
0°
1
C '
8n
T
—
— r
1
- _ >
-A
—
—
.04
OB
%
o
u
-k >
C~ ► *
T
a
'b
8
I
o
Cfc
— I -
qJ _
'. =
-5.4°
— |
+ -
—
' = -0.1
■ = 4.C
■ = 9.1
, - / ?
-o
po
Cf
□ -
r
9° -
■£y^
•?> 1
ii 1
60°
%=
r ’
V-
J
&
— y
h£=-
<?=--
--A-
- &
/
A
N
i
Li
-24 -16 -8 0 8 16
Aileron deflection, 6a, degrees
24
c
.0)
.0
$
O
O
'K.
8
§
i
b
O
.e
5;
.4
0
-.2
~tt
oC =
-C
<5
= O
14°;
c,-
1
--0.35
X
—
—
6f
l 7°;
o
/.0
f
k y-
-x-X
X-
-24 -16 -8 0 8 /6
Aileron deflection, 6a, degrees
6
24
Aileron deflection, Sa, degrees
-Rolling- and yawing-moment coefficients of 0.25c„, by 0.30 tapered
aileron on 5:1 tapered wing. Flaps neutral.
Figure 13. — Rolling- and yawing-moment coefficients of 0.25 cw by 0.30 ^ tapered
aileron on 5: 1 tapered wing. The O.loCw by 0.706 tapered split flaps deflected 00°.
Figure 14.— Flinge-moment coefficients of 0.25cw by 0.30 ^ tapered aileron on 5:1
tapered wing. Flaps neutral.
AILERON CHARACTERISTICS, 5 :3 TAPERED WING
Rolling-, yawing-, and hinge-moment coefficients of
the 0.25cw by 0.41 6/2 tapered aileron are given in
figures 16, 17, 18, and 19 for various aileron deflections
at several angles of attack, the 0.15cw by 0.596 tapered
split flap both neutral and deflected 60°. Similar
plots for the shorter aileron, 0.2oCa, by 0.30 6/2, with the
-16 -8 0 8 /6
Aileron deflection, 6a, degrees
Figure 15.— Hinge-moment coefficients of 0.25c«, by 0.30 ^ tapered aileron on 5:1
tapered wing. The 6.1oc«, by 0.706 tapered split flaps deflected 00°.
|-£
.0
£
.C
o
-K
<b ,
5 .C
o _
^ r c
i bj
.cT Q
1
o °
0
i
Ch
•b
'I
Til'
- cl = -50°
7
X
C '
^ l
+ -
- = -0.
' - 4.
- = 9.
2°
□ -
4°
3°-
\
\
6y =
0°
/"r-s
zV\\
N '
\
A
xmx-
\
\
>
. \
X N
r '
d—
•A
s*a
i= —
- — - -
— T
h
-i
-XV.
V
T
— ^0=
T
T-
’Y
— _
— -
~T
-24 ~/6 -8 0 8 /6
Aileron deflection, 6a, degrees
24
6
Figure 16.— Rolling- and yawing-moment coefficients of 0.25c„, by 0.41 g tapered
aileron on 5:3 tapered wing. Flaps neutral.
-24 -16 -8 0 8 /6 24
Ai/eron deflection, 6a> degrees
Figure 17. — Rolling- and yawing-moment coefficients of 0.25c„, by 0.41 | tapered
aileron on 5:3 tapered wing. The 0.15Cu, by 0.596 tapered split flaps deflected 60°.
longer flap, 0.1oc7C by 0.706, are given in figures 20, 21,
22, and 23.
TAPERED WINGS WITH ORDINARY AILERONS AND PARTIAL-SPAN SPLIT FLAPS
739
For the 5:3 tapered wing, the variation of rolling
moment with aileron deflection is much the same as
that of the ailerons on the 5 : 1 tapered wing except for
the case of the up aileron when the flap is deflected.
Figure IS- — Hinge-moment coefficients of 0.25 cw by 0.41 | tapered aileron on 5:3
tapered wing. Flaps neutral.
Figure 19. — Hinge-moment coefficients of 0.25c,* by 0.41 | tapered aileron on 5:3
tapered wdng. The 0.15c,* by 0.596 tapered split flaps deflected 60°.
Figure 20. — Rolling- and yawing-moment coefficients of 0.25c*, by 0.30 o tapered
aileron on 5:3 tapered wing. Flaps neutral.
In this condition on the 5:3 tapered wing the rolling
moments due to the up aileron increase almost directly
without falling off over the range of deflections tested
(0° to 30°). The moments due to the down aileron,
however, vary in a manner similar to those on the 5 : 1
tapered wing. As in the case of the ailerons on the
5:1 tapered wing, the rolling-moment coefficients for
the ailerons on the 5:3 tapered wing are somewhat
Figure 21. — Rolling- and yawing-moment coefficients of 0.25c,* by 0.30 | tapered
aileron on 5:3 tapered wing. The 0.15c,* by 0.706 tapered split flaps deflected 60°.
<o
SO
C
,<a
.o
$
<b
o
o
-o
c;
to
5
o
i
0)
o
I
0
-.2
-.4
H
a =
1
-C
6
= O
16°;
cL =
0.35 _
X
—
—
// —
o
fO
s
^2
'"A
'X-
T
-24 -16 -8 0 8 /6
Aileron deflection, 6a, degrees
b
24
Figure 22. — Hinge-moment coefficients of 0.25c,* by 0.30 ^ tapered aileron on 5:3
tapered wing. Flaps neutral.
Aileron deflection, 6a, degrees
Figure 23. — Hinge-moment coefficients of 0.25c,* by 0.30 g tapered aileron on 5:3
tapered wing. The 0.15c,* by 0.706 tapered split flaps deflected 60°.
increased when the flap is deflected. In addition, the
reduction in rolling-moment coefficient with decreased
aileron span is also directly proportional to the decrease
I in span.
740
REPORT NO. 611— NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Figure 21.— Effect of aileron span on rolling- and yawing-moment coefficients. The 0.25c,* tapered aileron with equal up-and-down deflection on tapered Clark Y w ings
The 0.15c* partial-span split flaps neutral and deflected.
COMPARISON OF THE TAPERED AILERONS ON TAPERED WINGS
The effect of aileron span on rolling- and yawing-
moment coefficients with equal up-and-down deflection
is shown in figure 24, with the partial-span flaps both
neutral and deflected. With the arrangements shown
it is evident that ailerons of the same span on the 5:3
tapered wing are capable of giving higher rolling-
moment coefficients, together with more adverse yaw¬
ing-moment coefficients, than those on the 5 : 1 tapered
wing, flaps neutral or deflected. This characteristic
may be attributed almost entirely to the difference in
area of the ailerons for the sizes investigated on the
two wings. The chords of the ailerons are the same
percentage of the wing chord so that, since the wings
have the same span and area, the aileron on the 5:3
tapered w ing has a larger area than an aileron of equal
span on the 5 : 1 tapered wing. At the same lift
coefficient of the wing, deflecting the flap has the same
general effect as in the case of single ailerons; i. e., the
rolling-moment coefficients are increased and the ad¬
verse yawing-moment coefficients are decreased for the
same aileron deflection.
Previous tests showed (reference 8) that the long
tapered ailerons on both the 5: 1 and 5:3 tapered wings,
flaps neutral, gave rolling moments equal in magnitude
to an assumed value that would provide satisfactory
lateral control up to the stall. At and beyond the
stall, however, the indicated control was poor.
The rolling-moment coefficient corresponding to the
foregoing conditions is approximately 0.065 at a lift
coefficient of 1.0 for the tapered ailerons and wings in
question. In addition, flight tests have show-n that in
some cases (7/ =0.04 gives satisfactory rolling control
(reference 11) so that the value of CV =0.065 may be
too high for most of the usual flight conditions.
Decreasing the span of the tapered ailerons to 0.30
6/2 gives an aileron that just meets the requirement of
the lower rolling-moment coefficient on the 5 : 1 tapered
wing, which is probably the highest taper likely to be
dealt with in practice. The use of the highly tapered
wing is accompanied by a decreased damping in roll
compared with the medium tapered or rectangular
wings, so that it seems likely that lowrer aileron rolling
moments will suffice to give the same degree of con¬
trol. In addition, the reduction in CL with partial-
span flaps is small (about 4 percent), so that the com¬
bination appears promising from considerations of both
high lift and rolling control.
CONCLUSIONS
1. There wns practically no difference in CL/nax ob¬
tained with Clark Y wings tapered 5:1 or 5:3 with
equal lengths of split flap.
2. A reduction in CLmi]X of tapered wings with split
flaps might be expected of the order of 4 to 7 percent,
if 30 percent of the flap outer span w'ere removed for
ailerons.
3. Ailerons of the same span on the 5:3 tapered
wing gave higher rolling-moment coefficients but also
greater adverse yawing-moment coefficients than those
on the 5:1 tapered wing, flaps neutral or deflected.
TAPERED WINGS WITH ORDINARY AILERONS AND PARTIAL-SPAN SPLIT FLAPS
741
4. Ailerons of the same span gave greater rolling-
moment coefficients and smaller adverse yawing-
moment coefficients at the same lift coefficient on the
tapered wings tested when partial-span split flaps were
deflected than when neutral.
Langley Memorial Aeronautical Laboratory,
National xLdvisory Committee for Aeronautics,
Langley Field, Va., January 14, 1937.
REFERENCES
1. Soule, H. A., and McAvoy, W. II.: Flight Investigation of
Lateral Control Devices for Use with Full-Span Flaps.
T. R. No. 517, N. A. C. A., 1935.
2. Weick, Fred E., and Shortal, Joseph A.: Development of the
N. A. C. A. Slot-Lip Aileron. T. N. No. 547, N. A. C. A.,
1935.
3. Wenzinger, Carl J.: The Effect of Partial-Span Split Flaps
on the Aerodynamic Characteristics of a Clark Y Wing.
T. N. No. 472, N. A. C. A., 1933.
4. Wenzinger, Carl J. : The Effects of Full-Span and Partial-
Span Split Flaps on the Aerodynamic Characteristics of a
Tapered Wing. T. N. No. 505, N. A. C. A., 1934.
5. Le choix des parametres de l’aile a fente. Cahiers Aero-
techniques, No. 13, 1934.
6. Weick, Fred E., and Wenzinger, Carl J.: Wind-Tunnel
Research Comparing Lateral Control Devices, Particu¬
larly at High Angles of Attack. I. — Ordinary Ailerons
on Rectangular Wings. T. R. No. 419, N. A. C. A., 1932.
7. Weick, Fred E., and Shortal, Joseph A.: Wind-Tunnel Re¬
search Comparing Lateral Control Devices, Particularly
at High Angles of Attack. VIII. — Straight and Skewed
Ailerons on Wings with Rounded Tips. T. N. No. 445,
N. A. C. A., 1933.
8. Weick, Fred E., and Wenzinger, Carl J.: Wind-Tunnel Re¬
search Comparing Lateral Control Devices, Particularly
at High Angles of Attack. IX. — Tapered Wings with
Ordinary Ailerons. T. N. No. 449, N. A. C. A., 1933.
9. Harris, Thomas A.: The 7 by 10 Foot Wind Tunnel of the
National Advisory Committee for Aeronautics. T. R.
No. 412, N. A. C. A., 1931.
10. Platt, Robert C.: Turbulence Factors of N. A. C. A. Wind
Tunnels as Determined by Sphere Tests. T. R. No. 558,
N. A. C. A., 1936.
11. Soule, Hartley A., and Wetmore, J. W.: The Effect of Slots
and Flaps on Lateral Control of a Low-Wing Monoplane
as Determined in Flight. T. N. No. 478, N. A. C. A.,
1933.
TABLE I.— COMPARISON OF RECTANGULAR AND
TAPERED CLARK Y WINGS WITH SPLIT FLAPS OF
VARIOUS SPANS
Flap span
Flap
chord
cL
"flifli
AC,
u m a x
CL lCD ■
^ max wmi»
L/D at C,
^ max
Rectangular wing •
No flap _ _
1.282
86. 7
9. 98
| Full span.. .
0. 20c „
2. 188
0. 906
148.0
4.86
0.706 _
. 20c
2. 040
.758
138.0
6. 03
0.506 _
. 20c „
1. 940
.658
131. 1
6. 45
0.506 _
. 20c„
1.845
. 563
124.7
6. 76
5:3 tapered wing
No flap .
1.300
95.5
10. 74
Full span _
0. 15c„
2. 129
0. 829
156. 6
5.68
0.706 _ _
• 1 DC uj
1.973
.673
145. 0
6.50
0.596 _ _
. 15c
1.881
.581
138. 4
6. 70
0.506 _
. 1 5c u?
1.810
.510
133. 1
7.15
5:1 tapered wing
No flap .. ..
1.312
96.5
9.01
Full span _
0. 15Cu>
2.055
0. 743
151.1
6.05
0.706 _ _
• 1 DC io
1.970
.658
144.9
6. 05
0.596 _
* loC w
1.895
.583
139. 4
6. 05
0.506 _
. 15c uj
1.816
.504
133. 5
6. 05
! Values obtained from data in reference 3, corrected for tunnel effects.
AERONAUTIC SYMBOLS
1. FUNDAMENTAL AND DERIVED UNITS
Symbol
Metric
English
Unit
Abbrevia¬
tion
Unit
Abbrevia¬
tion
Length _
Time _
Force.
l
t
F
meter _ _
second _ _
weight of 1 kilogram.
m
s
kg
foot (or mile)
second (or hour) _
weight of 1 pound _
ft. (or mi.)
sec. (or hr.)
lb.
Power _
Speed _
P
V
horsepower (metric) . _
/kilometers per hour _
(meters per second _
k.p.h.
m.p.s.
horsepower
miles per hour _
feet per second _
hp.
m.p.h.
f.p.s.
2. GENERAL
W, Weigh t=mg
g, Standard acceleration of gravity =9. 80665
m/s2 or 32.1740 ft. /sec. 2
A! ]r
m, Mass= —
9
I, Moment of inertia— mk2. (Indicate axis of
radius of gyration k by proper subscript.)
n, Coefficient of viscosity
SYMBOLS
v, Kinematic viscosity
p, Density (mass per unit volume)
Standard density of dry air, 0.12497 kg-nr4-s2 at
15° C. and 760 mm; or 0.002378 lb. -ft.-4 sec.2
Specific weight of “standard” air, 1.2255 kg/m3 or
0.07651 11). /cu. ft.
3. AERODYNAMIC SYMBOLS
s,
sw,
0.
i j
s
V,
fil
L,
D,
Do,
Di}
1)
C,
R,
in
Area
Area of wing
Gap
Span
Chord
Aspect ratio
True air speed
Dynamic pressure = ^ pi 72
Lift, absolute coefficient CL=
L_
qS
Drag, absolute coefficient CD=^L
q, 8
Profile drag, absolute coefficient CDo=
Induced drag, absolute coefficient CD.-
_Dp
7)0 qS
_Dj
qS
Parasite drag, absolute coefficient CDp = ^
C
Cross-wind force, absolute coefficient Cc=— ^
iw, Angle of setting of wings (relative to thrust
line)
it, Angle of stabilizer setting (relative to thrust
line)
Q, Resultant moment
kl, Resultant angular velocity
p— , Reynolds Number, where l is a linear dimension
(e.g., for a model airfoil 3 in. chord, 100
m.p.h. normal pressure at 15° C., the cor¬
responding number is 234,000; or for a model
of 10 cm chord, 40 m.p.s., the corresponding
number is 274,000)
Cp, Center-of-pressure coefficient (ratio of distance
of c.p. from leading edge to chord, length)
a, Angle of attack
e, Angle of downwash
a0, Angle of attack, infinite aspect ratio
au Angle of attack, induced
aa, Angle of attack, absolute (measured from zero-
lift position)
7, Flight-path angle
Resultant force
Y
X
Positive directions of axes and angles (forces and moments) are shown by arrows
Axis
Force
(parallel
to axis)
symbol
Moment about axis
Angle
Velocities
Designation
Sym¬
bol
Designation
Sym¬
bol
Positive
direction
Designa¬
tion
Sym¬
bol
Linear
(compo¬
nent along
axis)
Angular
Longitudinal _ _ _
A'
A
Rolling
L
Y - >Z
Roll _
V
u
V
Lateral
Y
Y
Pitching _
M
Z - >X
Pitch _
0
V
<1
Normal
Z
Z
Yawing _
N
X >Y
Yaw _
w
r
Absolute coefficients of moment
n L „ M
qbS
(rolling)
C —
m qcS
(pitching)
(yawing)
Angle of set of control surface (relative to neutral
position), 5. (Indicate surface by proper subscript.)
4. PROPELLER SYMBOLS
D, Diameter
p, Geometric pitch
p/D, Pitch ratio
V' , Inflow velocity
Vs, Slipstream velocity
T
T, Thrust, absolute coefficient Cr ~ vtt?
pii"I)
Q, Torque, absolute coefficient — tw,
pH" 1/
V,
n,
%
Power, absolute coefficient ( V
Spee< 1 - j x >wer coeffic ien t =
Efficiency
Revolutions per second, r.p.s.
r
pnV)5
Effective helix angle = tan 1
1 hp. = 76.04 kg-m/s=550 ft-lb./see.
1 metric horsepower=1.0132 hp.
1 m.p.h. =0.4470 m.p.s.
1 m.p.s. = 2.2369 m.p.h.
:t8."i48 — 88 - 4.8
5. NUMERICAL RELATIONS
1 lb. =0.4530 kg.
1 kg=2.2046 lb.
1 mi. = 1,609.35 m= 5,280 ft.
1 m=3.2808 ft.
O
Li b HAK I to oiv) l I nOuiiinn moiuunuii
W Z 00
LIBRARIES^ SMITHS0N.ANJ|NSTITUTI0NZN0linillSNI>m0SHimSzS3IHVyaiVLIBRARIESzSMITHS0NIAN^INSm
m m ' W z £
— ^ “i i r D/iR i cc ^SMITHSONIAN INSTITUTION NOIlfllllSNI NVIN0SH1IIAJS S3Id^
NOlinillSNI NVIN0SH1IWS S3 I d V d B IT 1 B R AR 1 E b wbMI Ionian i "UM ^
S i 5 vV. .. h /&srrK\ z ^ 2 ^
z /-#anw\ -T-
to to
W;, x Ww, O _
>'^/ s i' ' ' | vsr i i ".sr r 5
L I B RAR I ESMSM,THSON.AN JNSTITUTION ^OIXnXIXSNI-NV.NOSHXI^Sa I d V d 8 I 1 L I B R AR I ES^SMITHSONIAN 1NSTI1
-5 A § s dBffo 1 5 H <5 &
^ v^i^y s v5gs^ 5 5 “ ^ / o
. ,. _ o X*os>£x _ — z ‘ ^ _j z _j z
:NOUnillSN,-,NVINOSHlIWS2 S3 ! dVd a l/u BRAR I ES SMITHSONIAN^INSTITUTION^OlinillSNI^VINOSHilWS^B I d
Z
o
H
3
(—
3
to
Z
L , B RAR , ESWSMITHSONiAN-,NSTITUTIONr NO.XnX.XSN. NVINOSHX.HS^a I dVd 8 I^L , B RAR , ES SMITHSON, AN INSTI
%
_ _ _ <{ni usg> _
^ Ztriu&y 5 ^ fp 2 " to * Z CO
NOIUUIISN ^NVINOSHlIHS^Sa I dVd a n^LI BRAR I ES SMITHSONIAH_INSTITUTIONMNOIinillSNI MVIN0SHIIHSwS3 I X
Z
CO
z
CO
z
CO
4^
o " ^ ^ - '^d!d2>" o ^ _J o . _J
'l I B RAR I ES2SMITHS0N!AN'J|NSTiTUTI0N2N0IinillSNIr.NVIN0SHimSzS3 I d V U Q 11 L I B R A R I E S^ SMITHSONIAN^ INST
2 " - 2 ^ ° 5 p 4tb> S
1!!
m V^7
to
. n, 2 S
'MOIXniliSN|-NtflNOSHXIWSl/’s3ldVaan"'LIBRARIES</,SMITHSONIAN INSTITUTION^NOliniliSNI^NVINOSHilWS^San
z _ _ _ I V 2 x£^>\ < r 2 -dfe,, < - 4
^ iS25^ >• 2 ^ s | = _
:LIBRARIEs"sM.THS0NIANJNSTITUTI0H”N0,inilisNI-NVIN0SHXIHS<oS3ldVaan_LIBRARIESmSMITHS0NIAN INST
o;
<
^ ' /V" 5 5 *sr § 5 _
:N0lxnxlXSNfVlN0SHXIWS2S3 ! d Vda I Al B RAR I ES .^SMITHSONIAN ^INSTITUTION ^OlinXIlSNI^NVINOSHXIWS ^3 I
4?'^ 1 5 P / , - ® fZZSSy - /SOKUN »
t £/£<*)>& AI 5 !;■//# ” (gf
2 .<
o i ffAP ’ rf\i\ o X x '■{'%? jfyr o
S//,&Cv co n|P%%J co (ofc 3s) co x co <o
I « t ^ § la#1 § I %# |
> Vjr 2 ^ > N^uuVjX 2 > 2 _
t/} 2 CO * 2 CO fc 2 CO 2 CO
:\ r I E S SMITHSONIAN INSTITUTION NOIlfUllSNI NVIN0SH1IWS S3IHVaail LIBRARIES SMITHSONIAN _ INSTITUTION I
m — co — co X _ co -* __ _ __ co
i , i Z *5^ i * t xflcvlN. ^ ><uvuN. LlJ Xw50v\ LU
*0T 5 5 v 5 N^S£?' “ y%W 5 m
. 2 _ i 2 _ I 2 _ l 2
1IJ.SNI NVINOSHlItNS SBIHVaail LIBRARIES SMITHSONIAN INSTITUTION NOlinillSNI NVIN0SH1IINS S3 I B V 8 8 11
r- v 2 r- 2 «“ 2 — ~ z
m «' \w '■■ m x^vosv^ r; m X^os>^ ^ m 2 m
co — CO — co — co — co
\ R I E S SMITHSONIAN INSTITUTION NOIlfUllSNI NVIN0SH1IWS SIIBVBail LI B RAR I ES SMITHSONIAN INSTITUTION
2- co 2 CO Z -* _ _ z CO
^Tiri>v < v 2 ^ <
± \&J****ffi/ h3
> -g ■ ' \NjV y, 2 X^OS>^2 > 5 ^
iiisni^nvinoshims^sb i avaa iizlibrar i es^smithsonian^institution NoiiniiiSNi_NviNOSHiiiMS S3 i avaa n_
— tr\ — rn — tn _ T X CO _
O ^ O Z O ^
2 ^ ^ -J
ft R I ES SMITHSONIAN INSTITUTION NOIlfUllSNI NVIN0SH1IINS S3IBVBan LIBRARIES SMITHSONIAN INSTITUTION
m ‘^uTTvjX rn yj‘ xgn m xg\, oc^x " rn
— CO _ co \ 5 co — CO _
UI1SNI NVIN0SH1IWS S3IBVBan LIBRARIES SMITHSONIAN INSTITUTION NOlinillSNI NVIN0SH1IINS S3 1 h VB 8 11
2 CO Z to 2 ... co 2 — to 2
Z
o
CO
X
5
co
ARIES SMITHSONIAN INSTITUTION NOlinillSNI NVIN0SH1IWS S3IHVB8n LIBRARIES SMITHSONIAN _ INSTITUTION
to ~ CO — CO 2 to — CO
. N v ^Tr*- Li ^ ___
q o " L_ ><cuuv>' o XgN.pC^/ Z O
llllSNl^NVINOSHHIAIS^Sa I UVB 8 II^LI B RAR I E S^ SMITHSONIAN-" INSTITUTION NOlinillSNI NVINOSHlItNS S3 I BVU 8 11
r* ... 2 r- Z r- 2 r~ •>» z
ARIES SMITHSONIAN INSTITUTION NOlinillSNI NVINOSHIIWS S3iaVH8l1 LI B RAR I ES SMITHSONIAN INSTITUTION
CO 2 * CO Z CO Z , ^ _ _ 2 \ ^
z ^ ^ ^ i d g 5 z
^ CO s.
CO
X
2 X^osv^x > ' w z ^
UllSNI^NVINOSHimS^Sa I avy 8 II^LI BRAR I ES^SMITHSONIAN INSTITUTION NOlinillSNI^ NVIN0SH1IWS S3 I BVB 8 I1_
2 X to _ - CO ^ to z \ 00 -
= A. I s ^
5 I
- /@2S®\ o
— /'rJkl -
< fcf
o
2
m
^ s W = | / " g “ . “ '
ARIES SMITHSONIAN INSTITUTION NOlinillSNI^NVINOSHlIIAIS S3IBVa8l1 L I B R A R I E S SMITHSONIAN INSTITUTION
z r- _ z r* 2
#%;in
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11